Question

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

Answer 1

Note that `\int x^{n}\ dx=x^{n+1}/(n+1)+C` when `n!=-1` and that `\int af(x)\ dx=a\int f(x)\ dx` for any constant `a`.

Hence `\int 6/(x^5)\ dx=6\int x^{-5}\ dx=6* x^{-4}/(-4)+C=-3/(2x^4)+C`