Question

How do you integrate `h(s)=s^(4/5)` using the power rule?

Answer 1

See below.

Explanation:

The power rule for integration is the opposite of the power rule for differentiation.

For integrals we have: `int x^n dx = 1/(n+1) x^(n+1) +C` for `n != -1`.

So

`int s^(4/5) ds = 1/(4/5+1) s^(4/5+1) +C`

Or, quicker using `4/5+1 = 9/5` and `1/(9/5) = 5/9`,

`int s^(4/5) ds = 5/9s^(9/5) +C`