# What is the antiderivative of int (1/y^3 - 2/sqrty )dy?

Feb 19, 2016

$- \frac{1}{2 {y}^{2}} - 4 \sqrt{y} + C$

#### Explanation:

We can re write this as:

$\int {y}^{-} 3 - 2 {y}^{- \frac{1}{2}} \mathrm{dy}$

Now we can integrate by increasing the power by one and dividing by the new power as usual:

$= {y}^{-} \frac{2}{-} 2 - 4 {y}^{\frac{1}{2}} + C$

Re writing this back into a more familiar form gives us:

$= - \frac{1}{2 {y}^{2}} - 4 \sqrt{y} + C$