# What's wrong with Лобачевский function?

Hello,

I tried to plot the following function $$Л(\theta) = -\int_0^\theta \log |2 \sin(u)| du$$ (called the Lobatchevski function). So I started with

sage: theta, u = var('theta', 'u')
sage: assume(0 < theta < pi)
sage: assume(theta, 'real')
sage: el(theta) = - integral(log(abs(2*sin(u))), u, 0, theta)


The last command just asks maxima. Maxima starts computing (one CPUS is running 100%) but never stops.

Vincent

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Even that does not work:

sage: integral(log(abs(2*sin(u))), u, 0, pi/3)


This is actually pretty bizarre, and (sadly) yet another error in Maxima's abs_integrate. I'm getting really frustrated with that package about now, even though it adds a lot of awesome integrals. See http://trac.sagemath.org/ticket/17468

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If what you are interested in is computing values of this function, you can use numerical integration instead of symbolic:

sage: el = lambda theta: -numerical_integral(log(abs(2*sin(u))), 0, theta)
sage: plot(el, 0, pi)

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