1-find-x-1-x-1-x-dx-2-calculate-1-3-x-1-x-1-x-dx-

Question Number 41845 by maxmathsup by imad last updated on 13/Aug/18

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

2) c a l c u l a t e \int_{1}^{3} \frac{x}{\sqrt{1 + x} + \sqrt{1 - x}} d x

Answered by MJS last updated on 13/Aug/18

\int \frac{x}{\sqrt{1 + x} + \sqrt{1 - x}} d x = \frac{1}{2} \int \sqrt{1 + x} d x - \frac{1}{2} \int \sqrt{1 - x} d x =

= \frac{1}{3} (\sqrt{{(1 + x)}^{3}} + \sqrt{{(1 - x)}^{3}}) + C

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