Integral problems from my college calculus course
Here are some of the problems that my college integral calculus class professor gave as homework and I think became part of the final grade. Back then, there weren't any apps that could do the symbolic math (or computational algebra) to solve these – we had to use pencil and paper. See how many you can do, or just use one of the many apps that can solve these indefinite integrals.
Note: The integrals below were rendered using the MathJax Javascript script from a site called Hostmath, except for the last one, which uses MathML. MathJax can take LaTeX strings and outputs the symbols in a way that browsers can display. Many moons ago I managed to translate the original written symbols into LaTeX for displaying. MathML is a markup language that has special tages for displaying math symbols. \[\int \dfrac {\cos x}{\sqrt {1+\sin x}}dx\] \[\int \dfrac {\sin ^{-1}x}{\sqrt {1-x^{2}}}dx\] \[\int \dfrac {\tan x}{\cos ^{2}x}dx\] \[\int \dfrac {1}{1-\sin x}dx\] \[\int e^{\ln \sqrt {x}}dx\] \[\int \dfrac {\cos \sqrt {x}}{\sqrt {x}}dx\] \[\int \dfrac {1}{\sqrt {x^{2}+2x+2}}dx\] \[\int \dfrac {3x-7}{\left( x-1\right) \left( x-2\right) \left( x-3\right) }dx\] \[\int x^{2}e^{x}dx\] \[\int \sqrt {x^{2}+1}dx\] \[\int \dfrac {e^{x}}{1+e^{2x}}dx\] \[\int \dfrac {1}{e^{x}+e^{-x}}dx\] \[\int \dfrac {1}{1+\sqrt {x}}dx\] \[\int \dfrac {1}{\sqrt {1+\sqrt {x}}}dx\] \[\int x^{\frac {2}{3}}\left( x^{\frac {5}{3}}+1\right) ^{\frac {2}{3}}dx\] \[\int \dfrac {\cot x}{\ln \left( \sin x\right) }dx\] \[\int \dfrac {1}{\sqrt {e^{x}+1}}dx\]
Note: The integrals below were rendered using the MathJax Javascript script from a site called Hostmath, except for the last one, which uses MathML. MathJax can take LaTeX strings and outputs the symbols in a way that browsers can display. Many moons ago I managed to translate the original written symbols into LaTeX for displaying. MathML is a markup language that has special tages for displaying math symbols. \[\int \dfrac {\cos x}{\sqrt {1+\sin x}}dx\] \[\int \dfrac {\sin ^{-1}x}{\sqrt {1-x^{2}}}dx\] \[\int \dfrac {\tan x}{\cos ^{2}x}dx\] \[\int \dfrac {1}{1-\sin x}dx\] \[\int e^{\ln \sqrt {x}}dx\] \[\int \dfrac {\cos \sqrt {x}}{\sqrt {x}}dx\] \[\int \dfrac {1}{\sqrt {x^{2}+2x+2}}dx\] \[\int \dfrac {3x-7}{\left( x-1\right) \left( x-2\right) \left( x-3\right) }dx\] \[\int x^{2}e^{x}dx\] \[\int \sqrt {x^{2}+1}dx\] \[\int \dfrac {e^{x}}{1+e^{2x}}dx\] \[\int \dfrac {1}{e^{x}+e^{-x}}dx\] \[\int \dfrac {1}{1+\sqrt {x}}dx\] \[\int \dfrac {1}{\sqrt {1+\sqrt {x}}}dx\] \[\int x^{\frac {2}{3}}\left( x^{\frac {5}{3}}+1\right) ^{\frac {2}{3}}dx\] \[\int \dfrac {\cot x}{\ln \left( \sin x\right) }dx\] \[\int \dfrac {1}{\sqrt {e^{x}+1}}dx\]
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