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Question Number 20243 by tammi last updated on 24/Aug/17

$$\int \frac{dx}{x+\sqrt{x}}$$

Answered by $@ty@m last updated on 25/Aug/17

$$HereI=\int \frac{\frac{1}{\sqrt{x}}}{\sqrt{x}+1}dx\left(dividing{N}^r\mathrm{\&}{D}^{r}by\sqrt{x}\right)$$$$Let\sqrt{x}+1=t$$$$\frac{-1}{2\sqrt{x}}dx=dt$$$$\therefore I=\int \frac{-2dt}{t}$$$$=-2ln\mid t\mid +C$$$$=-2ln\mid \sqrt{x}+1\mid +C$$

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