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Integral of sin(2x)x^2

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

Step-by-step explanation

Problem

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

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

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

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

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

Main topic:

Integration by parts

~ 0.37 seconds