Question

Evaluate the ∫√5xdx

Answer 1

The indefinite integral is evaluated as,

$\int\sqrt{5x}dx=\sqrt{5}\int\sqrt{x}dx$

Use formula, $\int x^ndx=\frac{x^{n+1}}{n+1}$ to find the integral. Here, $n=\frac{1}{2}$

So, the integral is,

$\int\sqrt{5x}dx=\sqrt{5}[\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}]$

$=\sqrt{5}[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]$

$=\frac{2\sqrt{5}}{3}x^{\frac{3}{2}}$

Therefore, the indefinite integral is $\int\sqrt{5x}dx=\frac{2\sqrt{5}}{3}x^{\frac{3}{2}}$