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Question Number 153563 by ZiYangLee last updated on 08/Sep/21

$$\int \frac{1}{1+\sqrt{2x}}dx=?$$

Answered by puissant last updated on 08/Sep/21

$$u=\sqrt{2x}\to u^2=2x\to x=\frac{u^2}{2}\Rightarrow dx=udu$$$$K=\int \frac{1}{1+\sqrt{2x}}dx=\int \frac{u}{1+u}du$$$$=\int (1-\frac{1}{1+u})du$$$$=u-ln\mid 1+u\mid +C$$$$$$$$\therefore \because K=\sqrt{2x}-ln\mid 1+\sqrt{2x}\mid +C..$$

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