1: This integral does not fit any box. One usually hopes that some substitution would help, but after each root there is a different expression, so substitution is out of question. Another hope is some tricky integration by parts, but there is no opening here. Algebraic tricks remain as the only hope. If you look at the problem closer, you may notice that the expression in the denominator can be written and factored as a difference of squares. In the resulting fraction one can cancel.