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Durch elementare und elementare transzendente Funktionen ausdrückbare Integrale

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Part of the Praktische Funktionenlehre book series (FUNKTIONEN, volume 1)

Zusammenfassung

Wie man durch Differentiation leicht bestätigt, ergibt sich
$$\left. \begin{gathered} \int {\frac{{{{(a + bz)}^\lambda }{{\mkern 1mu} ^{}}}}{{{{(c + dz)}^\lambda }^{ + 1}}}{\mkern 1mu} } dz{\mkern 1mu} = {\mkern 1mu} \frac{1}{{\lambda {\mkern 1mu} (bc - ad)}}{\mkern 1mu} {\left( {\frac{{a + bz}}{{c + dz}}} \right)^\lambda }{\mkern 1mu} , \hfill \\ \int {\frac{{{z^\lambda }^{ - 1}{\mkern 1mu} }}{{{{(c \pm z)}^\lambda }^{ + 1}}}{\mkern 1mu} } dz{\mkern 1mu} = {\mkern 1mu} \frac{1}{{\lambda {\mkern 1mu} }}{\mkern 1mu} {\left( {\frac{z}{{1 \pm z}}} \right)^\lambda }{\mkern 1mu} , \hfill \\ \int {\frac{{{{(1 \pm z)}^\lambda }^{ - 1}{\mkern 1mu} }}{{{z^\lambda }^{ + 1}}}{\mkern 1mu} } dz{\mkern 1mu} = {\mkern 1mu} - \frac{1}{{\lambda {\mkern 1mu} }}{\mkern 1mu} {\left( {\frac{{1 \pm z}}{z}} \right)^\lambda }{\mkern 1mu} . \hfill \\ \end{gathered} \right\}$$
(1)

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Copyright information

© Springer-Verlag Berlin Heidelberg 1950

Authors and Affiliations

  1. 1.KarlsruheDeutschland

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