I've tried to integrate cos(x)/(1+sin(x)) on [-pi/6 , pi/6] with the "integral()" command in a Sage Worksheet in SageMathCloud and on SageMathCell as well. Each time I was told that the integral is divergent... As far as I know, this function is continuous on this interval, and the integral is equal to ln(3).
Here is what I get on SageMathCell: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw1C7OzAOyNHUUKnQUdAsy9c10FECkJi9XcUZ-uYanJgDa5Q_i&lang=sage With "integrate()", now: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSixJ1UjOL9ao0NTXMNQuzswDsjR1FCp0FHQLMvXNdBRApCYvV3FGfrmGpyYA8jMQTw==&lang=sage And now with numerical_integral(): https://sagecell.sagemath.org/?z=eJzzVLBVyCvNTS3KTE7Mic_MK0lNL0rM0UjOL9ao0NTXMNQuzswDsjR1FCp0FHQLMvXNdBRApCYvV3FGfrmGpyYA0DkUAQ==&lang=sage Interestingly, here is what we get - with cos(x)/(2+sin(x)) instead: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw0i7OzAOyNHUUKnQUdAsy9c10FECkJi9XcUZ-uYanJgDbCA_j&lang=sage - with cos(x)/(1.1+sin(x)) instead: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw1DPULs7MA7I1dRQqdBR0CzL1zXQUQKQmL1dxRn65hqcmAPXGEEE=&lang=sage - with cos(x)/(1.01+sin(x)) instead: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw1DMw1C7OzANyNHUUKnQUdAsy9c10FECkJi9XcUZ-uYanJgADnhBx&lang=sage -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
