What is the integral of xsin(3x-2) ?

The integral of xsin(3x-2) is -1/3 xcos(3x-2)+1/9 sin(3x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xsin(3x-2)

\int x sin (3 x - 2) d x

- \frac{1}{3} x cos (3 x - 2) + \frac{1}{9} sin (3 x - 2) + C

Solution steps

\int x sin (3 x - 2) d x

Apply Integration By Parts

= - \frac{1}{3} x cos (3 x - 2) - \int - \frac{1}{3} cos (3 x - 2) d x

\int - \frac{1}{3} cos (3 x - 2) d x = - \frac{1}{9} sin (3 x - 2)

= - \frac{1}{3} x cos (3 x - 2) - (- \frac{1}{9} sin (3 x - 2))

Simplify

= - \frac{1}{3} x cos (3 x - 2) + \frac{1}{9} sin (3 x - 2)

Add a constant to the solution

= - \frac{1}{3} x cos (3 x - 2) + \frac{1}{9} sin (3 x - 2) + C

What is the integral of xsin(3x-2) ?
The integral of xsin(3x-2) is -1/3 xcos(3x-2)+1/9 sin(3x-2)+C