What is the integral of (x-5)sin(pix) ?

The integral of (x-5)sin(pix) is -1/pi cos(pix)(x-5)+1/(pi^2)sin(pix)+C

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integral of (x-5)sin(pix)

\int (x - 5) sin (π x) d x

- \frac{1}{π} cos (π x) (x - 5) + \frac{1}{π ^{2}} sin (π x) + C

Solution steps

\int (x - 5) sin (π x) d x

Apply Integration By Parts

: - \frac{1}{π} cos (π x) (x - 5) - \int - \frac{1}{π} cos (π x) d x

= - \frac{1}{π} cos (π x) (x - 5) - \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 - 5) - (- \frac{1}{π ^{2}} sin (π x))

Simplify

= - \frac{1}{π} cos (π x) (x - 5) + \frac{1}{π ^{2}} sin (π x)

Add a constant to the solution

= - \frac{1}{π} cos (π x) (x - 5) + \frac{1}{π ^{2}} sin (π x) + C

\frac{\partial}{\partial x} (- \frac{8 x}{y})

x \to 2 - lim (2 - x - 2)

\int \frac{8 t - 3}{t + 1} d t

x \to 4 lim (x^{2} + 5 - x)

What is the integral of (x-5)sin(pix) ?
The integral of (x-5)sin(pix) is -1/pi cos(pix)(x-5)+1/(pi^2)sin(pix)+C