Hi guys. I have two problems that revolve around trig sub and just want to make sure that I got these right.
1) integral of cos (sqrt(x))^2 / (sqrt(x))
I got (sqrt) x + (1/2)sin(2(sqrt(x)) + C.
2) integral of (x^3) / sqrt (x^2 + 4), with limits from 0 to 2.
For this one, I'm a little confused on how to set this one up. Which trig identity do I use that will successfully satisfy this beginning?
Sorry, hate to bring this topic back up, but I would like to know the answer to #2.
It seems like after I do a substitiution of x = 2 tan (theta), my limits of integration go to 0 to -4.37. Then, after some algebra, and another substitution (this time of u = sec (theta), my limits of integration is now 1 to -2.98.