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2018-01-28 02:00:46 +0200 received badge  Nice Question (source)
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2018-01-27 18:35:16 +0200 commented answer Difference between integral(csc(x)) and integral(1/sin(x))?

And that also exactly explains the change of sign in my rough working of the second form producing ln(-t). Thanks for the quickly supplied and thorough answer.

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2018-01-27 16:21:06 +0200 commented question Difference between integral(csc(x)) and integral(1/sin(x))?

SageMath version 8.1, Release Date: 2017-12-07

2018-01-27 16:21:06 +0200 asked a question Difference between integral(csc(x)) and integral(1/sin(x))?

integral(csc(x),x) gives -log(cot(x) + csc(x)) as expected. integral(1/sin(x),x) gives -1/2log(cos(x) + 1) + 1/2log(cos(x) - 1). Evaluation of the second log is problematic because cos(x)-1 < 0 for all x except n*2pi. Choosing the sympy or maxima algorithms makes no difference.

Also (and this is less reliable) if I perform a substitution t=tan(x/2) by hand in the first case I get ln(t), again as expected. But in the second ln(-t). That maybe my fault but I can't see what I did wrong.

Is there any fundamental difference between asking that same question in two different ways?