# Step-by-step Solution

## Trigonometric integral int(x*sin(x))dx&0&6

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e
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ln
log
lim
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sin
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asin
acos
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sinh
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sech
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asinh
acosh
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asech
acsch

### Videos

$-6.0833$

## Step-by-step explanation

Problem to solve:

$\int_{0}^{6} x\cdot \sin\left(x\right)dx$
1

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

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

First, identify $u$ and calculate $du$

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

$-6.0833$
$\int_{0}^{6} x\cdot \sin\left(x\right)dx$

### Main topic:

Trigonometric integrals

~ 0.84 seconds