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Lösung 2.2:4d

Aus Online Mathematik Brückenkurs 2

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The integral can be simplified by a so-called polynomial division. We add and take away 1 in the numerator and can thus eliminate the x2-term from the numerator

x2x2+1=x2+1x2+1−1=x2+1x2+1−1x2+1=1−1x2+1.

Thus, we have

x2x2+1dx=1−1x2+1dx=x−arctanx+C. 
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.2:4d“