1. The problem statement, all variables and given/known data I have to integrate using u-substitution (probably). Ex. 1 Integrate (sin^4x)/(cos^6x)dx 2. Integrate (2x)/(sqrt(e^(2x^2)-1))dx 3. Integrate (cos^-1x)/(sqrt(1-x^2))dx Thank you ! 2. Relevant equations I do not want the solutions. I just need to be pointed in the right direction (i.e. I need you to help me start off) **It should be noted that I am doing a calculus II course (Integral Calc, mostly) in university, so it's not very advanced integrals that I'm doing. Basically what I know is how to integrate using u-substitution, and I know the integrals for the inverse trig functions (which is supposed to be relevant to examples 2 & 3), and that's what information I have to work with. **It should also be noted that I may just not know how to rewrite the equations before I can integrate them. I have trouble 'seeing through' the equation and automatically knowing which way I'm going to solve it. 3. The attempt at a solution Ex. 1 I tried rewriting the equation using trig identities, e.g. (1-cos(x))/(1-sin(x))^3. I found this got me nowhere. I also tried rewriting it is (sin^4)(x)/(cos^4)(x)*1/cos(x), and rewriting and rewriting until I ended up with a big mess, so that got me nowhere as well. 2. Here's my dilemma: -if I substitute e^2x for u, I end up needing an e to the power in my numerator, so that doesn't work out. -if I instead substitute 2x^2 for u, I end up with the e to the power of u on the bottom and I don't have a formula for that. 3. I have no ideas on this one.