Optimal. Leaf size=18 \[ \frac {1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
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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 = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {74} \[ \frac {1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin {align*} \int \sqrt {-1+x} x \sqrt {1+x} \, dx &=\frac {1}{3} (-1+x)^{3/2} (1+x)^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 17, normalized size = 0.94 \[ \frac {1}{3} \, {\left (x^{2} - 1\right )} \sqrt {x + 1} \sqrt {x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.32, size = 39, normalized size = 2.17 \[ \frac {1}{6} \, {\left ({\left (2 \, x - 5\right )} {\left (x + 1\right )} + 9\right )} \sqrt {x + 1} \sqrt {x - 1} + \frac {1}{2} \, \sqrt {x + 1} \sqrt {x - 1} {\left (x - 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.72 \[ \frac {\left (x -1\right )^{\frac {3}{2}} \left (x +1\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 9, normalized size = 0.50 \[ \frac {1}{3} \, {\left (x^{2} - 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 17, normalized size = 0.94 \[ \frac {\left (x^2-1\right )\,\sqrt {x-1}\,\sqrt {x+1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x \sqrt {x - 1} \sqrt {x + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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