Integration

Question

Integration

anonymous · Answer

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

anonymous · Answer

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

experimentx · Answer

\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.

anonymous · Answer

i believe u-sub will work

anonymous · Answer

$$u=\sqrt{x}$$  ha?

experimentx · Answer

woops!! that also works!!

anonymous · Answer

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

anonymous · Answer

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

experimentx · Answer

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

zepdrix · Answer

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

hartnn · Answer

x= tan^2 theta might work

experimentx · Answer

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

experimentx · Answer

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

anonymous · Answer

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. -.-