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

= \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

\frac{d}{d x} ((- x^{3} - x^{2} + x) cos (x))

f (x) = x \cdot 1 - x^{2}, [0, 1]

\frac{1}{p ( p + 1 )}

x \to - 3 lim (x^{2} + 27)

\int x^{2} (x - \frac{2}{x}) d x

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