# Integral of xe^(7x)

## Answer

$-\frac{1}{49}e^{7x}+\frac{1}{7}x\cdot e^{7x}+C_0$

## Step-by-step explanation

Problem

$\int xe^{7x}dx$

1

Use the integration by parts theorem to calculate the integral $\int e^{7x}xdx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

## Answer

$-\frac{1}{49}e^{7x}+\frac{1}{7}x\cdot e^{7x}+C_0$