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

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

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integral of x^2cos(2pix)

\int x^{2} cos (2 π x) d x

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

Solution steps

\int x^{2} cos (2 π x) d x

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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