(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# I'm having trouble finding the integral using u-substitution.

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