What is the integral of-xsin(nx) ?

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

Popular >

integral of-xsin(nx)

\int - x sin (n x) d x

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

Solution steps

\int - x sin (n x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int x sin (n x) d x

Apply Integration By Parts

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1}{x} ln (x))

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x e^{3 x}

\int (cos (3 x)) d x

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

\int 5 cos^{2} (x) sin (2 x) d x

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