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I've tried to compute the following integral wth integral() in a SageMathCloud worksheet: $\displaystyle \int_{-\pi/6}^{\pi/6}\frac{\cos x}{1+\sin x}dx$.

The output was an error message (saying the integral is divergent), just like the one I got in SageMathCell (see link): https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw1C7OzAOyNHUUKnQUdAsy9c10FECkJi9XcUZ-uYanJgDa5Q_i&lang=sage

So I tried with integrate() and with numerical_integral() as well. I was never able to obtain the value of this integral, which turns out to be $\ln(3)$ after an obvious substitution.

Is this a bug?

Note that replacing 1 by 1.1 yields this: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw1DPULs7MA7I1dRQqdBR0CzL1zXQUQKQmL1dxRn65hqcmAPXGEEE=&lang=sage

while we get that when replacing 1 by 2: https://sagecell.sagemath.org/?z=eJzzVLBVyMwrSU0vSszRSM4v1qjQ1Ncw0i7OzAOyNHUUKnQUdAsy9c10FECkJi9XcUZ-uYanJgDbCA_j&lang=sage