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

The integral of x^2cos(mpix) is 1/(pim)x^2sin(pimx)-2/(pi^3m^3)(-pimxcos(pimx)+sin(pimx))+C

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integral of x^2cos(mpix)

\int x^{2} cos (mπ x) d x

\frac{1}{πm} x^{2} sin (πm x) - \frac{2}{π ^{3} m ^{3}} (- πm x cos (πm x) + sin (πm x)) + C

Solution steps

\int x^{2} cos (mπ x) d x

Apply Integration By Parts

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

\int \frac{2}{πm} x sin (πm x) d x = \frac{2}{π ^{3} m ^{3}} (- πm x cos (πm x) + sin (πm x))

= \frac{1}{πm} x^{2} sin (πm x) - \frac{2}{π ^{3} m ^{3}} (- πm x cos (πm x) + sin (πm x))

Add a constant to the solution

= \frac{1}{πm} x^{2} sin (πm x) - \frac{2}{π ^{3} m ^{3}} (- πm x cos (πm x) + sin (πm x)) + C

What is the integral of x^2cos(mpix) ?
The integral of x^2cos(mpix) is 1/(pim)x^2sin(pimx)-2/(pi^3m^3)(-pimxcos(pimx)+sin(pimx))+C