# Step-by-step Solution

## Trigonometric integral $\int x\cos\left(nx\right)dx$

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
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

### Videos

$x\frac{1}{n}\sin\left(nx\right)+\left(\frac{1}{n}\right)^2\cos\left(nx\right)+C_0$

## Step-by-step explanation

Problem to solve:

$\int\left(X\:\cos\left(nx\right)\right)dx$
1

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

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

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

$x\frac{1}{n}\sin\left(nx\right)+\left(\frac{1}{n}\right)^2\cos\left(nx\right)+C_0$
$\int\left(X\:\cos\left(nx\right)\right)dx$

### Main topic:

Integration by substitution

~ 0.84 seconds

### Struggling with math?

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