What is the integral of x^3cos(x) ?

The integral of x^3cos(x) is x^3sin(x)-3(-x^2cos(x)+2(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 x^3cos(x)

\int x^{3} cos (x) d x

x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

Solution steps

\int x^{3} cos (x) d x

Apply Integration By Parts

= x^{3} sin (x) - \int 3 x^{2} sin (x) d x

\int 3 x^{2} sin (x) d x = 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

= x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

Add a constant to the solution

= x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

What is the integral of x^3cos(x) ?
The integral of x^3cos(x) is x^3sin(x)-3(-x^2cos(x)+2(xsin(x)+cos(x)))+C