Thread: integration...

Can I get some help with this integral?

$\displaystyle \int\frac{\sqrt{1-x}}{\sqrt{x}}~dx$

I have thought of integration by parts and substitution. Nothing seems to be clicking yet. I am thinking that I need to multiply this fraction by something but have no idea.

Set $\displaystyle x=\sin^2u$

Originally Posted by Possible actuary

Can I get some help with this integral?

$\displaystyle \int\frac{\sqrt{1-x}}{\sqrt{x}}~dx$

I have thought of integration by parts and substitution. Nothing seems to be clicking yet. I am thinking that I need to multiply this fraction by something but have no idea.

this question was asked by another user and answered here.

i believe the method was to use a $\displaystyle u = \sqrt {x}$ substitution followed by a $\displaystyle u = \sin \theta$ trig substitution. but Krizalid's method may be easier come to think of it

Originally Posted by Krizalid

Set $\displaystyle x=\sin^2u$

That definately helped me out a lot. Thanks!

Originally Posted by Jhevon

this question was asked by another user and answered here.

i believe the method was to use a $\displaystyle u = \sqrt {x}$ substitution followed by a $\displaystyle u = \sin \theta$ trig substitution. but Krizalid's method may be easier come to think of it

How would you search for an integral that was solved before? I know that there is a search engine to use but how would you search for a specific integral?

Probably Jhevon looked that thread time ago and remembered who answered it.

This way it's easy to find known threads.

Originally Posted by Possible actuary

How would you search for an integral that was solved before? I know that there is a search engine to use but how would you search for a specific integral?

i believe you can type the LaTex code for the integral into the search bar and it will find it. however, it is usually easier to find a thread if you remember a phrased used in the thread.

for this, i remember seeing this question a while back, so i estimated the date i saw it to minimize my search. i also remembered that i subscribed to the thread and that "trig substitution" was used. so i searched for "trig substitution" and browsed through only the threads that i was subscribed to around the date that i estimated the thread was psoted and found it