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Lösung 2.3:1a

Aus Online Mathematik Brückenkurs 2

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The formula for partial integration reads


fxgxdx=FxgxFxgxdx ,

where Fx  is a primitive function of fx  and gx  is a derivative of gx .

If we are to use partial integration, the integrand has to be divided up into two factors, a factor fx  which we integrate and a factor gx  which we differentiate. It is only when the product Fxgx  becomes simpler than fxgx  that there is any point in partially integrating.

In the integral


2xexdx ,

it can seem appropriate to choose fx=ex  and gx=2x , because then gx=2  and we have only Fx=ex  left,


2xexdx=2xex2exdx=2xex+2exdx 


It remains only to integrate ex and we are finished:


=2xex+2ex+C=2xex2ex+C=2x+1ex+C