It seems sympy can not integrate sqrt(sin(x)).
I did the following:
import sympy as sm
from sympy.abc import x,y,z
tointegrate=sm.sqrt(sm.sin(y))
sm.integrate(tointegrate)
output is : Integral(sqrt(sin(y)), y)
After a simple change of variable the integral is doable:
def ytoz(z):
return(sm.asin(z))
def dydz(z):
return(sm.diff(ytoz(z),z))
subdict={y:cvytoz(z)}
sm.integrate(dydz(z)*tointegrate.subs(subdict))
output is : z**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,),
z**2*exp_polar(2*I*pi))/(2*gamma(7/4))
best,
Pallab
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