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Lösung 2.2:3c

Aus Online Mathematik Brückenkurs 2

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It is simpler to investigate the integral if we write it as


lnxx1dx ,

The derivative of lnx is x1, so if we choose u=lnx, the integral can be expressed as


uudx 


Thus, it seems that u=lnx is a useful substitution,


lnxx1dx=u=lnxdu=lnxdx=x1dx=udu=21u2+C=21lnx2+C

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.2:3c“