# Step-by-step Solution

## Trigonometric integral $\int1x^2\sin\left(ax\right)dx$

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### 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

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

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

### Main topic:

Integration by substitution

~ 0.93 seconds

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