## experimentX 3 years ago find the shortest method to evaluate this $\int \frac{\sin x}{\sin x + \cos x} \; dx$

1. anonymous

|dw:1347566427407:dw|

2. experimentX

yeah that it is.

3. anonymous

Do you know anything shorter?

4. experimentX

nope ... haven't found any other.

5. experimentX

just noted how similar these two integrals look like $\int \frac{\sin x}{\sin x + \cos x} \; dx \\ \int \frac{\cos x}{\sin x + \cos x} \; dx$

6. anonymous

Note one more way. Although the same really, |dw:1347566670806:dw|

7. anonymous

2I=pi/2 :)

8. anonymous

^^ No limits here.

9. experimentX

well ... pretty clever manipulation on the last problem

10. anonymous

lol i thought there are ;)

11. experimentX

yeah ... that is also very nice problem. i wish this one had too http://math.stackexchange.com/questions/198083/integrate-sin3x-sin3x-cos3x/198122#198122

12. experimentX

interesting technique ...

13. anonymous

maybe it does. |dw:1347567374847:dw|

14. experimentX
15. anonymous

For 2, Taking six + cosx as t, |dw:1347567485586:dw|

16. experimentX

this is just a back hack

17. anonymous

back hack?

18. experimentX

find the answer first ... differentiate the answer to get the get the middle portion.

19. anonymous

How do you find the answer first?

20. experimentX

make it easy as much a possible ... that's how i approach most of the problems. i to honest ... i can't work without answer.

21. anonymous

Okay. Back hack, eh. Hmmmm.

22. experimentX

Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.

23. anonymous

Agreed.

24. experimentX

well ... good night!!

25. anonymous

26. anonymous

Hold onn. What about the current solution to that, It does work quite easily or not?

27. anonymous

To the sin^3x/sin^3x + cos^3x

28. experimentX

there isn't nice manipulation like sin(x)/sin(x)+cos(x) for this one.