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Step-by-step Solution

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

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asin
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Answer

$\sin\left(x\right)+\left(-1-x\right)\cos\left(x\right)+C_0$

Step-by-step explanation

Problem to solve:

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

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

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Answer

$\sin\left(x\right)+\left(-1-x\right)\cos\left(x\right)+C_0$
$\int\left(x+1\right)\sin\left(x\right)dx$

Main topic:

Integration by parts

Used formulas:

5. See formulas

Time to solve it:

~ 0.87 seconds

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