f(x) = 2x² + 1 / [tex]x^{4}[/tex] + 5
Integrate f'(x) to obtain f(x) using the power rule
∫ a[tex]x^{n}[/tex] dx = [tex]\frac{a}{n+1}[/tex] [tex]x^{n+1}[/tex]
note that 4 / [tex]x^{5}[/tex] = 4[tex]x^{-5}[/tex]
∫(4x - 4[tex]x^{-5}[/tex])dx
= 2x² + [tex]x^{-4}[/tex] + c ← c is the constant of integration
to find c use f(1) = 8, hence
2 + 1 + c = 8 ⇒ c = 5
f(x) = 2x² + 1 / [tex]x^{4}[/tex] + 5
