integral {eq}\displaystyle \int \frac {e^x}{1+e^{2x} } \ dx {/eq}

Question:

integral {eq}\displaystyle \int \frac {e^x}{1+e^{2x} } \ dx {/eq}

U-Substitution:

U-substitution is an integration method that is only permissible if the integral is expressed in the following form:

{eq}\displaystyle \int f'(g(x))g'(x) \ \mathrm{d}x {/eq}

Notice that the integral becomes {eq}\displaystyle \int f'(u) \ \mathrm{d}u {/eq} if we let {eq}u= g(x) {/eq}.

Answer and Explanation: 1

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To solve {eq}\displaystyle \int \frac {e^x}{1+e^{2x} } \ \mathrm{d}x {/eq}, let {eq}u=e^x {/eq}.

Calculating the derivative of {eq}u {/eq}...

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.


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