Optimal. Leaf size=15 \[ -\frac {1}{2} \sqrt {1-x^4} \]
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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 = {267}
\begin {gather*} -\frac {1}{2} \sqrt {1-x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x^3}{\sqrt {1-x^4}} \, dx &=-\frac {1}{2} \sqrt {1-x^4}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{2} \sqrt {1-x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 12, normalized size = 0.80
method | result | size |
derivativedivides | \(-\frac {\sqrt {-x^{4}+1}}{2}\) | \(12\) |
default | \(-\frac {\sqrt {-x^{4}+1}}{2}\) | \(12\) |
trager | \(-\frac {\sqrt {-x^{4}+1}}{2}\) | \(12\) |
risch | \(\frac {x^{4}-1}{2 \sqrt {-x^{4}+1}}\) | \(17\) |
elliptic | \(\frac {\left (x^{2}-1\right ) \left (x^{2}+1\right )}{2 \sqrt {-x^{4}+1}}\) | \(22\) |
gosper | \(\frac {\left (x -1\right ) \left (x +1\right ) \left (x^{2}+1\right )}{2 \sqrt {-x^{4}+1}}\) | \(23\) |
meijerg | \(-\frac {-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {-x^{4}+1}}{4 \sqrt {\pi }}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 11, normalized size = 0.73 \begin {gather*} -\frac {1}{2} \, \sqrt {-x^{4} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 11, normalized size = 0.73 \begin {gather*} -\frac {1}{2} \, \sqrt {-x^{4} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} - \frac {\sqrt {1 - x^{4}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.04, size = 11, normalized size = 0.73 \begin {gather*} -\frac {1}{2} \, \sqrt {-x^{4} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.22, size = 11, normalized size = 0.73 \begin {gather*} -\frac {\sqrt {1-x^4}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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