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

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

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integral of x^2*cos(mpix)

\int x^{2} \cdot 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

= \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

\frac{d}{d x} (- \frac{1}{( 5 + x ) ^{2}})

x \to 0 lim (2 x^{2} - 10 x + 12)

\int sin (2 x + 3) d x

\int_{0}^{1} (x^{2} + 8) e^{- x} d x

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{''}} (0) = - 6

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