[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{x\;dx}{\sqrt[3]{1+x}}[/math]
• [math]\int \frac{x\;dx}{1+\sqrt[3]x}[/math]
• [math]\int \frac{\sin x\;dx}{1+\sin x}[/math]
• [math]\int \frac{3\;dx}{\sin x + \cos x}[/math]
• [math]\int \frac{dt}{2+\cos t}[/math]
• [math]\int \frac{(1+x)^{\frac15}}{(1+x)^{\frac13}}\;dx[/math]
• [math]\int \frac{dy}{\sqrt y + \sqrt[3]y}[/math]
• [math]\int \frac{\tan x \; dx}{1+\tan^2x}[/math]
• [math]\int \frac{x^2}{\sqrt{5x+3}}\;dx[/math]
• [math]\int \frac{dx}{(1+\sqrt x)^5}[/math]
• [math]\int \frac{e^x\;dx}{\sqrt{1+e^x}}[/math]
• [math]\int \frac{dx}{\sqrt{1+e^x}}[/math].