What is the integral of xsin(x+y) ?

The integral of xsin(x+y) is -xcos(y+x)+sin(y+x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xsin(x+y)

\int x sin (x + y) d x

- x cos (y + x) + sin (y + x) + C

Solution steps

\int x sin (x + y) d x

Apply Integration By Parts

= - x cos (y + x) - \int - cos (y + x) d x

\int - cos (y + x) d x = - sin (y + x)

= - x cos (y + x) - (- sin (y + x))

Simplify

= - x cos (y + x) + sin (y + x)

Add a constant to the solution

= - x cos (y + x) + sin (y + x) + C

What is the integral of xsin(x+y) ?
The integral of xsin(x+y) is -xcos(y+x)+sin(y+x)+C