Fails to Solve Definite Integral

[programizer]

integrate(u**2*sqrt(1-u**2),(u,0,1))

This doesn't return a proper result in SymPy. It talks about a u>1 case, which we don't have, gives complicated expressions and doesn't plug in the limits.

Despite being SymPy syntax this exact same line works fine in WolframAlpha:
https://www.wolframalpha.com/input/?i=integrate%28u**2*sqrt%281-u**2%29%2C%28u%2C0%2C1%29%29

[ayushbisht2001]

@programizer , you can try integrate(u**2*sqrt(1-u**2),(u,0,1)).evalf() to get the result.

[hyadav2k]

It breaks the integrand in Piecewise equations as:

Piecewise((_Dummy_23**5*I/(4*sqrt(_Dummy_23**2 - 1)) - 3*_Dummy_23**3*I/(8*sqrt(_Dummy_23**2 - 1)) + _Dummy_23*I/(8*sqrt(_Dummy_23**2 - 1)) - I*acosh(_Dummy_23)/8, _Dummy_23**2 > 1), (-_Dummy_23**5/(4*sqrt(1 - _Dummy_23**2)) + 3*_Dummy_23**3/(8*sqrt(1 - _Dummy_23**2)) - _Dummy_23/(8*sqrt(1 - _Dummy_23**2)) + asin(_Dummy_23)/8, True))

This occurs at:

sympy/sympy/integrals/integrals.py

Line 1069 in 9e8f62e

h = meijerint_indefinite(g, x)

which is called in doit at:

sympy/sympy/integrals/integrals.py

Lines 593 to 594 in 9e8f62e

	antideriv = self._eval_integral(
	function, xab[0], **eval_kwargs)

[programizer]

@ayushbisht2001 Thanks. Based on your comment, this hack would have done what I wanted:
nsimplify(integrate(u**2*sqrt(1-u**2),(u,0,1)).evalf(),[pi,E])
(which gives pi/16)
Still, I think fixing this issue would be an improvement for sympy.

[techiepriyansh]

Surprisingly, taking the u**2 inside the sqrt gives the desired result.

>>> integrate(sqrt(u**4-u**6),(u,0,1))
pi/16