## anonymous 3 years ago int. calculus $\int\limits_{}^{}\sin ^{2}x \cos ^{2}x \tan ^{2} x dx$

1. anonymous

Write them as sin squared x = (1/2)(1 - cos 2x) cos squared x = (1/2)(1 + cos 2x) maybe..that'll be easier for you to integrate.

2. anonymous

can i do that, even if sin or cos is not raised two?

3. hartnn

doesn't that simplify to sin^4 x when tan is written as sin/cos ?

4. anonymous

Write tan^2 x = sin^2 x / cos^2 x

5. anonymous

yea

6. anonymous

i did that before

7. anonymous

$\large{\int { sin^4x dx}}$ Can you do this?

8. anonymous

then i lost any of ideas after that

9. anonymous

OK no problem, where are you lost?

10. hartnn

can u integrate sin^2 x ?

11. anonymous

after i got the $\int\limits_{?}^{?}\sin ^{4}xdx$

12. anonymous

Well if integration of sin x dx= -cosx + C then that of sin^4 x dx = ?

13. anonymous

-cos^4x + C ??

14. hartnn

write sin^4 x = (sin^2 x)(1-cos^2 x)

15. hartnn

no, its not that direct

16. anonymous

then distribute?

17. hartnn

= (sin^2 x)(1-cos^2 x) = sin^2 x - sin^2x cos^2 x yes

18. hartnn

= sin^2 x - sin^2x cos^2 x = sin^2 x - (1/4) (sin 2x)^2

19. anonymous

how did you get (1/4)(sin 2x)^2?

20. hartnn

sin 2x = 2 sin x cos x to get sin^2x cos^2 x , i squared the above .....

21. hartnn

got that ? ^ and can u integrate sin^2 x - (1/4) (sin 2x)^2

22. anonymous

can you show me the whole process of that sin 2x = 2 sin x cos x

23. hartnn

u want me to prove 2sin x cos x = sin 2x or u wanted this : sin 2x = 2 sin x cos x (sin 2x)^2 = (2 sin x cos x)^2 = 4 sin^2x cos^2 x so sin^2 x cos^2 x = (1/4) (sin 2x)^2

24. hartnn

so if u can integrate sin^2 x you can also integrate sin^2 x - (1/4) (sin 2x)^2