Evaluate the integral of x / (x+1)²

by RoRi

December 3, 2015

Compute the following integral.

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

Here we compute directly,

$\begin{align*} \int \frac{x}{(x+1)^2} \, dx &= \int \frac{x+1-1}{(x+1)^2} \, dx \\ &= \int \frac{dx}{x+1} - \int \frac{dx}{(x+1)^2} \\ &= \log |x+1| + \frac{1}{x+1} + C. \end{align*}$

Stumbling Robot

Evaluate the integral of x / (x+1)²

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