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

The integral of x^2sin(yx) is -1/y x^2cos(yx)+2/(y^3)(yxsin(yx)+cos(yx))+C

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integral of x^2sin(yx)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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What is the integral of x^2sin(yx) ?
The integral of x^2sin(yx) is -1/y x^2cos(yx)+2/(y^3)(yxsin(yx)+cos(yx))+C