On Tue, 17 Jan 2023 at 10:39, 'Tom van Woudenberg' via sympy
<sympy@googlegroups.com> wrote:
>
> Hi there,
>
> I'm trying to symbolically evaluate an integral with SymPy:
>
> import sympy as sp
> q, L, H = sp.symbols('q L H',positive=True,real=True)
> x = sp.symbols('x',real=True)
> Lexact = sp.integrate(sp.sqrt((L*q/(2*H) - q*x/H)**2 + 1),(x,0,L))
> print(Lexact)
>
> The result is:
> Integral(sqrt(4*H**2 + L**2*q**2 - 4*L*q**2*x + 4*q**2*x**2), (x, 0, L))/(2*H)
> So the integral isn't evaluated.
Which version of sympy are you using?
I just tried sympy 1.11.1 and also latest master and the integral does evaluate:
In [1]: import sympy as sp
...: q, L, H = sp.symbols('q L H',positive=True,real=True)
...: x = sp.symbols('x',real=True)
...: Lexact = sp.integrate(sp.sqrt((L*q/(2*H) - q*x/H)**2 + 1),(x,0,L))
...: print(Lexact)
-(-H**2*asinh(L*q/(2*H))/q - L*sqrt(4*H**2 + L**2*q**2)/4)/(2*H) +
(H**2*asinh(L*q/(2*H))/q + L*sqrt(4*H**2 + L**2*q**2)/4)/(2*H)
> It should evalute to
> (4*H**2*arcsinh(q*L/(2*H))+q*L*sqrt(L882*q**2+4*H**2))/(4*q*H)
I'm guessing that L882 is supposed to be L**2 because then it matches
what I get from sympy:
In [3]: print(Lexact.factor())
(4*H**2*asinh(L*q/(2*H)) + L*q*sqrt(4*H**2 + L**2*q**2))/(4*H*q)
--
Oscar
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