Integration Help? (1 Viewer)

[Lukybear]

When I intergrated:

1/sqrt(x)sqrt(1-x) = I, Ive got sinh sqrtx. This i used a subsitution x=u^2

However, expanding the bottom;
I = 1/sqrt(x-x^2), then chaging the denominator to a perfect square:
I = 1/sqrt (1/4 - (1/2-x)^2), then using the same sin inverse identity, i got a complete different answer.

Can someone please explain to me this?<!-- google_ad_section_end -->

 

[omgmynameislong]

http://www.wolframalpha.com/input/?i=2arcsin%28%28x%29^1%2F2%29

arcsin(2x-1) - Wolfram|Alpha


These 2 are the answers to the integration, they're the same graph but one is shifted up and this is because of the +C.

 

[fullonoob]

probably what long said