Having trouble with a Calculs Integration

The integration is [dx / (x Sqrt[1 - x])

Seems pretty simple but the question specify to not use the Tanh integration formula...

Now i'm stuck if my calculation are correct. Using the Pythagore i get to a point where i integrate Sec (theta)

and stuck... got Ln ¦ sec (theta) + Tan (theta) ¦ + c... then nothing i can't find the right answer that fit with the real anwer that is

If anyone could tell me if i made a mistake or send me in the right direction would be great

Log[1 - Sqrt[1 - x]] - Log[1 + Sqrt[1 - x]]

Re: Having trouble with a Calculs Integration

If you observe that:

and then make the substitution:

you get:

and now factor the denominator, and use partial fractions...

Re: Having trouble with a Calculs Integration

Wow fast answer and right answer just did the whole thing it work very well!!!

Sorry if the problem was to easy I tought I'd put more of a challenge!

Thanks MarkFl