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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? |
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