What is the integral of r^2sin(r) ?

The integral of r^2sin(r) is -r^2cos(r)+2(rsin(r)+cos(r))+C

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integral of r^2sin(r)

\int r^{2} sin (r) d r

- r^{2} cos (r) + 2 (r sin (r) + cos (r)) + C

Solution steps

\int r^{2} sin (r) d r

Apply Integration By Parts

: - r^{2} cos (r) - \int - 2 r cos (r) d r

= - r^{2} cos (r) - \int - 2 r cos (r) d r

\int - 2 r cos (r) d r = - 2 (r sin (r) + cos (r))

= - r^{2} cos (r) - (- 2 (r sin (r) + cos (r)))

Simplify

= - r^{2} cos (r) + 2 (r sin (r) + cos (r))

Add a constant to the solution

= - r^{2} cos (r) + 2 (r sin (r) + cos (r)) + C

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What is the integral of r^2sin(r) ?
The integral of r^2sin(r) is -r^2cos(r)+2(rsin(r)+cos(r))+C