Integration of (x+1 x ) with respect to x : - Vidyadip

Question

Integration of $\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$ with respect to $x$ :

✓

Answer

Let $I =\int\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right) d x$
$=\int\left(x^{\frac{1}{2}}+x^{-\frac{1}{2}}\right) d x$
$=\frac{x^{\frac{3}{2}}}{\frac{3}{2}}+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C$
$=\frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+C$
Hence correct option is $(C).$

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