the question was:
integral of squareroot(x^2-1) over x^2 dx
I substituted x for secx(t), and now I have tan^2(t)/sec(t) dt. I have no idea what to do from here, please help!
EDIT: Now I figured out it can be simplified to the integral of sin^2t/cost dt , or (1-cos(2t))/2cost dt. Still can't figure it out or know which one to continue with...
Oh, also tried to do another problem,
integral of x^3 times squareroot(9+4x^2)dx
I think I'm supposed to substitute 3tan(t) in for x, but then I have the integral of 27tan^3(t) times 3 the squareroot of (1+4tan^2(t)) dt
and with the 4 in there I can't change it to sec^2(t), so what do I do?
Any help with either would be much appreciated, thank you!!
Doing some rearrangement:
The first part is:
but I tried integration by parts and all sorts of substitutions but still couldn't get that second part.
However using a calculator I got the answer for the second part and worked back, but this process would not be obvious unless you knew the answer:
Hence the answer is:
as for the second part, put and you'll get a very easy integral to solve.