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\QTR{small}{Matematick\U{e1} anal\U{fd}za I online - Met\U{f3}dy integr\U{e1}lneho po\U{10d}tu - \U{160}peci\U{e1}lne integra\U{10d}n\U{e9} met\U{f3}dy\dotfill \thepage }}
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\begin{document}
\author{A. U. Thor}
\title{Lab Report}
\date{The Date }
\maketitle
\begin{abstract}
A Laboratory report created with Scientific Notebook
\end{abstract}
\section{Met\'{o}dy integr\'{a}lneho po\v{c}tu}
\subsection{\v{S}peci\'{a}lne integra\v{c}n\'{e} met\'{o}dy}
\subsubsection{\label{1}Trigonometrick\'{e} substit\'{u}cie pre v\'{y}razy $%
\protect\sqrt{a^{2}-x^{2}},\,\protect\sqrt{a^{2}+x^{2}},\,\protect\sqrt{%
x^{2}-a^{2}},\,\protect\sqrt{\pm a^{2}\pm b^{2}x^{2}}$}
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
V\'{y}raz & Substit\'{u}cia & Zjednodu\v{s}enie \\ \hline
$\sqrt{a^{2}-x^{2}}$ & $x=a\sin t,\,t\in \left\langle -\frac{\pi }{2},\frac{%
\pi }{2}\right\rangle $ & $\sqrt{a^{2}-a^{2}\sin ^{2}t}=a\cos t$ \\ \hline
$\sqrt{a^{2}+x^{2}}$ & $x=a\limfunc{tg}t,\,t\in \left( -\frac{\pi }{2},\frac{%
\pi }{2}\right) $ & $\sqrt{a^{2}+a^{2}\limfunc{tg}{}^{2}t}=\frac{a}{\cos t}$
\\ \hline
$\sqrt{x^{2}-a^{2}}$ & $x=\frac{a}{\cos t},0\leq t\leq \pi ,\,t\neq \frac{%
\pi }{2}\,$ &
\begin{tabular}{c}
$\sqrt{\frac{a^{2}}{\cos ^{2}t}-a^{2}}=a\limfunc{tg}t,\,0\leq t<\frac{\pi }{2%
}$ \\
$\sqrt{\frac{a^{2}}{\cos ^{2}t}-a^{2}}=-a\limfunc{tg}t,\,\frac{\pi }{2}%