Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)2 Marks
Question
Evalute : $\int \frac{1}{\sqrt{x}+x} d x$
✓
Answer
$ \begin{aligned} & \text { Let } I=\int \frac{1}{\sqrt{x}+x} d x \\ & =\int \frac{1}{\sqrt{x}(1+\sqrt{x})} d x \end{aligned} $ Put $1+\sqrt{ x }= t$ $ \begin{aligned} & \therefore \frac{1}{2 \sqrt{ x }} dx = dt \\ & \therefore \frac{1}{\sqrt{ x }} dx =2 dt \\ & \therefore I =\int \frac{2 \cdot dt }{ t } \\ & =2 \int \frac{1}{ t } dt \\ & =2 \log | t |+ c \\ & \therefore I =2 \log |1+\sqrt{ x }|+ c \end{aligned} $
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