Question

How do you integrate by substitution `int [x^2+1/(3x)^2]dx`?

Answer 1

`int \ x^2 + 1/(3x)^2 \ dx = x^3/3 - 1/(9x) \+c`

Explanation:

You do not need to use a substitution, just the power rule, as:

`int \ x^2 + 1/(3x)^2 \ dx = int \ x^2 + 1/(9x^2) \ dx`
`" "= int \ x^2 + 1/9x^-2 \ dx`
`" "= x^3/3 + 1/9(-1)x^-1 \+c`
`" "= x^3/3 - 1/(9x) \+c`