Lösung 2.2:3f

Aus Online Mathematik Brückenkurs 2

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.