Optimal. Leaf size=29 \[ \frac {2 \sqrt {\sqrt {x}-1} \sqrt {\sqrt {x}+1}}{\sqrt {x}} \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {265} \[ \frac {2 \sqrt {\sqrt {x}-1} \sqrt {\sqrt {x}+1}}{\sqrt {x}} \]
Antiderivative was successfully verified.
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Rule 265
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {-1+\sqrt {x}} \sqrt {1+\sqrt {x}} x^{3/2}} \, dx &=\frac {2 \sqrt {-1+\sqrt {x}} \sqrt {1+\sqrt {x}}}{\sqrt {x}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \[ \frac {2 \sqrt {\sqrt {x}-1} \sqrt {\sqrt {x}+1}}{\sqrt {x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 25, normalized size = 0.86 \[ \frac {2 \, {\left (\sqrt {x} \sqrt {\sqrt {x} + 1} \sqrt {\sqrt {x} - 1} + x\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 25, normalized size = 0.86 \[ \frac {16}{{\left (\sqrt {\sqrt {x} + 1} - \sqrt {\sqrt {x} - 1}\right )}^{4} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.69 \[ \frac {2 \sqrt {\sqrt {x}-1}\, \sqrt {\sqrt {x}+1}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.21, size = 10, normalized size = 0.34 \[ \frac {2 \, \sqrt {x - 1}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.56, size = 19, normalized size = 0.66 \[ \frac {2\,\sqrt {\sqrt {x}-1}\,\sqrt {\sqrt {x}+1}}{\sqrt {x}} \]
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 \[ \int \frac {1}{x^{\frac {3}{2}} \sqrt {\sqrt {x} - 1} \sqrt {\sqrt {x} + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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