The integral 9 To x (1 + x) is improper for two reasons: The interval [0, o) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows. 9 So x (1 + x) dx 9 dx = = S x ( + x) dx + 1^ x ( + x) dx