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

The integral of x^2sin(Bx) is -1/B x^2cos(Bx)+2/(B^3)(Bxsin(Bx)+cos(Bx))+C

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integral of x^2sin(Bx)

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

- \frac{1}{B} x^{2} cos (B x) + \frac{2}{B ^{3}} (B x sin (B x) + cos (B x)) + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{2}{B} x cos (B x) d x = - \frac{2}{B ^{3}} (B x sin (B x) + cos (B x))

= - \frac{1}{B} x^{2} cos (B x) - (- \frac{2}{B ^{3}} (B x sin (B x) + cos (B x)))

Simplify

= - \frac{1}{B} x^{2} cos (B x) + \frac{2}{B ^{3}} (B x sin (B x) + cos (B x))

Add a constant to the solution

= - \frac{1}{B} x^{2} cos (B x) + \frac{2}{B ^{3}} (B x sin (B x) + cos (B x)) + C

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What is the integral of x^2sin(Bx) ?
The integral of x^2sin(Bx) is -1/B x^2cos(Bx)+2/(B^3)(Bxsin(Bx)+cos(Bx))+C