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

The integral of x^3cos(nx) is 1/n x^3sin(nx)-3/n (-1/n x^2cos(nx)+2/(n^3)(nxsin(nx)+cos(nx)))+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(nx)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

x \to - 7 lim (\frac{x}{x - 2})

e^{x} + 1

x^{2} y + y^{^{'}} = - 7 x^{2}

x \to \infty lim (3 x + 6)

What is the integral of x^3cos(nx) ?
The integral of x^3cos(nx) is 1/n x^3sin(nx)-3/n (-1/n x^2cos(nx)+2/(n^3)(nxsin(nx)+cos(nx)))+C