What is the integral of x^3cos(8x) ?

The integral of x^3cos(8x) is 1/8 x^3sin(8x)-3/8 (-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3cos(8x)

\int x^{3} cos (8 x) d x

\frac{1}{8} x^{3} sin (8 x) - \frac{3}{8} (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))) + C

Solution steps

\int x^{3} cos (8 x) d x

Apply Integration By Parts

: \frac{1}{8} x^{3} sin (8 x) - \int \frac{3}{8} x^{2} sin (8 x) d x

= \frac{1}{8} x^{3} sin (8 x) - \int \frac{3}{8} x^{2} sin (8 x) d x

\int \frac{3}{8} x^{2} sin (8 x) d x = \frac{3}{8} (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)))

= \frac{1}{8} x^{3} sin (8 x) - \frac{3}{8} (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)))

Add a constant to the solution

= \frac{1}{8} x^{3} sin (8 x) - \frac{3}{8} (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))) + C

\int \frac{1 - sin ( x )}{2 + cos ( x )} d x

\int x^{5} ln (x^{3} + 1) d x

\int (2 x + 3)^{- 4} d x

\int 3 sec^{2} (2 x) d x

\int sin (2 x) (cos (2 x))^{15} d x

What is the integral of x^3cos(8x) ?
The integral of x^3cos(8x) is 1/8 x^3sin(8x)-3/8 (-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x)))+C