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Lösung 2.2:3c

Aus Online Mathematik Brückenkurs 2

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Version vom 10:23, 11. Mär. 2009

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

lnxx1dx 

The derivative of lnx is 1x, so if we choose u=lnx, the integral can be expressed as

uudx. 

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

lnxx1dx=udu=lnx=(lnx)dx=(1x)dx=udu=21u2+C=21(lnx)2+C.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.2:3c“