What is the integral of x^3cos(6x) ?

The integral of x^3cos(6x) is 1/6 x^3sin(6x)-1/2 (-1/6 x^2cos(6x)+1/108 (6xsin(6x)+cos(6x)))+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(6x)

\int x^{3} cos (6 x) d x

\frac{1}{6} x^{3} sin (6 x) - \frac{1}{2} (- \frac{1}{6} x^{2} cos (6 x) + \frac{1}{108} (6 x sin (6 x) + cos (6 x))) + C

Solution steps

\int x^{3} cos (6 x) d x

Apply Integration By Parts

: \frac{1}{6} x^{3} sin (6 x) - \int \frac{1}{2} x^{2} sin (6 x) d x

= \frac{1}{6} x^{3} sin (6 x) - \int \frac{1}{2} x^{2} sin (6 x) d x

\int \frac{1}{2} x^{2} sin (6 x) d x = \frac{1}{2} (- \frac{1}{6} x^{2} cos (6 x) + \frac{1}{108} (6 x sin (6 x) + cos (6 x)))

= \frac{1}{6} x^{3} sin (6 x) - \frac{1}{2} (- \frac{1}{6} x^{2} cos (6 x) + \frac{1}{108} (6 x sin (6 x) + cos (6 x)))

Add a constant to the solution

= \frac{1}{6} x^{3} sin (6 x) - \frac{1}{2} (- \frac{1}{6} x^{2} cos (6 x) + \frac{1}{108} (6 x sin (6 x) + cos (6 x))) + C

\int sin (\frac{nπ t}{2}) d t

\int (2 x^{2} + \frac{1}{( 2 x ) ^{2}}) d x

f (x) = - 2 x sin (x^{2})

\frac{\partial}{\partial c} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

f (x) = arccos (x)

What is the integral of x^3cos(6x) ?
The integral of x^3cos(6x) is 1/6 x^3sin(6x)-1/2 (-1/6 x^2cos(6x)+1/108 (6xsin(6x)+cos(6x)))+C