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17 Uneigentliche Integrale

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Zusammenfassung

Aufgabe 1 (17.A, Teil von Aufg. 1) Man berechne die folgenden uneigentlichen Integrale:
$$\begin{array}{*{35}{l}} \int\limits_{0}^{\infty }{\frac{dt}{1+{{t}^{2}}};}\ \ \ \int\limits_{0}^{\infty }{\frac{dt}{1+{{t}^{3}}};}\ \ \ \int\limits_{0}^{\infty }{\frac{dt}{1+{{t}^{4}}};}\ \ \ \int\limits_{0}^{\infty }{\frac{{{t}^{2}}dt}{1+{{t}^{4}}};}\ \ \ \int\limits_{0}^{\infty }{\frac{dt}{\sqrt{1-t}};}\ \ \ \int\limits_{0}^{\infty }{\frac{t\;dt}{\sqrt{1-{{t}^{2}}}};}\ \ \ \int\limits_{0}^{\pi /2}{\sqrt{\text{tan}\;t\;}dt;} \\ \int\limits_{0}^{\pi /2}{\frac{dt}{\sqrt{\text{tan}\;t}};}\ \ \ \int\limits_{-\infty }^{\infty }{{{e}^{-|t|}}dt;}\ \ \ \int\limits_{0}^{1}{\text{ln}\;t\;dt;}\ \ \ \int\limits_{0}^{\infty }{\frac{{{e}^{2t}}dt}{{{({{e}^{2t}}+1)}^{2}}};}\ \ \ \int\limits_{0}^{\infty }{{{e}^{-at}}\sin\; bt\;dt,}\ a\in \mathbb{R}_{+}^{\times },b\in \mathbb{R} \\ \end{array}.$$

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität-BochumBochumDeutschland

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