The integral

$6$

x

$(1+$ x$)$

$$dx$0$

is improper for two reasons: The interval $[0,$ $)$ 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.

$6$

x

$(1+$ x$)$

$$dx$0$

$=$

$1$

$6$

x

$(1+$ x$)$

$$dx$0$

$+$

$6$

x

$(1+$ x$)$

$$dx$1$