# Step-by-step Solution

## Integrate x^2sin(a*x)*1

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

### Videos

$-x^2\frac{1}{a}\cos\left(ax\right)+\frac{2}{a}\left(x\frac{1}{a}\sin\left(ax\right)+\left(\frac{1}{a}\right)^2\cos\left(ax\right)\right)+C_0$

## Step-by-step explanation

Problem to solve:

$\int\left(x^2\sin ax\right)dx$
1

Any expression multiplied by $1$ is equal to itself

$\int x^2\sin\left(ax\right)dx$
2

Use the integration by parts theorem to calculate the integral $\int x^2\sin\left(ax\right)dx$, using the following formula

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

$-x^2\frac{1}{a}\cos\left(ax\right)+\frac{2}{a}\left(x\frac{1}{a}\sin\left(ax\right)+\left(\frac{1}{a}\right)^2\cos\left(ax\right)\right)+C_0$

### Struggling with math?

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

$\int\left(x^2\sin ax\right)dx$

### Main topic:

Integration by parts

~ 0.69 seconds