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

Popular >

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

= - \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

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

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

\int (x + 5) 3 - x d x

\int \frac{1}{y cos ^{2} ( ln ( y ) )} d y

\int (x^{2} + 6 x) cos (2 x) d x

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