# Integration by parts Calculator

## Get detailed solutions to your math problems with our Integration by parts step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

1

Solved example of Integration by parts

$\int x\cdot sin\left(x\right)dx$
2

Use the integration by parts theorem to calculate the integral $\int x\sin\left(x\right)dx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
3

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=x}\\ \displaystyle{du=dx}\end{matrix}$
4

Now, identify $dv$ and calculate $v$

$\begin{matrix}\displaystyle{dv=\sin\left(x\right)dx}\\ \displaystyle{\int dv=\int \sin\left(x\right)dx}\end{matrix}$
5

Solve the integral

$v=\int\sin\left(x\right)dx$
6

Apply the integral of the sine function

$-\cos\left(x\right)$
7

Now replace the values of $u$, $du$ and $v$ in the last formula

$-x\cos\left(x\right)+\int\cos\left(x\right)dx$
8

Apply the integral of the cosine function

$-x\cos\left(x\right)+\sin\left(x\right)$
9

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$-x\cos\left(x\right)+\sin\left(x\right)+C_0$

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