Question

Not sure how to do this

Answer 1

f(x) = 2x² + 1 /
`x^(4)` + 5

Integrate f'(x) to obtain f(x) using the power rule

∫ a
`x^(n)` dx =
`(a)/(n+1)`
`x^(n+1)`

note that 4 /
`x^(5)` = 4
`x^(-5)`

∫(4x - 4
`x^(-5)`)dx

= 2x² +
`x^(-4)` + 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 /
`x^(4)` + 5