Optimal. Leaf size=17 \[ 2 \sqrt {\sqrt {x^2+1}+1} \]
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Rubi [A] time = 0.11, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6686} \[ 2 \sqrt {\sqrt {x^2+1}+1} \]
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {1+x^2} \sqrt {1+\sqrt {1+x^2}}} \, dx &=2 \sqrt {1+\sqrt {1+x^2}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 17, normalized size = 1.00 \[ 2 \sqrt {\sqrt {x^2+1}+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 13, normalized size = 0.76 \[ 2 \, \sqrt {\sqrt {x^{2} + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 13, normalized size = 0.76 \[ 2 \, \sqrt {\sqrt {x^{2} + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.82 \[ 2 \sqrt {\sqrt {x^{2}+1}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 13, normalized size = 0.76 \[ 2 \, \sqrt {\sqrt {x^{2} + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 13, normalized size = 0.76 \[ 2\,\sqrt {\sqrt {x^2+1}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 14, normalized size = 0.82 \[ 2 \sqrt {\sqrt {x^{2} + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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