[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]

Evaluate the following definite integrals.

• [math]\int_0^1 (3x^2 + 4x + 1) \; dx[/math]
• [math]\int_{-1}^1 (2t^3 + t) \; dt[/math]
• [math]\int_{-1}^1 (x^3 + 1)^{17}x^2 \; dx[/math]
• [math]\int_{-1}^2 \frac{s+1}{\sqrt{s^2 + 2s + 3}} \; ds[/math]
• [math]\int_1^3 \left(x^2 + \frac1x\right)^3 \left(2x - \frac1{x^2} \right) \; dx[/math]
• [math]\int_0^2 \frac1{(x+1)^2} \; dx[/math]
• [math]\int_{-2}^2 \sqrt{4-x^2} \, x \; dx[/math]
• [math]\int_{-2}^2 (2|x| + 1) \; dx[/math]
• [math]\int_0^1 t(t^3 + 3t^2 - 1)^3 (t + 2) \; dt[/math]
• [math]\int_1^2 \frac{x^4 + 2x^3 - 2}{x^2} \; dx[/math].