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

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

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integral of x^2*cos(2x)

\int x^{2} \cdot 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

\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

\frac{\partial}{\partial x} (9 x^{2} cos (y^{6}))

\frac{d}{d x} (4 3 x + 2 ln (x) - 3 e^{x})

\frac{d}{d x} (\frac{5 x ^{4} + 2 x}{2 x ^{9}})

\int \frac{5 ^{x}}{5 ^{x} - 1} d x

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