What is the integral of xsin(nx) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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} (- 2 cot (x))

\frac{1}{7 x ^{\frac{6}{7}}}

8 x e^{x}, 0

\int ln (x^{2} + y^{2}) d x

\int 2 sin (3 t) d t

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