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

\int x^{4} (x^{5} - 4)^{5} d x

\int e^{l n (s i n (x))} d x

\int \frac{1}{x \cdot ( x + 1 )} d x

\int (\frac{y}{5} + \frac{2}{y}) d y

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