## Problem Statement

Calculate the indefinite integral:

$$
\int(5 x-2) e^{3 x} d x
$$
## Solution

$$
\int(5 x-2) e^{3 x} d x=
$$

Let's denote:

$$
\begin{aligned}
& u=5 x-2 ; d u=5 d x \\
& d v=e^{3 x} d x ; v=\frac{1}{3} e^{3 x}
\end{aligned}
$$

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

$$
\begin{aligned}
& =(5 x-2) \cdot \frac{1}{3} e^{3 x}-\int \frac{1}{3} e^{3 x} \cdot 5 d x=(5 x-2) \cdot \frac{1}{3} e^{3 x}-\frac{5}{9} e^{3 x}+C= \\
& =\frac{1}{9} \cdot(15 x-11) e^{3 x}+C
\end{aligned}
$$

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 $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B}+1-6$ »

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

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## Problem Kuznetsov Integrals 1-7

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