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Lösung 2.3:1b

Aus Online Mathematik Brückenkurs 2

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we look at the formula for partial integration,


fxgxdx=FxgxFxgxdx 


we see that if we choose fx=sin x   and gx=x+1 , then the factor gx  will be differentiated to a constant on the right-hand side of the integral. Naturally, this presupposes that we can find a primitive function for fx  (which we can) and that we can then integrate it. Let's try!


x+1sinxdx=x+1cosx1cosxdx=x+1cosx+cosxdx=x+1cosx+sinx+C