Help complete exercise with integrals

Hi there
I was given the following task, which I need to solve as soon as possible.

Find the value of the constant C for which the integral
∫0∞(xx2+1−C3x+1)dx
converges. Evaluate the integral for this value of C.

On the website plainmath.net/33554/find-the-value-of-the-constant-c-for-which-the-integral-int-infty0-lef I received an answer, but did not quite understand the calculations, I offered this service. I will be very grateful for your help and detailed explanation.

 

I advise you to first integrate the integral on the right and then everything will become clearer.