# How do you find the antiderivative of f(x)=10/x^9?

You can start by writing your function as: $f \left(x\right) = 10 {x}^{-} 9$
$\int k {x}^{n} \mathrm{dx} = k {x}^{n + 1} / \left(n + 1\right) + c$ (where $k$ is a constant);
$\int 10 {x}^{-} 9 \mathrm{dx} = 10 {x}^{-} \frac{8}{- 8} + c = - \frac{5}{4} \cdot \frac{1}{x} ^ 8 + c$