## anonymous 3 years ago integrate (x)(cos^3 x) dx

1. anonymous

do you know the reduction formula for $\int \cos^n x \,\mathrm dx$

2. anonymous

reduction?? nope...

3. anonymous

first simplify cos^3 x in terms of cosine of 3x and x and then integrate by parts

4. anonymous

i don't think here u should use reduction formula

5. anonymous

its $\cos ^3 x$ .. where did u get 3x and x @matricked

6. anonymous

use cos3x =4 cos^3 (x) - 3cos x

7. anonymous

why not? it solves the problem too, but the solution may not be attractive to @bii17

8. anonymous

i mean use cos^3 (x) =1/4 *(cos3x +3cosx)

9. anonymous

oh okay.. then what will happen next ? @matricked

10. anonymous

and then use by parts

11. anonymous

$1/4 [x(\cos 3x + 3\cos x)]dx$ is this correct? @matricked

12. anonymous

yup

13. anonymous

so there will be u and du den dv and v... i used Dv as cos 3x dx the V will be 1/3 sin 3x ???

14. anonymous

for both integration of 1/4 *xcos3x take x as the first function

15. anonymous

i get it.. thanks a lot :) @matricked