Optimal. Leaf size=22 \[ -\frac {4 \left (-x+x^4\right )^{3/4}}{3 \left (-1+x^3\right )} \]
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Rubi [A]
time = 0.03, antiderivative size = 16, normalized size of antiderivative = 0.73, number of steps
used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {2081, 270}
\begin {gather*} -\frac {4 x}{3 \sqrt [4]{x^4-x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rule 2081
Rubi steps
\begin {align*} \int \frac {1}{\left (-1+x^3\right ) \sqrt [4]{-x+x^4}} \, dx &=\frac {\left (\sqrt [4]{x} \sqrt [4]{-1+x^3}\right ) \int \frac {1}{\sqrt [4]{x} \left (-1+x^3\right )^{5/4}} \, dx}{\sqrt [4]{-x+x^4}}\\ &=-\frac {4 x}{3 \sqrt [4]{-x+x^4}}\\ \end {align*}
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Mathematica [A]
time = 10.01, size = 16, normalized size = 0.73 \begin {gather*} -\frac {4 x}{3 \sqrt [4]{x \left (-1+x^3\right )}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.43, size = 13, normalized size = 0.59
method | result | size |
gosper | \(-\frac {4 x}{3 \left (x^{4}-x \right )^{\frac {1}{4}}}\) | \(13\) |
risch | \(-\frac {4 x}{3 \left (x \left (x^{3}-1\right )\right )^{\frac {1}{4}}}\) | \(13\) |
trager | \(-\frac {4 \left (x^{4}-x \right )^{\frac {3}{4}}}{3 \left (x^{3}-1\right )}\) | \(19\) |
meijerg | \(-\frac {4 \left (-\mathrm {signum}\left (x^{3}-1\right )\right )^{\frac {1}{4}} x^{\frac {3}{4}}}{3 \mathrm {signum}\left (x^{3}-1\right )^{\frac {1}{4}} \left (-x^{3}+1\right )^{\frac {1}{4}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 18, normalized size = 0.82 \begin {gather*} -\frac {4 \, {\left (x^{4} - x\right )}^{\frac {3}{4}}}{3 \, {\left (x^{3} - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt [4]{x \left (x - 1\right ) \left (x^{2} + x + 1\right )} \left (x - 1\right ) \left (x^{2} + x + 1\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.50 \begin {gather*} \frac {4}{3 \, {\left (-\frac {1}{x^{3}} + 1\right )}^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.15, size = 20, normalized size = 0.91 \begin {gather*} -\frac {4\,{\left (x^4-x\right )}^{3/4}}{3\,\left (x^3-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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