Question

Oops, accidentally closed instead of going to/bumping
Consider the function f(x) = 8/x^3 - 4/x^5.
Let F(x) be the antiderivative of f(x) with F(1) = 0.
Then F(5) equals

Answer 1

Have to go but if anyone can help with this I will be checking in when I can

Answer 2

\[f(x)={8\over x^3}-{4\over x^5}=8x^{-3}-4x^{-5}\\
F(x)=\int(8x^{-3}-4x^{-5})dx=8{x^{-2}\over-2}-4{x^{-4}\over-4}+C\\
F(x)=-4x^{-2}+x^{-4}+C\\
F(1)=0=-4+1+C\implies C=3\\
F(5)=-4(5^{-2})+(5^{-4})+3\\
\implies F(5)={-4\over25}+ {1\over625}+3=?
\]