Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

Lösung 2.3:2c

Aus Online Mathematik Brückenkurs 2

Wechseln zu: Navigation, Suche

If we use the definition of tanx and write the integral as

tanxdx=sinxcosxdx 

we see that the numerator sinx is the derivative of the denominator (apart from the minus sign). Hence, the substitution u=cosx will work,

sinxcosxdx=udu=cosx=(cosx)dx=−sinxdx=−udu=−lnu+C=−lncosx+C.


Note: −lncosx+C is only a primitive function in intervals in which cosx=0.

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