Problems for Cauchy Integral Formula

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shirokuma
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Hello everyone!
I am currently stuck at the two type of questions below, because I am not really sure what method should be used to calculate these question...
Could you give me a hint how to do these questions? :(
View attachment 8449View attachment 8450
 
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  • Exam question 5 worth 4 marks: evaluate J equals the contour integral over C(3,2) of e^(3z) divided by z(z-2)(z-4)^2, dz, where C(3,2) is the anticlockwise circle centre 3 radius 2.
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    20.9 KB · Views: 214
  • Typeset exam question: evaluate J = integral over C(2,2) of e^(3z) [1/(2z - 1)^3 + 1/((z + 5)(z - 3))] dz, where C(2,2) is the circle of centre 2 and radius 2, traversed once anti-clockwise, using Cauchy-Goursat or Cauchy Integral Formula.
    43241561_942734292587763_8988574515608944640_n.jpg
    21.7 KB · Views: 212
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Welcome, Shirokuma!

Consider using partial fraction decomposition. You might need to use Cauchy's differentiation formula at some points.