# How do you integrate 67/x - 5sqrt(x)?

Feb 1, 2015

You can manipulate your function to get:

$\int \left[\frac{67}{x} - 5 {x}^{\frac{1}{2}}\right] \mathrm{dx} =$

that can be written as:

$\int \frac{67}{x} \mathrm{dx} - \int 5 {x}^{\frac{1}{2}} \mathrm{dx} =$

Now you can use the fact that $\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + c$ and $\int \frac{1}{x} \mathrm{dx} = \ln \left(x\right) + c$

To get:

$= 67 \ln \left(x\right) - 5 {x}^{\frac{3}{2}} / \left(\frac{3}{2}\right) + c$
$= 67 \ln \left(x\right) - 10 x \frac{\sqrt{x}}{3} + c$