## Problem Statement

Calculate the indefinite integral:

$$
\int(5 x+6) \cos 2 x \, dx
$$
## Solution

$$
\int(5 x+6) \cos 2 x d x=
$$

Let:

$$
\begin{aligned}
& u=5 x+6 ; d u=5 d x \\
& d v=\cos 2 x d x ; v=\frac{1}{2} \sin 2 x
\end{aligned}
$$

Using the integration by parts formula $\int u d v=u v-\int v d u$, we get:

$$
\begin{aligned}
& =(5 x+6) \cdot \frac{1}{2} \sin 2 x-\int \frac{1}{2} \sin 2 x \cdot 5 d x=\frac{1}{2} \cdot(5 x+6) \sin 2 x-\frac{5}{2} \int \sin 2 x d x= \\
& =\frac{1}{2} \cdot(5 x+6) \sin 2 x+\frac{5}{2} \cdot \frac{1}{2} \cdot \cos 2 x+C=\frac{1}{2} \cdot(5 x+6) \sin 2 x+\frac{5}{4} \cdot \cos 2 x+C
\end{aligned}
$$

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 $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B}+1-17$ »

Categories: Kuznetsov's Problem Book Integrals Problem 1 | Integrals

- Last modified: 22:59, 18 February 2009.
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## Problem Kuznetsov Integrals 1-18

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