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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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      <p>http://keisan.casio.com/exec/system/1180573428</p>
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        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">k</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">k</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operand">0</e>
        <e type="operand">30</e>
        <e type="function" preserve="true" args="4">sum</e>
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  <region id="2" left="297" top="54" width="159" height="66" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>CONFLICT_1fails @ accuracy 10000.low [0] is suitable</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Si</e>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">int</e>
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      <result action="numeric">
        <e type="operand">1.7947</e>
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        <e type="operand">γ</e>
        <e type="operand">0.577215664901532860606512</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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  <region id="5" left="18" top="171" width="211" height="63" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">γ</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="operand">k</e>
        <e type="operator" args="2">^</e>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">40</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">+</e>
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        <p>Conflict_2accepts accuracy 10000.rejects ε &lt; 10e-5</p>
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        <e type="operand">5</e>
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        <e type="operand">3</e>
        <e type="function" preserve="true" args="4">int</e>
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        <e type="operand">γ</e>
        <e type="operand">x</e>
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        <e type="bracket">(</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operator" args="2">^</e>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
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        <e type="operator" args="2">/</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">40</e>
        <e type="function" preserve="true" args="4">sum</e>
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        <p>SineIntegral ... accurate</p>
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        <p>Ei(x) &amp;  Li(x) ... accurate</p>
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        <e type="operator" args="2">/</e>
        <e type="operand">t</e>
        <e type="operand">10</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
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        <e type="function" args="1">Ei</e>
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    <math>
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        <e type="operand">x</e>
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        <e type="operand">x</e>
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        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">solve</e>
        <e type="operand">x</e>
        <e type="function" args="1">Li</e>
        <e type="operand">x</e>
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        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
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        <e type="operand">0.3725</e>
        <e type="operand">1.4514</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
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    <math optimize="2">
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        <e type="operand">X</e>
        <e type="operand">sol</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
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  <region id="15" top="639" color="#000000" bgColor="#ffffff">
    <area collapsed="true">
      <title lang="eng">
        <p>     Hatch      </p>
      </title>
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      <math>
        <description active="true" position="Top" lang="ger">
          <p>Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Generates a matrix for 2*N vertical lines (hatching) between functions f(x) and g(x) in x-range from x1 to x2</p>
        </description>
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          <e type="operand">x.1</e>
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          <e type="operand">N</e>
          <e type="function" args="5">hatch</e>
          <e type="operand">dx</e>
          <e type="operand">x.2</e>
          <e type="operand">x.1</e>
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          <e type="operand">N</e>
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          <e type="operand">x.2</e>
          <e type="operand">dx</e>
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          <e type="function" preserve="true" args="3">range</e>
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          <e type="operand">h</e>
          <e type="operand">x</e>
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          <e type="operand">2</e>
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          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
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          <e type="operand">x</e>
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          <e type="operand">2</e>
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          <e type="function" args="1">f</e>
          <e type="operand">x</e>
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          <e type="operand">x</e>
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          <e type="function" args="1">f</e>
          <e type="operand">x</e>
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          <e type="operand">x</e>
          <e type="operand">dx</e>
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          <e type="function" args="1">g</e>
          <e type="operand">4</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="10">mat</e>
          <e type="function" preserve="true" args="2">stack</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">h</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="6">line</e>
          <e type="operator" args="2">:</e>
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    <region id="17" top="990" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
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        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" args="1">Ei</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
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    </math>
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    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">X</e>
        <e type="operator" args="2">:</e>
        <e type="operand">b</e>
        <e type="operand">8</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
    </math>
  </region>
  <region id="20" left="279" top="1053" width="196" height="66" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">x</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="4">int</e>
      </input>
      <result action="numeric">
        <e type="operand">21.2883</e>
      </result>
    </math>
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    <math>
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        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand" style="string" />
        <e type="function" preserve="true" args="3">cases</e>
        <e type="operator" args="2">:</e>
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    </math>
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    <plot type="2d" render="lines" scale_x="1.7363069361" scale_y="5.05447028499294" scale_z="8.7761118141446" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-74" transpose_y="1" transpose_z="0">
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        <e type="operand">x</e>
        <e type="function" args="1">li</e>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="23" left="279" top="1143" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="1" scale_y="1" scale_z="1" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">f</e>
        <e type="operand">g</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">10</e>
        <e type="function" args="5">hatch</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="24" left="18" top="1386" width="752" height="31" border="true" color="#ff0000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true">http://nvlpubs.nist.gov/nistpubs/jres/73B/jresv73Bn3p191_A1b.pdf</p>
    </text>
  </region>
  <region id="25" left="18" top="1431" width="418" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">Read more about Σ series code error</p>
    </text>
  </region>
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    <picture>
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    <math optimize="2">
      <description active="true" position="Top" lang="eng">
        <p>CONFLICT_3Rmanujan: the 'k' correction term freaks Smath =&gt; "n_not defined" ... Found no way to doctor the error.Is useful for applications of short range w/o the 'k' term.</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Li</e>
        <e type="operand">γ</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operand">n</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">n</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operand">20</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">k</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">k</e>
        <e type="operand">0</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">Floor</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="28" left="504" top="1566" width="43" height="32" color="#000000" bgColor="#ffffff">
    <picture>
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    </picture>
  </region>
  <region id="29" left="378" top="1710" width="221" height="45" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">10</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand" style="string" />
        <e type="function" preserve="true" args="3">cases</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="30" left="18" top="1737" width="81" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="2">
      <description active="true" position="Right" lang="eng">
        <p>won't plot either !</p>
      </description>
      <input>
        <e type="operand">4</e>
        <e type="function" args="1">Li</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="31" left="378" top="1755" width="366" height="66" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>limit of use: accuracy ≥ 10*D for x ≤ e</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">λi</e>
        <e type="operand">γ</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">n</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operand">100</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="32" left="18" top="1854" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">X</e>
        <e type="operand">e</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="33" left="378" top="1854" width="363" height="158" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <plot type="2d" render="lines" scale_x="1.11652108025778" scale_y="1.85321057216998" scale_z="2.06914866998438" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-127" transpose_y="-44" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">λi</e>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">e</e>
        <e type="operand">5</e>
        <e type="operand">e</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">sys</e>
      </input>
    </plot>
  </region>
  <region id="34" left="18" top="1899" width="253" height="51" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="15">
      <input>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">X</e>
        <e type="function" args="1">λi</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">1.89511781635594</e>
        <e type="operand">1.87465820630179</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="35" left="18" top="2052" width="371" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">Reconciliate Ei(x) two branches</p>
    </text>
  </region>
  <region id="36" left="432" top="2052" width="329" height="90" border="true" color="#000000" bgColor="#ffffe1">
    <writer lang="eng"><![CDATA[<span style="font-family: 'Arial'; font-size: 10pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; text-align: left; line-height: 115%">
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 14pt"><strong><span style="text-decoration: underline"><span style="color: Red">Caution</span></span><span style="color: Red">:</span></strong></span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">Be careful integrating the steep region of li(x), Ei(x).</span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">They fall in the category of <strong>difficult</strong> integration that</span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">Smath may not manage accurately enough !</span></span></div></span>]]></writer>
  </region>
  <region id="37" left="18" top="2088" width="220" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>complementary Ei(x)</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">E1</e>
        <e type="operand">γ</e>
        <e type="operator" args="1">-</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operator" args="2">-</e>
        <e type="operand">x</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operator" args="2">^</e>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">40</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="38" left="18" top="2160" width="382" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.86005835464129" scale_y="5.53111851253885" scale_z="1.66732916218701" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Ei</e>
        <e type="operand">x</e>
        <e type="operator" args="1">-</e>
        <e type="function" args="1">E1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="39" left="432" top="2160" width="258" height="174" border="true" color="#000000" bgColor="#ffffff">
    <picture>
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</regions>