#2810 Incorrect definite integral, singularity on interval of integration

[RCV]

Maxima takes integral

factor(integrate(log(1+cos(x)),x,0,2*%pi));

correctly:

-2%pi(log(4)-log(2))

But for almost the same integral:

factor(integrate(log(1+sin(x)),x,0,2*%pi));

it gives:

-%pi(2log(2)-3i %pi)

Obviuously, the answer can not be complex number.

Maxima 5.34.0 using Lisp SBCL 1.2.2

[Aleksas]

Function log(sin(x)+1) has singularity at x=3*%pi/2.
Integral 'integrate(log(sin(x)+1),x,0,2*%pi) is equal.

(%i1) 'integrate(log(sin(x)+1),x,0,3*%pi/2)+
'integrate(log(sin(x)+1),x,3*%pi/2,2*%pi)$

(%i2) ev(%, nouns),expand;
(%o2) -2*%pi*log(2)

best
Aleksas D

[Robert Dodier]

I just tried these examples, both in the original report and in the comment dated 2014-09-15, and I get the same result in each case.

The bug appears to be that Maxima is not looking for singularities on the interval of integration.