[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]

Integrate each of the following.

• [math]\int \frac{(3x+1)\;dx}{x^3+2x^2+x}[/math]
• [math]\int \frac{(x^2+1)\;dx}{x^2-3x+2}[/math]
• [math]\int \frac{(x-2)\;dx}{(2x+1)(x^2+1)}[/math]
• [math]\int \frac{x^2-3x-2}{(x-2)^2(x-3)}\;dx[/math]
• [math]\int \frac{dx}{x^2+2x+2}[/math]
• [math]\int \frac{(2x+1)\;dx}{x^2+2x+2}[/math]
• [math]\int \frac{\sec^2x\;dx}{\tan^2x-4\tan x+3}[/math]
• [math]\int \frac{\sec y \tan y \; dy}{2\sec^2y+5\sec y+2}[/math]
• [math]\int \frac{y^2+1}{y^2+y+1}\;dy[/math]
• [math]\int \frac{10+5z-z^2}{(z+4)(z^2+z+1)}\;dz[/math]
• [math]\int \frac{(6x+3)\;dx}{(x-1)(x+2)(x^2+x+1)}[/math]
• [math]\int \frac{(x^3+4)\;dx}{(x+1)(x+2)^2}[/math]
• [math]\int \frac{x^2+2x+5}{(2x-1)(x^2+1)^2}\;dx[/math]
• [math]\int \frac{dx}{(x^2+x+5)^3}[/math].