Optimal. Leaf size=26 \[ -2 \sqrt{1-x} \, _2F_1\left (\frac{1}{2},-n;\frac{3}{2};1-x\right ) \]
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Rubi [A] time = 0.0042752, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {65} \[ -2 \sqrt{1-x} \, _2F_1\left (\frac{1}{2},-n;\frac{3}{2};1-x\right ) \]
Antiderivative was successfully verified.
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Rule 65
Rubi steps
\begin{align*} \int \frac{x^n}{\sqrt{1-x}} \, dx &=-2 \sqrt{1-x} \, _2F_1\left (\frac{1}{2},-n;\frac{3}{2};1-x\right )\\ \end{align*}
Mathematica [A] time = 0.0045975, size = 26, normalized size = 1. \[ -2 \sqrt{1-x} \, _2F_1\left (\frac{1}{2},-n;\frac{3}{2};1-x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.03, size = 23, normalized size = 0.9 \begin{align*}{\frac{{x}^{1+n}}{1+n}{\mbox{$_2$F$_1$}({\frac{1}{2}},1+n;\,2+n;\,x)}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{n}}{\sqrt{-x + 1}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{x^{n} \sqrt{-x + 1}}{x - 1}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] time = 0.929018, size = 26, normalized size = 1. \begin{align*} - 2 i \sqrt{x - 1}{{}_{2}F_{1}\left (\begin{matrix} \frac{1}{2}, - n \\ \frac{3}{2} \end{matrix}\middle |{\left (x - 1\right ) e^{i \pi }} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{n}}{\sqrt{-x + 1}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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