# How do you find the indefinite integral of int 4/sqrt(5t)dt?

Apr 13, 2017

THe answer is $= \frac{8 \sqrt{t}}{\sqrt{5}} + C$

#### Explanation:

We need

$\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C$

$\int \frac{1}{\sqrt{x}} \mathrm{dx} = \int {x}^{- \frac{1}{2}} \mathrm{dx} = {x}^{\frac{1}{2}} / \left(\frac{1}{2}\right) = 2 \sqrt{x}$

So,

$\int \frac{4 \mathrm{dt}}{\sqrt{5 t}} = \frac{4}{\sqrt{5}} \cdot 2 \sqrt{t} + C$

$= \frac{8 \sqrt{t}}{\sqrt{5}} + C$