What is the integral of (x+1)sin(nx) ?

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

integral of (x+1)sin(nx)

\int (x + 1) sin (n x) d x

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

Solution steps

\int (x + 1) sin (n x) d x

Apply Integration By Parts

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

Simplify

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

Add a constant to the solution

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

(2 y - 3 x) \frac{d y}{d x} = 3 y - 4 x

\int_{- \infty}^{0} e^{- ∣ x ∣} d x

y^{^{''}} + 2 y^{^{'}} + y = x^{- 6} e^{- x}

\int \frac{x + 2}{x ^{2} + 3 x - 4} d x

s l o p e (2) (- 3.1)

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