The integral [infinity] 8 x (1 + x) dx 0 is improper for two reasons: The interval [0, [infinity]) 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. [infinity] 8 x (1 + x) dx 0 = 1 8 x (1 + x) dx 0 + [infinity] 8 x (1 + x) dx 1