Nevermind, my answer only works for 1 over your problem
Hey forum how would I go about in order to compute this indefinite integral,
I can't seem to eliminate all -variables using . I know I can simply compute it by expanding the integrand but I want to do it using substitution in particular.
I'll rephrase that. You can't perform a u substitution, because doing so requires the substituted function's derivative being a factor of your integrand. If you let u = x^2 + 1, then you need to have a factor of 2x in your integrand as well. You don't, so you can't use u substitution.
You could possibly use a trigonometric or hyperbolic substitution, but doing so is time consuming and pointless, when a perfect square is quick and easy to expand and the resulting integrand easy to integrate using the power rule.