Chapter 7.8, Problem 1ES

In each part, determine whether the integral is improper, and if so, explain why.

$\begin{array}{l}\left(\text{a}\right){\displaystyle {\int }_1^5\frac{dx}{x-3}}\\ \left(\text{b}\right){\displaystyle {\int }_1^5\frac{dx}{x+3}}\\ \text{(c)}{\displaystyle {\int }_0^1\ln xdx}\\ \text{(d)}{\displaystyle {\int }_1^{+\infty }{e}^{-x}dx}\\ \left(\text{e}\right){\displaystyle {\int }_{-\infty }^{+\infty }\frac{dx}{\sqrt[3]{x-1}}}\\ \left(\text{f}\right){\displaystyle {\int }_0^{\pi /4}\tan xdx}\end{array}$