# How do you find the indefinite integral of int (-2x^-3+10x^-5) dx?

Aug 24, 2016

$\frac{1}{x} ^ 2 - \frac{5}{2 {x}^{4}} + c$

#### Explanation:

integrate each term using the $\textcolor{b l u e}{\text{power rule for integration}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\int \left(a {x}^{n}\right) \mathrm{dx} = \frac{a}{n + 1} {x}^{n + 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \frac{- 2}{- 2} {x}^{-} 2 + \frac{10}{- 4} {x}^{-} 4 + c$

$\Rightarrow \int \left(- 2 {x}^{-} 3 + 10 {x}^{-} 5\right) \mathrm{dx} = \frac{1}{x} ^ 2 - \frac{5}{2 {x}^{4}} + c$