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

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

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integral of (pi-x)*cos(nx)

\int (π - x) \cdot cos (n x) d x

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

Solution steps

\int (π - x) cos (n x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{x ^{2}}{( x ^{3} - 5 ) ^{2}} d x

\frac{d y}{d x} = - \frac{1}{x}

y^{^{'}} + y = e^{2 t}, y (0) = - 1

\int (1 - ln (x)) d x

\frac{\partial}{\partial y} (\frac{e ^{x} + e ^{y}}{2})

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