# How do you find the antiderivative f(x)=6/x^5?

Note that $\setminus \int {x}^{n} \setminus \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C$ when $n \ne - 1$ and that $\setminus \int a f \left(x\right) \setminus \mathrm{dx} = a \setminus \int f \left(x\right) \setminus \mathrm{dx}$ for any constant $a$.
Hence $\setminus \int \frac{6}{{x}^{5}} \setminus \mathrm{dx} = 6 \setminus \int {x}^{- 5} \setminus \mathrm{dx} = 6 \cdot {x}^{- 4} / \left(- 4\right) + C = - \frac{3}{2 {x}^{4}} + C$