# Step-by-step Solution

## Trigonometric integral int(x^2*cos(x))dx

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ln
log
lim
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sin
cos
tan
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csc

asin
acos
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

$x^2\sin\left(x\right)-2\left(-x\cos\left(x\right)+\sin\left(x\right)\right)+C_0$

## Step-by-step explanation

Problem to solve:

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

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

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

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=x^2}\\ \displaystyle{du=2xdx}\end{matrix}$

$x^2\sin\left(x\right)-2\left(-x\cos\left(x\right)+\sin\left(x\right)\right)+C_0$
$\int x^2\cos\left(x\right)dx$

### Main topic:

Integration by parts

~ 1.08 seconds

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