# How do you find the antiderivative of 2/(xsqrtx)?

Dec 6, 2017

Rewrite it as $2 {x}^{- \frac{3}{2}}$ then apply the power rule for antiderivatives.

#### Explanation:

Add $1$ to the exponent and divide by the new exponent.

$2 {x}^{- \frac{3}{2} + 1} / \left(- \frac{3}{2} + 1\right) = 2 {x}^{- \frac{1}{2}} / \left(- \frac{1}{2}\right) = - 4 {x}^{- \frac{1}{2}} + C$

$\frac{- 4}{x} ^ \left(\frac{1}{2}\right) + C$
$\frac{- 4}{\sqrt{x}} + C$