koreanub Group Title Integration one year ago one year ago

1. koreanub Group Title

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

2. koreanub Group Title

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

3. experimentX Group Title

\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 Group Title

i believe u-sub will work

5. mukushla Group Title

$u=\sqrt{x}$ ha?

6. experimentX Group Title

woops!! that also works!!

7. koreanub Group Title

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

8. koreanub Group Title

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

9. experimentX Group Title

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

10. zepdrix Group Title

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

11. hartnn Group Title

x= tan^2 theta might work

12. experimentX Group Title

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

13. experimentX Group Title

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

14. koreanub Group Title

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. -.-