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

$$1)find\int \frac{x}{\sqrt{1+x}+\sqrt{1-x}}dx$$$$2)calculate{\int }_1^3\frac{x}{\sqrt{1+x}+\sqrt{1-x}}dx$$

Answered by MJS last updated on 13/Aug/18

$$\int \frac{x}{\sqrt{1+x}+\sqrt{1-x}}dx=\frac{1}{2}\int \sqrt{1+x}dx-\frac{1}{2}\int \sqrt{1-x}dx=$$$$=\frac{1}{3}(\sqrt{{(1+x)}^3}+\sqrt{{(1-x)}^3})+C$$

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