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<title>Integrals of Simple Exponential Functions</title>
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<h2 id="heading">Integrals of Simple Exponential Functions</h2>
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&#160;<math><mstyle mathcolor="blue"><mtext>I =&#160;</mtext><mstyle displaystyle="true"><mo>&#x222b;</mo><mrow><msup><mrow><mi>e</mi></mrow><mrow><mi></mi><mi>x</mi><mo stretchy="false">+</mo><mfrac><mrow><mn>11</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></msup><mtext>&#160;</mtext><mi>d</mi><mi>x</mi></mrow></mstyle></mstyle></math><br/><br/>Put &#160;<math><mstyle mathcolor="blue"><mi>u</mi><mtext>&#160;=&#160;</mtext><mi></mi><mi>x</mi><mo stretchy="false">+</mo><mfrac><mrow><mn>11</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mtext>, then</mtext></mstyle></math><br/><br/>&#160;<math><mstyle mathcolor="blue"><mtext>&#160;</mtext><mi>d</mi><mi>u</mi><mtext>&#160;=&#160;</mtext><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mtext>&#160;</mtext><mi>d</mi><mi>x</mi></mstyle></math><br/><br/>Or, &#160;<math><mstyle mathcolor="blue"><mtext>&#160;</mtext><mi>d</mi><mi>u</mi><mtext>&#160;=&#160;</mtext><mtext>&#160;</mtext><mi>d</mi><mi>x</mi></mstyle></math><br/><br/>So, &#160;<math><mstyle mathcolor="blue"><mtext>I =&#160;</mtext><mstyle displaystyle="true"><mo>&#x222b;</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup></mstyle><mtext>&#160;</mtext><mi>d</mi><mi>u</mi></mstyle></math><br/><br/>Or, &#160;<math><mstyle mathcolor="blue"><mtext>I =&#160;</mtext><mstyle displaystyle="true"><mo>&#x222b;</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup></mstyle><mtext>&#160;</mtext><mi>d</mi><mi>u</mi></mstyle></math><br/><br/>Or, &#160;<math><mstyle mathcolor="blue"><mtext>I =&#160;</mtext><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup><mo stretchy="false">+</mo><mi>C</mi></mstyle></math><br/><br/>Or, &#160;<math><mstyle mathcolor="blue"><mtext>I =&#160;</mtext><msup><mrow><mi>e</mi></mrow><mrow><mi></mi><mi>x</mi><mo stretchy="false">+</mo><mfrac><mrow><mn>11</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></msup><mo stretchy="false">+</mo><mi>C</mi></mstyle></math>
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<hr/>Copyright &#169; Dayal D. Purohit, Ph.D.(Mathematics)
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