What is the integral of 3xcos(x) ?

The integral of 3xcos(x) is 3(xsin(x)+cos(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3xcos(x)

\int 3 x cos (x) d x

3 (x sin (x) + cos (x)) + C

Solution steps

\int 3 x cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x cos (x) d x

Apply Integration By Parts

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

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

= 3 (x sin (x) - (- cos (x)))

Simplify

= 3 (x sin (x) + cos (x))

Add a constant to the solution

= 3 (x sin (x) + cos (x)) + C

What is the integral of 3xcos(x) ?
The integral of 3xcos(x) is 3(xsin(x)+cos(x))+C