can you solve the integral in the attachment ?? ..
i integrated it by parts 4 times !! ..
I started it with :
u = arctan x ---> du = [1/(1+x^2)] dx
dv = arcsin dx ---> v = by parts it self
i didnt try to get u = (arctan x)(arcsin x)
You would not be able to use U-Subst as using either arcsin x, or arctan x as dV would cause never ending loop because the integral of arcsin or arctan contains arcsin or arctan in the answer. If this had limits I'd tell you to approximate using one of the approximation rule.