Integral of 1/x^2 from 1 to inf in 0 recursions (correct value is 1):
0.9999999999999999

Integral of exp(-x^2) from -inf to +inf in 82 recursions (correct value is sqrt(pi) = 1.77245):
1.772690516678527

Integral of 1/(1-x^3) from -inf to 0 in 40 recursions (correct value is 2*pi/3^(3/2)=1.2091996):
1.209201497168205