![[Graphics:Images/IntegralsIndentedContourMod_gr_60.gif]](../Images/IntegralsIndentedContourMod_gr_60.gif){kind=small}
by
using complex analysis. Example
8.20. Evaluate by
using complex analysis.
![[Graphics:Images/IntegralsIndentedContourMod_gr_61.gif]](../Images/IntegralsIndentedContourMod_gr_61.gif)
Explore Solution 8.20.
Enter the function and ![[Graphics:../Images/IntegralsIndentedContourMod_gr_68.gif]](../Images/IntegralsIndentedContourMod_gr_68.gif){kind=small}
and
locate the singularities.
![[Graphics:../Images/IntegralsIndentedContourMod_gr_69.gif]](../Images/IntegralsIndentedContourMod_gr_69.gif)
![[Graphics:../Images/IntegralsIndentedContourMod_gr_70.gif]](../Images/IntegralsIndentedContourMod_gr_70.gif)
Which poles lie in the upper half plane ? Which poles lie on the real axis ?
![[Graphics:../Images/IntegralsIndentedContourMod_gr_71.gif]](../Images/IntegralsIndentedContourMod_gr_71.gif)
![[Graphics:../Images/IntegralsIndentedContourMod_gr_72.gif]](../Images/IntegralsIndentedContourMod_gr_72.gif)
![[Graphics:../Images/IntegralsIndentedContourMod_gr_73.gif]](../Images/IntegralsIndentedContourMod_gr_73.gif)
Compute the residues at ![[Graphics:../Images/IntegralsIndentedContourMod_gr_74.gif]](../Images/IntegralsIndentedContourMod_gr_74.gif){kind=small}
, and
use the residue calculus to compute the value of the integral.
![[Graphics:../Images/IntegralsIndentedContourMod_gr_75.gif]](../Images/IntegralsIndentedContourMod_gr_75.gif)
![[Graphics:../Images/IntegralsIndentedContourMod_gr_76.gif]](../Images/IntegralsIndentedContourMod_gr_76.gif)
![[Graphics:../Images/IntegralsIndentedContourMod_gr_77.gif]](../Images/IntegralsIndentedContourMod_gr_77.gif)
![[Graphics:../Images/IntegralsIndentedContourMod_gr_78.gif]](../Images/IntegralsIndentedContourMod_gr_78.gif)