Lösung 2.3:1b

Aus Online Mathematik Brückenkurs 2

we look at the formula for partial integration,

fxgxdx=Fxgx−Fxgxdx 

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+1−cosx−1−cosxdx=−x+1cosx+cosxdx=−x+1cosx+sinx+C