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Description
Archive of removed doctests testing the abs_integrate Maxima package (removed with #12731).
sage: y = function('y')
sage: integrate(1/sqrt(abs(y(x))), y(x)) # ok
integrate(diff(y(x), x)/sqrt(abs(y(x))), x)
sage: integrate(sgn(x) - sgn(1-x), x) # ok
abs(x - 1) + abs(x)
sage: integrate(1 / (1 + abs(x-5)), x, -5, 6) # ok
log(11) + log(2)
sage: integrate(1/(1 + abs(x)), x) # ok
log(abs(x*sgn(x) + 1))/sgn(x)
sage: integrate(cos(x + abs(x)), x) # ok
sin(x*sgn(x) + x)/(sgn(x) + 1)
sage: integrate(sqrt(x + sqrt(x)), x).canonicalize_radical() # ok
1/12*(8*x + 2*sqrt(x) - 3)*sqrt(x + sqrt(x)) - 1/8*log(abs(2*sqrt(x + sqrt(x)) - 2*sqrt(x) - 1))
sage: integrate(abs(x^2 - 1), x, -2, 2) # ok
4
sage: f = sqrt(x + 1/x^2)
sage: integral(f, x) # to be checked
2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(sqrt(x^3 + 1) - 1)
sage: f1(x) = e^(-abs(x))
sage: f = Piecewise([[(-infinity, infinity), f1]])
sage: f.integral(definite=True) # ok
2
sage: f.integral()
Piecewise defined function with 1 parts, [[(-Infinity, +Infinity), x |--> -1/2*((sgn(x) - 1)*e^(2*x) - 2*e^x*sgn(x) + sgn(x) + 1)*e^(-x) - 1]]
Also, these have their own tickets:
integrate(x * sgn(x^2 - 1/4), x, -1, 0)(Integrating the sgn() function can produce incorrect results #11590)integral(log(abs(2*sin(u))), u, 0, pi/3)(Strange integration error/hang with log(abs(sin(x))) #17468)integrate(abs(cos(x)),x,0,pi)(Get integral of abs(sin(x)) and abs(cos(x)) right #17511)
CC: @kcrisman
Component: calculus
Keywords: integration
Issue created by migration from https://trac.sagemath.org/ticket/17910