Optimal. Leaf size=15 \[ \sqrt{x-1} \sqrt{x+1} \]
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Rubi [A] time = 0.0023761, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {74} \[ \sqrt{x-1} \sqrt{x+1} \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{-1+x} \sqrt{1+x}} \, dx &=\sqrt{-1+x} \sqrt{1+x}\\ \end{align*}
Mathematica [A] time = 0.0033634, size = 15, normalized size = 1. \[ \sqrt{x-1} \sqrt{x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.8 \begin{align*} \sqrt{-1+x}\sqrt{1+x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13206, size = 9, normalized size = 0.6 \begin{align*} \sqrt{x^{2} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58008, size = 34, normalized size = 2.27 \begin{align*} \sqrt{x + 1} \sqrt{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] time = 2.94514, size = 76, normalized size = 5.07 \begin{align*} \frac{{G_{6, 6}^{6, 2}\left (\begin{matrix} - \frac{1}{4}, \frac{1}{4} & 0, 0, \frac{1}{2}, 1 \\- \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 0 & \end{matrix} \middle |{\frac{1}{x^{2}}} \right )}}{4 \pi ^{\frac{3}{2}}} + \frac{i{G_{6, 6}^{2, 6}\left (\begin{matrix} -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 1 & \\- \frac{3}{4}, - \frac{1}{4} & -1, - \frac{1}{2}, - \frac{1}{2}, 0 \end{matrix} \middle |{\frac{e^{2 i \pi }}{x^{2}}} \right )}}{4 \pi ^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.79278, size = 15, normalized size = 1. \begin{align*} \sqrt{x + 1} \sqrt{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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