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

The integral of t^2sin(t) is -t^2cos(t)+2(tsin(t)+cos(t))+C

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integral of t^2sin(t)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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