How Do You Solve Integrals with Complex Bounds?

[Dassinia]

Hello,
I'm studying for the exam and in the previous one there's a question like:

Homework Statement

Find the value of
1/(2*i*pi) ∫ exp(s*u)/s² ds for s from 1-i∞ to 1+i∞

What is the way to solve integrals with complex bounds ? Is it to make a variable change to get real bounds, like here for example s=1+iz and then use residus to solve the integral ?

Thanks

 

[Dick]

Hello,
I'm studying for the exam and in the previous one there's a question like:

Homework Statement

Find the value of
1/(2*i*pi) ∫ exp(s*u)/s² ds for s from 1-i∞ to 1+i∞

What is the way to solve integrals with complex bounds ? Is it to make a variable change to get real bounds, like here for example s=1+iz and then use residus to solve the integral ?

Thanks

That sounds like a good first step.