\input amstex
\documentstyle{amsppt}
\parindent = 0 pt
\nopagenumbers
\overfullrule=0pt

\document
Určete integrál:

$$\int {x^3 \over \sqrt{a + bx^4}} dx$$

\subheading{Řešení}
Zavedeme substituci:
$$\align x^4&=z \\ 4x^3\/ dx&=dz \\ x^3\/ dx&={dz \over 4}\endalign$$

$$\int {x^3 \over \sqrt{a + bx^4}} dx = 4 \int {dz \over 4 \sqrt{a + bz}}=$$

Substituujeme dále:

$$\align \sqrt{a + bz}&=t \\ a+bz&=t^2 \\ dz&={2t\/dt \over b}\endalign$$

$$=\int {2t\/dt \over 4 b t} = \int{2\/dt \over 4 b} = {2\over 4 b} t = {2 \over 4b}\sqrt{a + bz} = {1 \over 2b}\sqrt{a + bx^4}$$

\enddocument
