Final answer:
The question asks to evaluate a definite integral, which is a calculus problem involving a limit as x approaches infinity, using substitution to simplify the expression and find an antiderivative for calculation.
Step-by-step explanation:
The question involves evaluating a definite integral which is a concept in calculus, a branch of mathematics. The integral in question is ∫ (1 / (x * ((ln(x))^2 + 9))) dx from 1 to infinity. To solve this, we can use substitution to simplify the integral. For example, let u = ln(x), which implies that du/dx = 1/x, and thus dx = du. Substituting these into the integral, it becomes an integral with respect to u, which may be easier to evaluate. Once we find the antiderivative, we can then calculate the limit as x approaches infinity, and subtract the value of the antiderivative at the lower limit, which is 1 in this case.