Evaluate the integral using substitution

by RoRi

October 17, 2015

Use the method of substitution to evaluate the following integral:

$\int \frac{\sin x \, dx}{(3+\cos x)^2}.$

Let

$u = 3 + \cos x \quad \implies \quad du = -\sin x \, dx.$

Then, we can evaluate the integral,

$\begin{align*} \int \frac{\sin x \, dx}{(3+\cos x)^2} &= - \int u^{-2} \, du \\ &= u^{-1} + C \\ &= \frac{1}{3+ \cos x} + C. \end{align*}$

Stumbling Robot