# Step-by-step Solution

## Integral of (x+1)sin(x)

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asin
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### Videos

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

## Step-by-step explanation

Problem to solve:

$\int\left(x+1\right)\cdot\sin\left(x\right)dx$
1

Multiplying polynomials $\sin\left(x\right)$ and $x+1$

$\int\left(x\sin\left(x\right)+\sin\left(x\right)\right)dx$
2

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int x\sin\left(x\right)dx+\int\sin\left(x\right)dx$

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

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$\int\left(x+1\right)\cdot\sin\left(x\right)dx$

### Main topic:

Integration by parts

~ 0.51 seconds