\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{enumerate}
\begin{document}
\flushleft\underline{Homework 1 --- MATH 1586 Spring 2018} \\
Recall that for $n\neq -1$, 
$$\displaystyle\int x^n \mathrm{d}x = \dfrac{x^{n+1}}{n+1}+C.$$
Recall that 
$$\displaystyle\int \dfrac{1}{x} \mathrm{d}x=\ln(x)+C.$$
Recall that 
$$\displaystyle\int e^x \mathrm{d}x = e^x+C.$$
Recall that 
$$\displaystyle\int f(x) + g(x) \mathrm{d}x=\displaystyle\int f(x) \mathrm{d}x + \displaystyle\int g(x) \mathrm{d}x.$$
Finally recall that if $F$ represents any antiderivative of $f$, then 
$$\displaystyle\int_a^b f(x) \mathrm{d}x = F(b)-F(a).$$
\noindent Compute the following definite and indefinite integrals.
\begin{enumerate}[1.]
\item $\displaystyle\int x^{17} \mathrm{d}x$ 
\item $\displaystyle\int x^3+3x^2+\dfrac{x}{9}+1 \mathrm{d}x$ 
\item $\displaystyle\int \dfrac{e^x}{10} + x^2 + \dfrac{9}{x} + 1 \mathrm{d}x$ 
\item $\displaystyle\int_{0}^1 4x^4+3x^2+1 \mathrm{d}x$ 
\item $\displaystyle\int_{-3}^4 -3e^x + \dfrac{1}{x} + x^5 - 2x^2 \mathrm{d}x$
\item Is it accurate to say that $\displaystyle\int e^{7x} \mathrm{d}x=e^{7x}+C$? How can you use differentiation to check if this is an accurate statement?
\end{enumerate}
\end{document}