What is the integral of x^2*cos(ax) ?

The integral of x^2*cos(ax) is 1/a x^2sin(ax)-2/a (-1/a xcos(ax)+1/(a^2)sin(ax))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^2*cos(ax)

\int x^{2} \cdot cos (a x) d x

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

Solution steps

\int x^{2} cos (a x) d x

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

What is the integral of x^2*cos(ax) ?
The integral of x^2*cos(ax) is 1/a x^2sin(ax)-2/a (-1/a xcos(ax)+1/(a^2)sin(ax))+C