Step 1 :The integral is of the form ∫f'(x)f(x) dx, where f(x) = (ln x)^30 and f'(x) = 1/x. This is a standard form of integral that can be solved by the method of integration by substitution.
Step 2 :We can set u = f(x) = (ln x)^30, then du = f'(x) dx = 1/x dx. Substituting these into the integral, we get ∫u du, which is a simple integral to solve.
Step 3 :After solving, we substitute back u = (ln x)^30 to get the final answer.
Step 4 :Final Answer: \(\boxed{\frac{(\ln x)^{31}}{31} + C}\) where C is the constant of integration.