What is the integral of x*sin(n*x) ?

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

Popular >

integral of xsin(nx)

\int x \cdot sin (n \cdot 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

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

\int (\frac{- 2}{x}) d x

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

\int \frac{6 x ^{3} - 6 x}{1 - 3 x ^{2} + 2 x ^{3}} d x

\int \frac{5 x}{25 - x ^{2}} d x

\int \frac{arcsin ( t )}{1 - t ^{2}} d t

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