Processing Math: Done
Lösung 2.3:1a
Aus Online Mathematik Brückenkurs 2
The formula for partial integration reads
f
x
g
x
dx=F
x
g
x
−
F
x
g
x
dx
where
x
x
x
x
If we are to use partial integration, the integrand has to be divided up into two factors, a factor
x
x
x
g
x
x
g
x
In the integral
2xe−xdx
it can seem appropriate to choose
x
=e−x
x
=2x
x
=2
x
=−e−x
2xe−xdx=2x
−e−x
−
2
−e−x
dx=−2xe−x+2
e−xdx
It remains only to integrate
−e−x
+C=−2xe−x−2e−x+C=−2
x+1
e−x+C