Evaluate the integral e^x / (1+e^2x)

by RoRi

November 30, 2015

Evaluate the following integral

$\int \frac{e^x}{1+e^{2x}} \, dx.$

We make the substitution $u = e^x$ and $du = e^x \, dx$ . Then we have

$\begin{align*} \int \frac{e^x}{1+e^{2x}} \, dx &= \int \frac{e^x}{1+(e^x)^2} \, dx \\ &= \int \frac{du}{1+u^2} \\ &= \arctan u + C \\ &= \arctan e^x + C. \end{align*}$

Stumbling Robot

Evaluate the integral e^x / (1+e^2x)

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