What is the integral of x^3cos(9x) ?

The integral of x^3cos(9x) is 1/9 x^3sin(9x)-1/3 (-1/9 x^2cos(9x)+2/729 (9xsin(9x)+cos(9x)))+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(9x)

\int x^{3} cos (9 x) d x

\frac{1}{9} x^{3} sin (9 x) - \frac{1}{3} (- \frac{1}{9} x^{2} cos (9 x) + \frac{2}{729} (9 x sin (9 x) + cos (9 x))) + C

Solution steps

\int x^{3} cos (9 x) d x

Apply Integration By Parts

: \frac{1}{9} x^{3} sin (9 x) - \int \frac{1}{3} x^{2} sin (9 x) d x

= \frac{1}{9} x^{3} sin (9 x) - \int \frac{1}{3} x^{2} sin (9 x) d x

\int \frac{1}{3} x^{2} sin (9 x) d x = \frac{1}{3} (- \frac{1}{9} x^{2} cos (9 x) + \frac{2}{729} (9 x sin (9 x) + cos (9 x)))

= \frac{1}{9} x^{3} sin (9 x) - \frac{1}{3} (- \frac{1}{9} x^{2} cos (9 x) + \frac{2}{729} (9 x sin (9 x) + cos (9 x)))

Add a constant to the solution

= \frac{1}{9} x^{3} sin (9 x) - \frac{1}{3} (- \frac{1}{9} x^{2} cos (9 x) + \frac{2}{729} (9 x sin (9 x) + cos (9 x))) + C

\int \frac{x ^{3}}{3} - 2 x^{2} - 5 x d x

\int (e^{\frac{- t}{6}} - e^{\frac{t}{6}})^{2} d t

\int 2 - 2 cos (4 x) d x

\int - 16 cos (4 x) d x

\int \frac{x - 3}{x ^{3} - x} d x

What is the integral of x^3cos(9x) ?
The integral of x^3cos(9x) is 1/9 x^3sin(9x)-1/3 (-1/9 x^2cos(9x)+2/729 (9xsin(9x)+cos(9x)))+C