∫ x ^ 2 sin2xdx = x ^ 2 ∫sin2xdx ∫[ d dx x ^ 2 .∫sin2xdx #160; ] #160; dx = x ^ 2 2 cos2x+∫ x.cos2xdx = x ^ 2 2 cos2x+ x 2 ...

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Integration by Parts

Solve: ∫ x2s...

Question

Solve: $\int x^{2} sin 2 x d x$

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Solution

$\int x^{2} sin 2 x d x = x^{2} \int sin 2 x d x - \int [\frac{d}{d x} x^{2} . \int sin 2 x d x] d x = - \frac{x^{2}}{2} cos 2 x + \int x . cos 2 x d x = - \frac{x^{2}}{2} cos 2 x + \frac{x}{2} sin 2 x - \frac{cos 2 x}{4} + C = \frac{2 x sin 2 x - 2 x^{2} cos 2 x - cos 2 x}{4} + C$

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