Vyjádřete uvedené primitivní
funkce na
maximálních
intervalech existence pomocí
elementárních funkcí

 $\int\root 3\of {1-3x}{\,\roman{d}x}\quad 

\int{(1-x)^3\over
x\root 3\of x}{\,\roman{d}x}\quad 
 \int {x^2\over(1-x)^{100}}{\,\roman{d}x}$\quad

 $\int\sqrt{x^6}{\,\roman{d}x}\quad 
 \int{2^{x+1}-5^{x-1}\over10^x}{\,\roman{d}x}
\int{e^{3x}+1\over e^x+1}{\,\roman{d}x}$

 $\int {\operatorname{tg}}^2x{\,\roman{d}x}\quad 
\int{\operatorname{cotg}}^2x{\,\roman{d}x}$\quad

 $\int {{\,\roman{d}x}\over2+3x^2}\quad 
\int {{\,\roman{d}x}\over 1+\cos
x}$\quad

 $\int\vert\cos x\vert{\,\roman{d}x}\quad 
\int\sin^2x{\,\roman{d}x}
\int cos^4x{\,\roman{d}x}$\quad 


$\int{x^2{\,\roman{d}x}\over\cos^2\left(x^3\right)}\quad
 \int {x\over
1+4x^2}{\,\roman{d}x}
\int{x\over1+x^4}{\,\roman{d}x}$\quad 

$\int {{\,\roman{d}x}\over
x\log x\log\log x}\quad 
\int {\operatorname{tg}} x{\,\roman{d}x}\quad 
\int{\operatorname{cotg}}
x{\,\roman{d}x}$

 $\int {{\,\roman{d}x}\over\sin x}
\quad 
\int {{\,\roman{d}x}\over\cos x}
\quad 
\int x^\alpha\log x{\,\roman{d}x}$ \quad 

$\int x^3\log^2x{\,\roman{d}x}
\int e^{\sqrt{x}}{\,\roman{d}x}\quad 
\int\log\left(x+\sqrt{x^2+1}\right){\,\roman{d}x}\quad 
\int{\sin
x\over
e^x}{\,\roman{d}x}$\quad

 $\int{{\,\roman{d}x}\over
\left(x^2+1\right)^2}$ pomocí substituce $x={\operatorname{tg}} t$

 $\int{dx\over\left(x^2-1\right)^{\frac32}}$ pomocí
substituce
$x={1\over\cos t}$

$\int{{\,\roman{d}x}\over\sqrt{(x-\alpha)(\beta-x)}},\,(\alpha<\beta)$
pomocí substituce $x=\alpha\cos^2x+\beta\sin^2x$

 $\int{{\,\roman{d}x}\over x^4+1}$\quad 
\int {x\cdot e^{{\operatorname{arctg}}
x}\over\left(1+x^2\right)^{\frac32}}{\,\roman{d}x}$

 $\int{dx\over
2\sin
x-\cos x+5}\quad 
\int {\sin x\cos x\over 1+\sin^4x}{\,\roman{d}x}$


\subsubsection {} 
Spočtěte primitivní funkce}

 $\int{x^8+x-1\over x^6+1}{\,\roman{d}x}\quad 
 \int{{\,\roman{d}x}\over\left(x^2+3x+4\right)^2}$\quad 

 $\int{{\,\roman{d}x}\over\left(\sin^2x+2\cos^2x\right)^2} \quad
\int{{\,\roman{d}x}\over(2+\cos x)\sin x}$

 $\int{e^{2x}\over 1+e^x}{\,\roman{d}x}
\int{{\,\roman{d}x}\over\sqrt{1+e^x}+\sqrt{1-e^x}}$

\subsubsection {} 
Spočtěte či převeďte na integrál z racionální
funkce}

$\int{{\,\roman{d}x}\over\sqrt{x^2+1}}\quad 
\int{{\,\roman{d}x}\over\left(4+x^2\right)\sqrt{4-x^2}}$ \quad 

$\int{1-\sqrt{x+1}\over 1-\root 3 \of{x+1}}{\,\roman{d}x} \quad 
\int{\sqrt{x+1}-\sqrt{x-1}\over\sqrt{x+1}+\sqrt{x-1}}{\,\roman{d}x}$\quad

$\int{{\,\roman{d}x}\over 1+\sqrt x+\sqrt{x+1}}\quad 
\int{x{\,\roman{d}x}\over
\root 4\of{x^3(5-x)}}$

