Question

Finding an Indefinite Integral dx/x(lnx^2)^3

Answer 1

Explanation:

Firstly, we'll try to simplify the integrand. By hint 1, we see that:

`\ln(x^2) = 2\ln(x)`

Simplifying the integrand gives us:

`(1)/(8)\left((1)/(x(\ln(x))^3)\right)`

Next, by hint 2, we observe that:

`(d)/(dx)\left(\ln(x)\right) = (1)/(x)`

So this tells us to make the substitution:
`u = \ln(x)`

Doing so gives us:

`\int (dx)/(x(ln(x^2))^3) = \int (du)/(8u^3)`, which should be trivial.