What is the integral of xcos(n)pix ?

The integral of xcos(n)pix is pi/3 x^3cos(n)+C

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integral of xcos(n)pix

\int x cos (n) π x d x

\frac{π}{3} x^{3} cos (n) + C

Solution steps

\int x cos (n) π x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (n) π \cdot \int xx d x

Simplify

xx : x^{2}

= cos (n) π \cdot \int x^{2} d x

Apply the Power Rule

= cos (n) π \frac{x ^{3}}{3}

Simplify

cos (n) π \frac{x ^{3}}{3} : \frac{π}{3} x^{3} cos (n)

= \frac{π}{3} x^{3} cos (n)

Add a constant to the solution

= \frac{π}{3} x^{3} cos (n) + C

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What is the integral of xcos(n)pix ?
The integral of xcos(n)pix is pi/3 x^3cos(n)+C