If you observe that:
and then make the substitution:
you get:
and now factor the denominator, and use partial fractions...
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]]