Question

How do you integrate `int y^2sqrtydy`?

Answer 1

`int \ y^2sqrt(y) \ dy = 2/7y^3sqrt(y) + c`

Explanation:

Using fractional powers, and the rule of indices `a^ma^n=a^(m+n)` we can write:

`int \ y^2sqrt(y) \ dy = int \ y^2 \ y^(1/2) \ dy`
`" "= int \ y^(5/2) \ dy`

Then using the power rule for integration `int x^n \ dx=x^(n+1)/(n+1)` we have:

`int \ y^2sqrt(y) \ dy = y^(7/2)/(7/2) + c`
`" "= 2/7y^(7/2) + c`
`" "= 2/7y^3sqrt(y) + c`