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

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

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integral of t^2cos(t)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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