What is the integral of cos(n)pix ?

The integral of cos(n)pix is pi/2 x^2cos(n)+C

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integral of cos(n)pix

\int cos (n) π x d x

\frac{π}{2} x^{2} cos (n) + C

Solution steps

\int 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 x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= cos (n) π \frac{x ^{2}}{2}

Simplify

cos (n) π \frac{x ^{2}}{2} : \frac{π}{2} x^{2} cos (n)

= \frac{π}{2} x^{2} cos (n)

Add a constant to the solution

= \frac{π}{2} x^{2} cos (n) + C

\int (π - x) d x

\int x + 9 d x

\int e^{- 3 x + 2} d x

\frac{\partial}{\partial x} ((x^{2}) (y^{3}))

What is the integral of cos(n)pix ?
The integral of cos(n)pix is pi/2 x^2cos(n)+C