1. The problem statement, all variables and given/known data The problem is: integrate: (1/(4x2+4x+5)2)dx 2. Relevant equations 3. The attempt at a solution 4x2+4x+5=(2x+1)2+4 gives: ∫dx/((2x+1)2+4)2 use regular substitution: u=2x+1 du=2dx dx=1/2du gives: 1/2∫du/(u2+4)2) trigonometric substitution: u=tan(z) du=1/(cos(z))2dz gives: 1/2∫dz/((sin2(z)/cos2(z)) +4)2 I have tried most trigonometric tricks I can think off to make that last integral into something that I know how to integrate, but it has usually just gotten much worse, and certainly not better. I think it will be helpful to show my different attempts beyond this point.