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Lösung 2.2:3f

Aus Online Mathematik Brückenkurs 2

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Version vom 10:24, 11. Mär. 2009

Let's rewrite the integral somewhat,

2sinx12x.

Here, we see that the factor on the right, 12x , is the derivative of the expression x , which appears in the factor on the left, 2sinx . With the substitution u=x , the integrand can therefore be written as

2sinuu

and the integral becomes

xsinxdx=udu=x=(x)dx=12xdx=2sinudu=−2cosu+C=−2cosx+C.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.2:3f“