Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP

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.

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Solved example of Integration by parts

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

Use the integration by parts theorem to calculate the integral $\int x\cos\left(x\right)dx$, 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 $v$

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

Solve the integral

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

Apply the integral of the cosine function

$\sin\left(x\right)$
7

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

$x\sin\left(x\right)-\int\sin\left(x\right)dx$
8

Apply the integral of the sine function

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

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

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

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!