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Step-by-step Solution

Integrate xsin(2*x+3)

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Answer

$\frac{1}{4}\left(-\left(2x+3\right)\cos\left(2x+3\right)+\sin\left(2x+3\right)\right)+\frac{3}{4}\cos\left(2x+3\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\:x\:\sin\left(2x+3\right)dx$
1

Solve the integral $\int x\sin\left(2x+3\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=2x+3 \\ du=2dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{2}=dx$

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Answer

$\frac{1}{4}\left(-\left(2x+3\right)\cos\left(2x+3\right)+\sin\left(2x+3\right)\right)+\frac{3}{4}\cos\left(2x+3\right)+C_0$

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$\int\:x\:\sin\left(2x+3\right)dx$

Main topic:

Integration by parts

Used formulas:

8. See formulas

Time to solve it:

~ 0.55 seconds