Alright, these have been giving me heck all day. I have two short ones left. It's been a long day full of beating up on these monstrous ogres of problems ( Something like a 6x5 matrix for one of them ) and I'm glad to say these should be awesomely simple.
First, The integral of 1/(x(x^4+1) dx. My book has a hint: "Multiply by x^3/x^3" on this problem. I broke it out into A/X + (B*X+C)/(x^4+1) = 1/(x(x^4+1)). Then I eliminated fractions. It's pretty easy to see A=1.
Then I was promptly lost in the woods.
Second one that looks a bit more intimidating is the integral of 1/(x^(3/2) - x^(1/2)).
I started by letting U=x^(1/2) and DU=1/2(x^(1/2)) I ran through this one to the end, and ended up with LN(|U-1|/|u|)+C but that denominator should have been |u+1|.
Thanks for the help! I really appreciate what you guys do here and I am linking this site to friends.