#LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 620
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass article
\begin_preamble
\usepackage{siunitx}
\usepackage{pgfplots}
\usepackage{listings}
\usepackage{multicol}
\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}}
\DeclareMathOperator{\ctg}{ctg}
\end_preamble
\use_default_options true
\begin_modules
enumitem
theorems-ams
\end_modules
\maintain_unincluded_children no
\language slovene
\language_package default
\inputencoding auto-legacy
\fontencoding auto
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_roman_osf false
\font_sans_osf false
\font_typewriter_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures true
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\float_placement class
\float_alignment class
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry true
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification false
\use_refstyle 1
\use_formatted_ref 0
\use_minted 0
\use_lineno 0
\index Index
\shortcut idx
\color #008000
\end_index
\leftmargin 1cm
\topmargin 1cm
\rightmargin 1cm
\bottommargin 2cm
\headheight 1cm
\headsep 1cm
\footskip 1cm
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style german
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tablestyle default
\tracking_changes false
\output_changes false
\change_bars false
\postpone_fragile_content false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\docbook_table_output 0
\docbook_mathml_prefix 1
\end_header

\begin_body

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
newcommand
\backslash
euler{e}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
setlength{
\backslash
columnseprule}{0.2pt}
\backslash
begin{multicols}{2}
\end_layout

\end_inset


\begin_inset Formula $\log_{a}1=0$
\end_inset

,
 
\begin_inset Formula $\log_{a}a=1$
\end_inset

,
 
\begin_inset Formula $\log_{a}a^{x}=x$
\end_inset

,
 
\begin_inset Formula $a^{\log_{a}x}=x$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\binom{n}{k}\coloneqq\frac{n!}{k!\left(n-k\right)!}$
\end_inset

,
 
\begin_inset Formula $\log_{a}x^{n}=n\log_{a}x$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $D=b^{2}-4ac$
\end_inset

,
 
\begin_inset Formula $x_{1,2}=\frac{-b\pm\sqrt{D}}{2a}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right)$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\arctan a\pm\arctan b=\frac{a\pm b}{1\mp ab}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\sin\left(x\pm y\right)=\sin x\cdot\cos y\pm\sin y\cdot\cos x$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\cos\left(x\pm y\right)=\cos x\cdot\cos y\mp\sin y\cdot\sin x$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\tan\left(x\pm y\right)=\frac{\tan x\pm\tan y}{1\text{\ensuremath{\mp\tan}x\ensuremath{\cdot\tan y}}}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\euler^{1/k}\coloneqq\lim_{n\to\infty}\left(1+\frac{1}{nk}\right)^{n}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\lim_{x\to a}\left(\alpha f\left(x\right)\right)=\alpha\lim_{x\to a}f\left(x\right)$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sin$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cos$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\tan$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $30^{\circ}=\frac{\pi}{6}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{\sqrt{3}}{2}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{\sqrt{3}}{3}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $45^{\circ}=\frac{\pi}{4}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{\sqrt{2}}{2}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{\sqrt{2}}{2}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $60^{\circ}=\frac{\pi}{3}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{\sqrt{3}}{2}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sqrt{3}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Krožnica:
 
\begin_inset Formula $\left(x-p\right)^{2}+\left(y-q\right)^{2}=r^{2}$
\end_inset


\end_layout

\begin_layout Standard
Elipsa:
 
\begin_inset Formula $\frac{\left(x-p\right)^{2}}{a^{2}}+\frac{\left(y-q\right)^{2}}{b^{2}}=1$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Izraz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Odvod
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Izraz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Odvod
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{f}{g}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{f'g-fg'}{g^{2}}$
\end_inset

,
 
\begin_inset Formula $g\not=0$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $f\left(g\right)$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $f'\left(g\right)g'$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\tan x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cos^{-2}x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cot x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $-sin^{-2}x$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $a^{x}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $a^{x}\text{\ensuremath{\ln a}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $x^{x}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $x^{x}\left(1+\ln x\right)$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\log_{a}x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{x\ln a}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $f^{-1}\left(a\right)$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{f'\left(f^{-1}\left(a\right)\right)}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\arcsin x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\left(1-x^{2}\right)^{-\frac{1}{2}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\arccos x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $-\left(1-x^{2}\right)^{-\frac{1}{2}}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\arctan x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{1+x^{2}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\text{arccot\,}x$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $-\frac{1}{1+x^{2}}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $x^{n}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $nx^{n-1}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $f''\left(I\right)>0\Leftrightarrow f$
\end_inset

 konveksna na 
\begin_inset Formula $I$
\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $f''\left(I\right)<0\Leftrightarrow f$
\end_inset

 konkavna na 
\begin_inset Formula $I$
\end_inset


\begin_inset Formula 
\[
ab>0\wedge a<b\Leftrightarrow a^{-1}>b^{-1},\quad ab<0\wedge a<b\Leftrightarrow a^{-1}<b^{-1}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\lim_{x\to0}\frac{\sin x}{x}=1\quad\quad\tan\phi=\left|\frac{k_{1}-k_{2}}{1+k_{1}k_{2}}\right|
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\lim_{x\to0}x\ln x=0
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
f\text{ zv.+odv.@ }\left[a,b\right]\Rightarrow\exists\xi\in\left[a,b\right]\ni:f\left(b\right)-f\left(a\right)=f'\left(\xi\right)\left(b-a\right)
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
T_{f,a,n}\left(x\right)=\sum_{k=0}^{n}\frac{f^{\left(k\right)}\left(a\right)}{k!}\left(x-a\right)^{k}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\sinh x=\frac{e^{x}-e^{-x}}{2},\quad\cosh x=\frac{e^{x}+e^{-x}}{2}
\]

\end_inset


\end_layout

\begin_layout Paragraph
Razcep racionalnih
\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\frac{p\left(x\right)}{\left(x-a\right)^{3}}=\frac{A}{x-a}+\frac{B}{\left(x-1\right)^{2}}+\frac{C}{\left(x-1\right)^{3}}
\]

\end_inset


\begin_inset Formula 
\[
\frac{p\left(x\right)}{\left(x-a\right)\left(x-b\right)^{2}}=\frac{A}{x-a}+\frac{B}{x-b}+\frac{C}{\left(x-b\right)^{2}}
\]

\end_inset


\begin_inset Formula 
\[
\frac{p\left(x\right)}{\left(x-a\right)\left(x^{2}-b\right)}=\frac{A}{x-a}+\frac{Bx-C}{x^{2}-b}
\]

\end_inset


\end_layout

\begin_layout Paragraph
Integrali
\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\int\frac{1}{x^{2}+a^{2}}dx=\frac{1}{a}\arctan\frac{x}{a}+C
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{x^{2}-a^{2}}dx=\frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{a^{2}-x^{2}}dx=\frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right|+C
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{ax+b}dx=\frac{1}{a}\ln\left|ax+b\right|+C
\]

\end_inset


\begin_inset Formula 
\[
\int\left(ax+b\right)^{n}dx=\frac{\left(ax+b\right)^{n+1}}{a\left(n+1\right)}+C
\]

\end_inset


\begin_inset Formula 
\[
\int f\left(x\right)g'\left(x\right)dx=f\left(x\right)g\left(x\right)-\int f'\left(x\right)g\left(x\right)dx
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{\sin^{2}\left(x\right)}dx=-\ctg\left(x\right)
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{\cos^{2}\left(x\right)}=\tan\left(x\right)
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{\sqrt{a^{2}+x^{2}}}dx=\ln\left|x+\sqrt{x^{2}+a^{2}}\right|
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{1}{\sqrt{x^{2}-a^{2}}}dx=\ln\left|x+\sqrt{x^{2}-a^{2}}\right|
\]

\end_inset


\begin_inset Formula 
\[
\int\sqrt{a^{2}+x^{2}}dx=\frac{1}{2}\left(x\sqrt{a^{2}+x^{2}}+a^{2}\ln\left(\sqrt{a^{2}+x^{2}}+x\right)\right)
\]

\end_inset


\begin_inset Formula 
\[
\int\sqrt{a^{2}-x^{2}}dx=\frac{1}{2}\left(x\sqrt{a^{2}-x^{2}}+a^{2}\arctan\left(\frac{x}{\sqrt{a^{2}-x^{2}}}\right)\right)
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{A}{x-a}dx=A\ln\left|x-a\right|
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{A}{\left(x-a\right)^{n}}dx=\frac{-A}{n-1}\cdot\frac{1}{\left(x-a\right)^{n-1}}
\]

\end_inset


\begin_inset Formula 
\[
\int\frac{Bx+C}{x^{2}+bx+c}=\frac{B}{2}\ln\left|x^{2}+bx+c\right|+\frac{2C-Bb}{\sqrt{-D}}\arctan\left(\frac{2x+b}{\sqrt{-D}}\right)
\]

\end_inset

 In velja 
\begin_inset Formula $D=b^{2}-4c$
\end_inset

.
\end_layout

\begin_layout Standard
Pri 
\begin_inset Formula $\int\sin\left(x\right)^{p}\cos\left(x\right)^{q}dx$
\end_inset

 lih 
\begin_inset Formula $q$
\end_inset

 substituiramo 
\begin_inset Formula $t=\cos\left(x\right)$
\end_inset

,
 lih 
\begin_inset Formula $p$
\end_inset

 pa 
\begin_inset Formula $t=\sin\left(x\right)$
\end_inset

.
 Pri sodih nižamo stopnje s formulo dvonega kota.
\end_layout

\begin_layout Standard
\begin_inset Note Note
status open

\begin_layout Plain Layout
https://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions
\end_layout

\end_inset


\end_layout

\begin_layout Paragraph
Fiksne meje
\end_layout

\begin_layout Itemize
\begin_inset Formula $f\left(x,t\right)$
\end_inset

 zvezna na 
\begin_inset Formula $\left[a,b\right]\times\left[c,d\right]\Longrightarrow F\left(x\right)=\int_{c}^{d}f\left(x,t\right)dt$
\end_inset

 zvezna na 
\begin_inset Formula $\left[a,b\right]$
\end_inset

.
\end_layout

\begin_layout Itemize
\begin_inset Formula $f\left(x,t\right)$
\end_inset

 zvezna in zv.
 parc.
 odv.
 po 
\begin_inset Formula $x$
\end_inset

 na 
\begin_inset Formula $\left[a,b\right]\times\left[c,d\right]\Longrightarrow F\left(x\right)=\int_{c}^{d}f\left(x,t\right)dt$
\end_inset

 odvedljiva na 
\begin_inset Formula $\left[a,b\right]$
\end_inset

 in 
\begin_inset Formula $F'\left(x\right)=\int_{c}^{d}f_{x}\left(x,t\right)dt$
\end_inset

.
\end_layout

\begin_layout Itemize
\begin_inset Formula $f\left(x,t\right)$
\end_inset

 zvezna na 
\begin_inset Formula $\left[a,b\right]\times\left[c,d\right]\Longrightarrow F\left(x\right)=\int_{c}^{d}f\left(x,t\right)dt$
\end_inset

 integrabilna na 
\begin_inset Formula $\left[a,b\right]$
\end_inset

 in 
\begin_inset Formula $\int_{a}^{b}F\left(x\right)=\int_{a}^{b}\int_{c}^{d}f\left(x,t\right)dtdx=\int_{c}^{d}\int_{a}^{b}f\left(x,t\right)dxdt$
\end_inset

.
\end_layout

\begin_layout Standard

\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
end{multicols}
\end_layout

\end_inset


\end_layout

\end_body
\end_document