x^2 cosx dxx2cosxdx intregrate?

2 Answers
May 10, 2018

int x^2 cos x\ d x = ( x^2 - 2 ) sin x + 2 x cos x + C

Explanation:

This integral can be solved by using integration by parts twice:

int x^2 cos x\ d x =

= x^2 sin x - 2 int x sin x\ d x =

= x^2 sin x - 2 [ - x cos x + int cos x\ d x ] =

= x^2 sin x + 2 x cos x - 2 sin x + C =

= ( x^2 - 2 ) sin x + 2 x cos x + C.

May 10, 2018

int x^2 cos x dx =x^2 sin x + 2 x cos x - 2 sin x + c

Explanation:

int x^2 cos x dx let u= x^2:. du = 2x dx

dv = cosx dx or int dv = int cos x dx or v = sin x

int x^2 cos x dx = uv - int v du = x^2 sin x - int sinx *2x dx or

int x^2 cos x dx =x^2 sin x - 2int sinx *x dx

let u= x:. du = dx ,dv = sin x dx or v = -cos x

int sinx *x dx = - x cos x - int -cosx dx or

int sinx *x dx = - x cos x + int cosx dx or

int sinx *x dx = - x cos x + sinx

int x^2 cos x dx =x^2 sin x - 2(- x cos x + sin x ) or

int x^2 cos x dx =x^2 sin x + 2 x cos x - 2 sin x + c [Ans]