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

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

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integral of x^2cos(2x)

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

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{2} x^{2} sin (2 x) - \int x sin (2 x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

\int 9 x^{2} + 4 x - 7 d x

\frac{\partial}{\partial z} (ln (x^{2} + y^{2} + z^{2}))

\frac{\partial}{\partial x} (x^{8} y^{5} - x^{7} y^{4})

4^{x^{3}}

\frac{d}{d x} (x coth (6 + x^{2}))

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