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\newcommand{\R}{\mathbb{R}}
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\begin{document}

\section*{Luettelo integraalifunktioista}

\begin{tabbing}
\hspace{40mm} \= \hspace{40mm} \= \kill
\textbf{funktio} \> \textbf{integraalifunktio} \\[15pt]
$x^\alpha$ \> $\tfrac{1}{\alpha+1}\,x^{\alpha+1} + C$ \> $\alpha \in \R,\ \alpha \neq -1$ \\[7pt]
$e^x$ \> $e^x + C$ \\[7pt]
$\dfrac{1}{x}$ \> $\ln |x| + C$ \\[7pt]
$\cos x$ \> $\sin x + C$ \\[7pt]
$\sin x$ \> $-\cos x + C$ \\[7pt]
$\dfrac{1}{\cos^2 x}$ \> $\tan x + C$ \\[7pt]
$1 + \tan^2 x$ \> $\tan x + C$ \\[7pt]
$\dfrac{1}{\sin^2 x}$ \> $-\cot x + C$ \\[7pt]
$1 + \cot^2 x$ \> $-\cot x + C$ \\[7pt]
$\dfrac{1}{\sqrt{1-x^2}}$ \> $\arcsin x + C$ \> $|x| \le 1$ \\[7pt]
$\dfrac{1}{1+x^2}$ \> $\arctan x + C$ \\[7pt]
$\cosh x$ \> $\sinh x + C$ \\[7pt]
$\sinh x$ \> $\cosh x + C$ \\[7pt]
$\dfrac{1}{\cosh^2 x}$ \> $\tanh x + C$ \\[7pt]
$1 - \tanh^2 x$ \> $\tanh x + C$ \\[7pt]
$\dfrac{1}{\sinh^2 x}$ \> $-\coth x + C$ \\[7pt]
$1 - \coth^2 x$ \> $\coth x + C$ \\[7pt]
$\dfrac{1}{\sqrt{x^2+1}}$ \> $\arsinh x + C$ \\[7pt]
$\dfrac{1}{\sqrt{x^2-1}}$ \> $\arcosh x + C$ \> $x \ge 1$ \\[7pt]
$\dfrac{1}{1-x^2}$ \> $\artanh x + C$ \> $|x| < 1$ \\[7pt]
$\dfrac{1}{1-x^2}$ \> $\arcoth x + C$ \> $|x| > 1$ \\[7pt]
\end{tabbing}

\end{document}
