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

The integral of t^2cos(2t) is 1/2 t^2sin(2t)+1/2 tcos(2t)-1/4 sin(2t)+C

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integral of t^2cos(2t)

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

\frac{1}{2} t^{2} sin (2 t) + \frac{1}{2} t cos (2 t) - \frac{1}{4} sin (2 t) + C

Solution steps

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

Apply Integration By Parts

= \frac{1}{2} t^{2} sin (2 t) - \int t sin (2 t) d t

\int t sin (2 t) d t = - \frac{1}{2} t cos (2 t) + \frac{1}{4} sin (2 t)

= \frac{1}{2} t^{2} sin (2 t) - (- \frac{1}{2} t cos (2 t) + \frac{1}{4} sin (2 t))

Simplify

= \frac{1}{2} t^{2} sin (2 t) + \frac{1}{2} t cos (2 t) - \frac{1}{4} sin (2 t)

Add a constant to the solution

= \frac{1}{2} t^{2} sin (2 t) + \frac{1}{2} t cos (2 t) - \frac{1}{4} sin (2 t) + C

What is the integral of t^2cos(2t) ?
The integral of t^2cos(2t) is 1/2 t^2sin(2t)+1/2 tcos(2t)-1/4 sin(2t)+C