Omniscience 3 years ago $\int tanxdx$ integration by parts

1. Omniscience

i integrate it twice; but i dont know why it failed

2. irkiz

separate them into tanx and dx

3. Omniscience

i did$(tanx)(x) - \int\limits xsec^{2}dx$

4. hartnn

integral sin x /cos x put t= cos x

5. Omniscience

i know..but i want to do it by parts

6. mayankdevnani

- ln |cos x| + C proof int tan x dx = int sinx/cos x set u=cosx then we find du=-sinx dx substitute du=-sin x, u=cos x int sinx/cos x= - int of (-1) sin x dx / cosx =- int of du/u Solve the integral = - ln |u| + C substitute back u=cos x = - ln |cos x| + C

7. mayankdevnani

ok @Omniscience

8. Omniscience

i know u-sub i want to do it by parts

9. mayankdevnani
10. mayankdevnani

11. Omniscience

that's $$xtanx$$

12. mayankdevnani

oh!!! sorry

13. irkiz

maybe you could try converting tan x to sinx/cosx. then integrate sinxsecx by parts?

14. Omniscience

ok i will try it

15. irkiz

wait. is the ans ln|secx|?

16. Omniscience

-ln(cosx)

17. irkiz

looks the same lol

18. irkiz

sec x is (cosx)^-1 bring the -1 to the front

19. irkiz