# integration...

• Jun 18th 2007, 08:56 AM
Possible actuary
integration...
Can I get some help with this integral?

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

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.
• Jun 18th 2007, 09:25 AM
Krizalid
Set $x=\sin^2u$
• Jun 18th 2007, 09:29 AM
Jhevon
Quote:

Originally Posted by Possible actuary
Can I get some help with this integral?

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

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.

i believe the method was to use a $u = \sqrt {x}$ substitution followed by a $u = \sin \theta$ trig substitution. but Krizalid's method may be easier come to think of it
• Jun 18th 2007, 01:29 PM
Possible actuary
Quote:

Originally Posted by Krizalid
Set $x=\sin^2u$

That definately helped me out a lot. Thanks!
• Jun 18th 2007, 01:34 PM
Possible actuary
Quote:

Originally Posted by Jhevon

i believe the method was to use a $u = \sqrt {x}$ substitution followed by a $u = \sin \theta$ 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?
• Jun 18th 2007, 01:49 PM
Krizalid
Probably Jhevon looked that thread time ago and remembered who answered it.

This way it's easy to find known threads.
• Jun 18th 2007, 03:27 PM
Jhevon
Quote:

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