Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 3952 by omar.ant...@gmail.com: Sympy cannot compute the integral
of sqrt(tan(x))
http://code.google.com/p/sympy/issues/detail?id=3952
Sympy gives up on integrate(sqrt(tan(x)),x) and returns it unevaluated.
Mathematica answers (in Sympy notation):
-2*atan(1-sqrt(2)*sqrt(tan(x))) + 2*atan(sqrt(2)*sqrt(tan(x))+1) +
log(tan(x)-sqrt(2)*sqrt(tan(x))+1) -
log(tan(x)+sqrt(2)*sqrt(tan(x))+1))/(2*sqrt(2))
Trying to check Mathematica's answer in Sympy, by doing
simplify(diff(that_thing,x) - sqrt(tan(x)))
does not give 0, but plotting the difference shows it is zero from 0 to
pi/2.
Maxima gives the answer (again, in Sympy notation):
2*(-log(tan(x)+sqrt(2)*sqrt(tan(x))+1)/2**(S(5)/2)
+log(tan(x)-sqrt(2)*sqrt(tan(x))+1)/2**(S(5)/2)
+atan((2*sqrt(tan(x))+sqrt(2))/sqrt(2))/2**(S(3)/2)
+atan((2*sqrt(tan(x))-sqrt(2))/sqrt(2))/2**(S(3)/2))
and computing in Sympy
simplify(diff(that_thing,x) - sqrt(tan(x)))
does produce 0.
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