koreanub 3 years ago Integration

1. koreanub

$\int\limits_{?}^{?} \frac{ 1 }{ \sqrt{x}(1+x) }$

2. koreanub

The question marks are not suppose to be there, so it's the problem without the question marks.

3. experimentX

\int just use like this for integration ... seems like trig subs seems to work also changing 1 + x = (1 + i sqrt(x))(1 - i sqrt(x)) and then taking partial fraction might work.

4. mukushla

i believe u-sub will work

5. mukushla

$u=\sqrt{x}$ ha?

6. experimentX

woops!! that also works!!

7. koreanub

For this exercise, I'm technically not suposed to use partial fractions

8. koreanub

I may be missing something, but I can't seem to find the answer with u = $\sqrt{x}$

9. experimentX

change all x's into u's probably you would end up with 1/1+u^2 or something like that.

10. zepdrix

You have to mess with the U a little bit kore :) but it will work.

11. hartnn

x= tan^2 theta might work

12. experimentX

this is same as using trig subs x = tan^2 theta in original.

13. experimentX

but lol ... we know int 1/1+x^2 = arctan (x) which is one of the standard integral.

14. koreanub

I got it! Yes!!! I was substituting the first $\sqrt{x}$ in the integrand. Then, I realized that it gets canceled out. Thank you very much everyone! ... If it wasn't for you, I probably would have spent another 10 minutes on this. -.-

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