Chapter 7.8, Problem 43ES

In each part, try to evaluate the integral exactly with a CAS. If your result is not a simple numerical answer, then use the CAS to find a numerical approximation of the integral.

$\begin{array}{l}\left(\text{a}\right){\displaystyle {\int }_{-\infty }^{+\infty }\frac{1}{x^8+x+1}}dx\\ \left(\text{b}\right){\displaystyle {\int }_0^{+\infty }\frac{1}{\sqrt{1+x^3}}dx}\\ \left(\text{c}\right){\displaystyle {\int }_1^{+\infty }\frac{\ln x}{e^x}}dx\\ \left(\text{d}\right){\displaystyle {\int }_1^{+\infty }\frac{\sin x}{x^2}}dx\end{array}$