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

The integral of x^2*sin(ax) is -1/a x^2cos(ax)+2/(a^3)(axsin(ax)+cos(ax))+C

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integral of x^2*sin(ax)

\int x^{2} \cdot sin (a x) d x

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (e^{- 3 x} cos (3 y))

f (x) = ln (1 - x)

y^{^{'}} = - k y^{\frac{1}{2}}

\frac{d}{d x} (\frac{4}{3} x^{\frac{3}{2}})

\int csc^{4} (x) d x

What is the integral of x^2*sin(ax) ?
The integral of x^2*sin(ax) is -1/a x^2cos(ax)+2/(a^3)(axsin(ax)+cos(ax))+C