Optimal. Leaf size=16 \[ \frac{x^2}{2 \sqrt{x^4+1}} \]
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Rubi [A] time = 0.0022335, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {264} \[ \frac{x^2}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x}{\left (1+x^4\right )^{3/2}} \, dx &=\frac{x^2}{2 \sqrt{1+x^4}}\\ \end{align*}
Mathematica [A] time = 0.0021165, size = 16, normalized size = 1. \[ \frac{x^2}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 13, normalized size = 0.8 \begin{align*}{\frac{{x}^{2}}{2}{\frac{1}{\sqrt{{x}^{4}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964204, size = 16, normalized size = 1. \begin{align*} \frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.44875, size = 61, normalized size = 3.81 \begin{align*} \frac{x^{4} + \sqrt{x^{4} + 1} x^{2} + 1}{2 \,{\left (x^{4} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.648047, size = 12, normalized size = 0.75 \begin{align*} \frac{x^{2}}{2 \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21079, size = 16, normalized size = 1. \begin{align*} \frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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