Optimal. Leaf size=15 \[ -\frac {1}{2} \sqrt {16-x^4} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {261} \[ -\frac {1}{2} \sqrt {16-x^4} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^3}{\sqrt {16-x^4}} \, dx &=-\frac {1}{2} \sqrt {16-x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {1}{2} \sqrt {16-x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 11, normalized size = 0.73 \[ -\frac {1}{2} \, \sqrt {-x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 11, normalized size = 0.73 \[ -\frac {1}{2} \, \sqrt {-x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 23, normalized size = 1.53 \[ \frac {\left (x -2\right ) \left (x +2\right ) \left (x^{2}+4\right )}{2 \sqrt {-x^{4}+16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 11, normalized size = 0.73 \[ -\frac {1}{2} \, \sqrt {-x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.23, size = 11, normalized size = 0.73 \[ -\frac {\sqrt {16-x^4}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 10, normalized size = 0.67 \[ - \frac {\sqrt {16 - x^{4}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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