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Step-by-step Solution

Integrate x^2cos(2*x)

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Answer

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

Step-by-step explanation

Problem to solve:

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

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

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

Isolate $dx$ in the previous equation

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

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Answer

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

Main topic:

Integration by parts

Used formulas:

6. See formulas

Time to solve it:

~ 1.27 seconds