Optimal. Leaf size=13 \[ \frac {\sqrt {x^4+1}}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ \frac {\sqrt {x^4+1}}{2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^3}{\sqrt {1+x^4}} \, dx &=\frac {\sqrt {1+x^4}}{2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {\sqrt {x^4+1}}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 9, normalized size = 0.69 \[ \frac {1}{2} \, \sqrt {x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 9, normalized size = 0.69 \[ \frac {1}{2} \, \sqrt {x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \[ \frac {\sqrt {x^{4}+1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 9, normalized size = 0.69 \[ \frac {1}{2} \, \sqrt {x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.04, size = 9, normalized size = 0.69 \[ \frac {\sqrt {x^4+1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 8, normalized size = 0.62 \[ \frac {\sqrt {x^{4} + 1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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