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Is this a known bug with integral()

asked 2015-10-17 10:01:02 -0500

Julien gravatar image

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=eJzz...

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=eJzz...

while we get that when replacing 1 by 2: https://sagecell.sagemath.org/?z=eJzz...

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answered 2015-10-17 12:46:02 -0500

FrédéricC gravatar image

Maxima is apparently not able to do that, but sympy can:

sage: integral(cos(x)/(1+sin(x)),(x,-pi/6,pi/6),algorithm='sympy')
log(3)
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Asked: 2015-10-17 10:01:02 -0500

Seen: 178 times

Last updated: Oct 17 '15