What is the integral of (x-3)sin(pix) ?

The integral of (x-3)sin(pix) is -1/pi cos(pix)(x-3)+1/(pi^2)sin(pix)+C

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integral of (x-3)sin(pix)

\int (x - 3) sin (π x) d x

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

Solution steps

\int (x - 3) sin (π x) d x

Apply Integration By Parts

: - \frac{1}{π} cos (π x) (x - 3) - \int - \frac{1}{π} cos (π x) d x

= - \frac{1}{π} cos (π x) (x - 3) - \int - \frac{1}{π} cos (π x) d x

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{cot ( x )}{x} d x

\frac{\partial}{\partial x} (ln (x + 4 y + 7 z))

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

\frac{\partial}{\partial x} (cos (y e^{x \cdot y}))

\int [1 + \frac{1}{( x + 1 ) ^{2}}] d x

What is the integral of (x-3)sin(pix) ?
The integral of (x-3)sin(pix) is -1/pi cos(pix)(x-3)+1/(pi^2)sin(pix)+C