What is the integral of (3x+1)cos(x) ?

The integral of (3x+1)cos(x) is sin(x)(3x+1)+3cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3x+1)cos(x)

\int (3 x + 1) cos (x) d x

sin (x) (3 x + 1) + 3 cos (x) + C

Solution steps

\int (3 x + 1) cos (x) d x

Apply Integration By Parts

= (3 x + 1) sin (x) - \int 3 sin (x) d x

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

= (3 x + 1) sin (x) - (- 3 cos (x))

Simplify

= sin (x) (3 x + 1) + 3 cos (x)

Add a constant to the solution

= sin (x) (3 x + 1) + 3 cos (x) + C

What is the integral of (3x+1)cos(x) ?
The integral of (3x+1)cos(x) is sin(x)(3x+1)+3cos(x)+C