Optimal. Leaf size=18 \[ \frac {\sqrt {x-1} \sqrt {x+1}}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {95} \[ \frac {\sqrt {x-1} \sqrt {x+1}}{x} \]
Antiderivative was successfully verified.
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Rule 95
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {-1+x} x^2 \sqrt {1+x}} \, dx &=\frac {\sqrt {-1+x} \sqrt {1+x}}{x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \[ \frac {\sqrt {x-1} \sqrt {x+1}}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 17, normalized size = 0.94 \[ \frac {\sqrt {x + 1} \sqrt {x - 1} + x}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 21, normalized size = 1.17 \[ \frac {8}{{\left (\sqrt {x + 1} - \sqrt {x - 1}\right )}^{4} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.83 \[ \frac {\sqrt {x -1}\, \sqrt {x +1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 11, normalized size = 0.61 \[ \frac {\sqrt {x^{2} - 1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.17, size = 14, normalized size = 0.78 \[ \frac {\sqrt {x-1}\,\sqrt {x+1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 8.23, size = 58, normalized size = 3.22 \[ - \frac {{G_{6, 6}^{5, 3}\left (\begin {matrix} \frac {5}{4}, \frac {7}{4}, 1 & \frac {3}{2}, \frac {3}{2}, 2 \\1, \frac {5}{4}, \frac {3}{2}, \frac {7}{4}, 2 & 0 \end {matrix} \middle | {\frac {1}{x^{2}}} \right )}}{4 \pi ^{\frac {3}{2}}} - \frac {i {G_{6, 6}^{2, 6}\left (\begin {matrix} \frac {1}{2}, \frac {3}{4}, 1, \frac {5}{4}, \frac {3}{2}, 1 & \\\frac {3}{4}, \frac {5}{4} & \frac {1}{2}, 1, 1, 0 \end {matrix} \middle | {\frac {e^{2 i \pi }}{x^{2}}} \right )}}{4 \pi ^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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