What is the integral of x*sin(2x) ?

The integral of x*sin(2x) is -1/2 xcos(2x)+1/4 sin(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x*sin(2x)

\int x \cdot sin (2 x) d x

- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x) + C

Solution steps

\int x sin (2 x) d x

Apply Integration By Parts

= - \frac{1}{2} x cos (2 x) - \int - \frac{1}{2} cos (2 x) d x

\int - \frac{1}{2} cos (2 x) d x = - \frac{1}{4} sin (2 x)

= - \frac{1}{2} x cos (2 x) - (- \frac{1}{4} sin (2 x))

Simplify

= - \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)

Add a constant to the solution

= - \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x) + C

What is the integral of x*sin(2x) ?
The integral of x*sin(2x) is -1/2 xcos(2x)+1/4 sin(2x)+C