2.201 The integrals $\int R\left(x\text{,}{\left(\frac{\text{\alpha}x+\text{\beta}}{\text{\gamma}x+\text{\delta}}\right)}^{r},{\left(\frac{\text{\alpha}x+\text{\beta}}{\text{\gamma}x+\text{\delta}}\right)}^{s}\text{,}\dots \right)}\text{d}x\text{,$ where $r,s,\dots $ are rational numbers, can be reduced to integrals of rational functions by means of the substitution

$\frac{\text{\alpha}x+\text{\beta}}{\text{\gamma}x+\text{\delta}}={t}^{m},$

FI II 57

where m is the common denominator of the fractions $r\text{,}s\text{,\u2026}$

2.202 Integrals of the form ${\int}^{\text{}}{x}^{m}{(a+b{x}^{n})}^{p}dx$,^{∗} are rational ...

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