How do I solve this integral Calculus 2 question?

Question

Here's the link to the question: https://ibb.co/b1k3dTH The integral is improper for two reasons: the interval [0,∞][0,∞] is infinite and the integrand has an infinite discontinuity at x=0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows:

Answer 1

Here is a hint to get you started.

Let u = x^1/2

x = u²

dx = 2udu

After u-substitution:

-6 ∫ (2u/[u(u²+1)] du; with the u canceling out:

-12 ∫ du/(u²+1)

So the antiderivative is:

-12 arctan(√x)

Now you want to do something like:

lim_t->0⁺ [-12arctan(√x)|_t¹ + (similar for 1 to infinity).