Cauchy integral whose integrand has pole as singularity

Question

integration[1/(z-2)(z^3 - 1)^5] on |z|=1 Which of the following is true?

1. 2×pi×i/(2^15 - 1)
2. -2×pi×i/(2^15 - 1)
3. 2×pi×i/7^5
4. -2×pi×i/7^5

I've tried hard but I failed, since my confusion is about

• is "1" a point of singularity, since it lies on the circle

• the process is too long and too calculative to me so that I can't find any solutions.

I'm sure I'm mistaking somewhere, it can't so long.But where I'm overlooking I can't find.

Please help me to find this, please in the answer section rather in comments. Thanks in advance.

Answer 1

If 1/(z-2)(z^3 - 1)^5 means $\frac1{(z-2)(z^3-1)^5}$, then the question doesn't make sense, since, as you noticed, that function is not defined at all the points of the unit circle.