∫x^3dx/√(1+4x^2)=(1/64)∫d(4x^2)^2/√(1+4x^2)
4x^2=t
=(1/64)∫dt^2/√(1+t)
=(1/32)∫tdt/√(1+t)
=(1/32)∫√(1+t)dt-(1/32)∫dt/√(1+t)
=(1/48)√(1+t)^3-(1/16)√(1+t)+C
=(1/48)√(1+4x^2)^3 - (1/16)√(1+4x^2)+C