## Problem Statement

Calculate the indefinite integral:

$$
\int \frac{2 \cos x + 3 \sin x}{(2 \sin x - 3 \cos x)^{3}} d x
$$
## Solution

$$
\int \frac{2 \cos x+3 \sin x}{(2 \sin x-3 \cos x)^{3}} d x=\int \frac{d(2 \sin x-3 \cos x)}{(2 \sin x-3 \cos x)^{3}}=-\frac{1}{2 \cdot(2 \sin x-3 \cos x)^{2}}+C
$$

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 $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B} 3-21$ "

Categories: Kuznetsov's Problem Book Integrals Problem 3 | Integrals

Ukrainian Banner Network

- Last modified on this page: 13:14, 3 March 2009.
- Content is available under CC-BY-SA 3.0.

Created by GeeTeatoo

## Problem Kuznetsov Integrals 3-22

## Material from PlusPi