Step-by-step explanation:
Firstly, we'll try to simplify the integrand. By hint 1, we see that:
[tex]\ln(x^2) = 2\ln(x)[/tex]
Simplifying the integrand gives us:
[tex]\frac{1}{8}\left(\frac{1}{x(\ln(x))^3}\right)[/tex]
Next, by hint 2, we observe that:
[tex]\frac{d}{dx}\left(\ln(x)\right) = \frac{1}{x}[/tex]
So this tells us to make the substitution: [tex]u = \ln(x)[/tex]
Doing so gives us:
[tex]\int \frac{dx}{x(ln(x^2))^3} = \int \frac{du}{8u^3}[/tex], which should be trivial.
