find-dx-1-2-1-x-

Question Number 36421 by abdo.msup.com last updated on 01/Jun/18

f i n d \int \frac{d x}{1 + 2 \sqrt{1 - x}}

Commented by abdo.msup.com last updated on 04/Jun/18

c h a n g e m e n t \sqrt{1 - x} = t g i v e 1 - x = t^{2}

I = \int \frac{- 2 t d t}{1 + 2 t} = - \int \frac{2 t + 1 - 1}{2 t + 1} d t

= - t + \int \frac{d t}{2 t + 1} = - t + \frac{1}{2} l n ∣ 2 t + 1 ∣ + c