What is the integral of x^2sin(10x) ?

The integral of x^2sin(10x) is -1/10 x^2cos(10x)+1/500 (10xsin(10x)+cos(10x))+C

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integral of x^2sin(10x)

\int x^{2} sin (10 x) d x

- \frac{1}{10} x^{2} cos (10 x) + \frac{1}{500} (10 x sin (10 x) + cos (10 x)) + C

Solution steps

\int x^{2} sin (10 x) d x

Apply Integration By Parts

: - \frac{1}{10} x^{2} cos (10 x) - \int - \frac{1}{5} x cos (10 x) d x

= - \frac{1}{10} x^{2} cos (10 x) - \int - \frac{1}{5} x cos (10 x) d x

\int - \frac{1}{5} x cos (10 x) d x = - \frac{1}{500} (10 x sin (10 x) + cos (10 x))

= - \frac{1}{10} x^{2} cos (10 x) - (- \frac{1}{500} (10 x sin (10 x) + cos (10 x)))

Simplify

= - \frac{1}{10} x^{2} cos (10 x) + \frac{1}{500} (10 x sin (10 x) + cos (10 x))

Add a constant to the solution

= - \frac{1}{10} x^{2} cos (10 x) + \frac{1}{500} (10 x sin (10 x) + cos (10 x)) + C

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What is the integral of x^2sin(10x) ?
The integral of x^2sin(10x) is -1/10 x^2cos(10x)+1/500 (10xsin(10x)+cos(10x))+C