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

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

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integral of (x+pi)sin(nx)

\int (x + π) sin (n x) d x

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

Solution steps

\int (x + π) sin (n x) d x

Expand

(x + π) sin (n x) : x sin (n x) + π sin (n x)

= \int x sin (n x) + π sin (n x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x sin (n x) d x + \int π sin (n x) d x

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

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

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

Add a constant to the solution

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

y^{'} = 0.0014 y (1700 - y)

4 cos^{2} (2 t)

\frac{3 x + 7}{4 x - 5}

n = 0 \sum \infty 37.06

\frac{\partial}{\partial x} (6 y (3 x^{2} - y^{2}))

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