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Question: Strange integral

Question:Strange integral

Ku 10 Maple
October 07 2016
1

Hi!

 

Suppose, we need to compute this integral:

int(sqrt(exp(2*I*t)-1),t) from t=0 to t=Pi

If we write this as definite integral, we get right answer: 2*sqrt(2)-(1/2)*ln(17+12*sqrt(2))

But in case of indefinite integral (computing antiderivative) one gets I*arctan(sqrt(exp(2*I*t)-1))-I*sqrt(exp(2*I*t)-1). Substitution t=Pi and t=0 both lead to 0, so we can't transform antiderivative to definite integral. What is the reason?
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