# How do you integrate dy / (4(y^(1/2))?

Jun 3, 2016

$\frac{1}{2} {y}^{\frac{1}{2}} + C$

#### Explanation:

$\left[1\right] \text{ } \int \frac{\mathrm{dy}}{4 \left({y}^{\frac{1}{2}}\right)}$

First you can bring $\frac{1}{4}$ outside the integral symbol.

$\left[2\right] \text{ } = \frac{1}{4} \int \frac{\mathrm{dy}}{y} ^ \left(\frac{1}{2}\right)$

Next, bring ${y}^{\frac{1}{2}}$ to the numerator.

$\left[3\right] \text{ } = \frac{1}{4} \int {y}^{- \frac{1}{2}} \mathrm{dy}$

Use the power rule: $\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C$ (where C is a constant)

$\left[4\right] \text{ } = \frac{1}{4} \cdot {y}^{- \frac{1}{2} + 1} / \left(- \frac{1}{2} + 1\right) + C$

$\left[5\right] \text{ } = \frac{1}{4} \cdot {y}^{\frac{1}{2}} / \left(\frac{1}{2}\right) + C$

$\left[6\right] \text{ } = \textcolor{red}{\frac{1}{2} {y}^{\frac{1}{2}} + C}$