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

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

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integral of x^2cos(pix)

\int x^{2} cos (π x) d x

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

Solution steps

\int x^{2} cos (π x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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