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

Integral of x^2cos(2x)

Answer

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

Step-by-step explanation

Problem

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

Use the integration by parts theorem to calculate the integral $\int x^2\cos\left(2x\right)dx$, using the following formula

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

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Answer

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

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

Main topic:

Integration by parts

Used formulas:

8. See formulas

Time to solve it:

~ 0.64 seconds