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I executed the following,

def integral_R(f,a,b):
    from sage.symbolic.integration.integral import definite_integral
    return (definite_integral(f,x,a,b)).simplify_full()
alpha = 1/sqrt(3)
H = 2*arcsin(x/(sqrt(1-x^2))) 
integral_R(H,0,alpha).n()

and got

1.16869906991626

The same integral in Wolfram Alpha provides

0.38330

By inspection I know that Wolfram is right. What's wrong with sage math in the specific example?

I executed the following,

def integral_R(f,a,b):
    from sage.symbolic.integration.integral import definite_integral
    return (definite_integral(f,x,a,b)).simplify_full()
alpha = 1/sqrt(3)
H = 2*arcsin(x/(sqrt(1-x^2))) 
integral_R(H,0,alpha).n()

and got

1.16869906991626

The same integral in Wolfram Alpha provides

0.38330

By inspection I know that Wolfram is right. What's wrong with sage math in the specific example?

I executed the following,

def integral_R(f,a,b):
    from sage.symbolic.integration.integral import definite_integral
    return (definite_integral(f,x,a,b)).simplify_full()
alpha = 1/sqrt(3)
H = 2*arcsin(x/(sqrt(1-x^2))) 
integral_R(H,0,alpha).n()

and got

1.16869906991626

The same integral in Wolfram Alpha provides

0.38330

By inspection I know that Wolfram is right. What's wrong with sage math in the specific example?

I executed the following,

def integral_R(f,a,b):
    from sage.symbolic.integration.integral import definite_integral
    return (definite_integral(f,x,a,b)).simplify_full()
alpha = 1/sqrt(3)
H = 2*arcsin(x/(sqrt(1-x^2))) 
integral_R(H,0,alpha).n()

and got

1.16869906991626

The same integral in Wolfram Alpha provides

0.38330

By inspection I know that Wolfram is right. What's wrong with sage math in the specific example?