# How do you integrate 1 / (x^5)?

Nov 9, 2016

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

#### Explanation:

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

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\int \left(a {x}^{n}\right) \mathrm{dx} = \frac{a}{n + 1} {x}^{n + 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

Express $\frac{1}{x} ^ 5 = {x}^{-} 5$

$\Rightarrow \int {x}^{-} 5 \mathrm{dx} = \frac{1}{- 5 + 1} {x}^{- 5 + 1} + c$

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

where c is the constant of integration.