Optimal. Leaf size=17 \[ 2 \sqrt{\sqrt{x^2+1}+1} \]
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Rubi [A] time = 0.111079, antiderivative size = 17, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0125079, size = 17, normalized size = 1. \[ 2 \sqrt{\sqrt{x^2+1}+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 14, normalized size = 0.8 \begin{align*} 2\,\sqrt{\sqrt{{x}^{2}+1}+1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.939651, size = 18, normalized size = 1.06 \begin{align*} 2 \, \sqrt{\sqrt{x^{2} + 1} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.479772, size = 36, normalized size = 2.12 \begin{align*} 2 \, \sqrt{\sqrt{x^{2} + 1} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.346681, size = 14, normalized size = 0.82 \begin{align*} 2 \sqrt{\sqrt{x^{2} + 1} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06909, size = 18, normalized size = 1.06 \begin{align*} 2 \, \sqrt{\sqrt{x^{2} + 1} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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