What is the integral of (pi-x)sin(nx) ?

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

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integral of (pi-x)sin(nx)

\int (π - x) sin (n x) d x

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

Solution steps

\int (π - x) sin (n x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

(\frac{1 - 2 ln ( x )}{x ^{3}})^{^{'}}

\int \frac{e ^{x}}{4 - e ^{2 x}} d x

\frac{- 2 x ^{2} + x + 4}{x ^{2} + 4 x - 1}

\int (6 - x) d x

\int_{0}^{3} cos (\frac{π x}{3}) d x

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