# How do you find the indefinite integral of int (-24x^5-10x) dx?

Oct 17, 2016

$= - 4 {x}^{6} - 5 {x}^{2} + C$

#### Explanation:

Knowing the method of polynomial integration that says:
$\textcolor{red}{\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right)}$

$\int \left(- 24 {x}^{5} - 10 x\right) \mathrm{dx}$
$= \int \left(- 24 {x}^{5}\right) \mathrm{dx} - \int \left(10 x \mathrm{dx}\right)$
$= \left(- \frac{24}{\textcolor{red}{6}}\right) {x}^{\textcolor{red}{5 + 1}} - \frac{10}{\textcolor{red}{2}} \left({x}^{\textcolor{red}{1} + 1}\right)$
$= - 4 {x}^{6} - 5 {x}^{2} + C$