\[ \newcommand{\csch}{\mathop{\rm csch}\nolimits} \newcommand{\sech}{\mathop{\rm sech}\nolimits} \newcommand{\sgn}{\mathop{\rm sgn}\nolimits} \]
\[\int\exp x\;dx=\exp x+c\] \[\int\log|x|\;dx=x\log|x|-x+c\] \[\int\sin x\;dx=-\cos x+c\] \[\int\cos x\;dx=\sin x+c\] \[\int\tan x\;dx=-\log|\cos x|+c\] \[\int\cot x\;dx=\log|\sin x|+c\] \[\int\sec x\;dx=\tanh^{-1}\sin x+c\] \[\int\csc x\;dx=-\tanh^{-1}\cos x+c\] \[\int\sin^{-1}x\;dx=x\sin^{-1}x+\sqrt{1-x^2}+c\] \[\int\cos^{-1}x\;dx=x\cos^{-1}x-\sqrt{1-x^2}+c\] \[\int\tan^{-1}x\;dx=x\tan^{-1}x-{\scriptsize\frac{1}{2}}\log(1+x^2)+c\] \[\int\cot^{-1}x\;dx=x\cot^{-1}x+{\scriptsize\frac{1}{2}}\log(1+x^2)+c\] \[\int\sec^{-1}x\;dx=x\sec^{-1}x-\cosh^{-1}|x|+c\] \[\int\csc^{-1}x\;dx=x\csc^{-1}x+\cosh^{-1}|x|+c\] \[\int\sinh x\;dx=\cosh x+c\] \[\int\cosh x\;dx=\sinh x+c\] \[\int\tanh x\;dx=\log \cosh x+c\] \[\int\coth x\;dx=\log|\sinh x|+c\] \[\int\sech x\;dx=\tan^{-1}\sinh x+c\] \[\int\csch x\;dx=-\tanh^{-1}\sech x+c\] \[\int\sinh^{-1}x\;dx=x\sinh^{-1}x-\sqrt{x^2+1}+c\] \[\int\cosh^{-1}|x|\;dx=x\cosh^{-1}|x|-\sgn x\sqrt{x^2-1}+c\] \[\int\tanh^{-1}x\;dx=x\tanh^{-1}x+{\scriptsize\frac{1}{2}}\log(1-x^2)+c\] \[\int\coth^{-1}x\;dx=x\coth^{-1}x+{\scriptsize\frac{1}{2}}\log(x^2-1)+c\] \[\int\sech^{-1}|x|\;dx=x\sech^{-1}|x|+\sin^{-1}x+c\] \[\int\csch^{-1}x\;dx=x\csch^{-1}x+\sinh^{-1}|x|+c\]