Optimal. Leaf size=16 \[ \frac {x^2}{2 \sqrt {x^4+1}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {x^2}{2 \sqrt {x^4+1}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.84, size = 25, normalized size = 1.56 \[ \frac {x^{4} + \sqrt {x^{4} + 1} x^{2} + 1}{2 \, {\left (x^{4} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 12, normalized size = 0.75 \[ \frac {x^{2}}{2 \, \sqrt {x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {x^{2}}{2 \sqrt {x^{4}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 12, normalized size = 0.75 \[ \frac {x^{2}}{2 \, \sqrt {x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.05, size = 12, normalized size = 0.75 \[ \frac {x^2}{2\,\sqrt {x^4+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.66, size = 12, normalized size = 0.75 \[ \frac {x^{2}}{2 \sqrt {x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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