Optimal. Leaf size=17 \[ \text {Int}\left (\sqrt {x-x^2} F(x),x\right ) \]
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Rubi [A] time = 0.10, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \sqrt {1-x} \sqrt {x} F(x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \sqrt {1-x} \sqrt {x} F(x) \, dx &=\int \sqrt {x-x^2} F(x) \, dx\\ \end {align*}
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Mathematica [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \sqrt {1-x} \sqrt {x} F(x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {x} \sqrt {-x + 1} F\relax (x), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {x} \sqrt {-x + 1} F\relax (x)\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 0, normalized size = 0.00 \[ \int \sqrt {-x +1}\, \sqrt {x}\, F \relax (x )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {x} \sqrt {-x + 1} F\relax (x)\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \sqrt {x}\,F\relax (x)\,\sqrt {1-x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {x} \sqrt {1 - x} F{\relax (x )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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