Write the anti-derivative


Write the anti-derivative of $\left(3 \sqrt{x}+\frac{1}{\sqrt{x}}\right)$.


Anti-derivative is nothing but integration

Therefore its Anti-derivative can be found by integrating the above given equation.

$=\int 3 \sqrt{x}+\frac{1}{\sqrt{x}} d x$

$=\int 3 x^{\frac{1}{2}}+x^{-\frac{1}{2}} d x$

$=3 \frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}+\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+c\left[\right.$ since, $\left.\int x^{n} d x=\frac{x^{n+1}}{n+1}\right]$

$=3 \frac{x^{\frac{3}{2}}}{\frac{3}{2}}+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+c$

$=2 x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+c$


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