## Problem Statement

Calculate the indefinite integral:

$$
\int \frac{\sin x - \cos x}{(\cos x + \sin x)^{5}} d x
$$
## Solution

$$
\int \frac{\sin x-\cos x}{(\cos x+\sin x)^{5}} d x=-\int \frac{d(\cos x+\sin x)}{(\cos x+\sin x)^{5}}=\frac{1}{4} \cdot \frac{1}{(\cos x+\sin x)^{4}}+C
$$

Source — "http://pluspi.org/wiki/index.php/%D0%9A%D1%83%D0%B7%D0%BD%D0%B5%D1%86%D0%BE%D0%B2_%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D1%8B_3-11" Categories: Kuznetsov Problem Book Integrals Problem 3 | Integrals

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## Problem Kuznetsov Integrals 3-12

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