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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View this answerTo 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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Learn more about this topic:
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Chapter 13 / Lesson 5Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.