\(\displaystyle{\int_{{-\infty}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}\)

For the given integration the lower limit is infinity also, the integrand of the limit goes to infinity in the range of given integration at point x = -2.

Therefore, the given integral is improper.

Now to set up the integral:

\(\displaystyle{\int_{{-\infty}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}=\lim_{{{t}\rightarrow-\infty}}{\int_{{{t}}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}\)

For the given integration the lower limit is infinity also, the integrand of the limit goes to infinity in the range of given integration at point x = -2.

Therefore, the given integral is improper.

Now to set up the integral:

\(\displaystyle{\int_{{-\infty}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}=\lim_{{{t}\rightarrow-\infty}}{\int_{{{t}}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}\)