[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Among the following integrals identify those that can be evaluated using the techniques in this section. Evaluate them.

• [math]\int \left(x + \frac1x\right) \; dx[/math]
• [math]\int \left(\sqrt{x} + \frac1{\sqrt{x}}\right) \; dx[/math]
• [math]\int y^2(y^3 + 7)^4 \; dy[/math]
• [math]\int y(y^3 + 7)^4 \; dy[/math]
• [math]\int t\sqrt{t^3 - 1} \; dt[/math]
• [math]\int \frac{x+1}{x-1} \; dx[/math]
• [math]\int (3x^2 - 1)(x + 2) \; dx[/math]
• [math]\int (s+1)(s^2 + 2s - 3)^4 \; ds[/math]
• [math]\int \frac{x^2 - 1}{x + 1} \; dx[/math]
• [math]\int \frac{y + 2}{y^2 + 1} \; dy[/math]
• [math]\int \frac{x - 1}{(x + 1)^3} \; dx[/math].