What is the integral of sin(n)pix ?

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

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integral of sin(n)pix

\int sin (n) π x d x

\frac{π}{2} x^{2} sin (n) + C

Solution steps

\int sin (n) π x d x

Take the constant out:

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

= sin (n) π \cdot \int x d x

Apply the Power Rule

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

= sin (n) π \frac{x ^{2}}{2}

Simplify

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

= \frac{π}{2} x^{2} sin (n)

Add a constant to the solution

= \frac{π}{2} x^{2} sin (n) + C

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\int \frac{20}{x} + 3 cos (x) d x

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