Optimal. Leaf size=18 \[ \frac {4 \left (x^4-x\right )^{3/4}}{9 x^3} \]
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Rubi [A] time = 0.02, antiderivative size = 18, 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 = {2014} \begin {gather*} \frac {4 \left (x^4-x\right )^{3/4}}{9 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt [4]{-x+x^4}} \, dx &=\frac {4 \left (-x+x^4\right )^{3/4}}{9 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} \frac {4 \left (x \left (x^3-1\right )\right )^{3/4}}{9 x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.21, size = 18, normalized size = 1.00 \begin {gather*} \frac {4 \left (-x+x^4\right )^{3/4}}{9 x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 14, normalized size = 0.78 \begin {gather*} \frac {4 \, {\left (x^{4} - x\right )}^{\frac {3}{4}}}{9 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.47, size = 11, normalized size = 0.61 \begin {gather*} -\frac {4}{9} \, {\left (-\frac {1}{x^{3}} + 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 15, normalized size = 0.83
method | result | size |
trager | \(\frac {4 \left (x^{4}-x \right )^{\frac {3}{4}}}{9 x^{3}}\) | \(15\) |
risch | \(\frac {\frac {4 x^{3}}{9}-\frac {4}{9}}{x^{2} \left (x \left (x^{3}-1\right )\right )^{\frac {1}{4}}}\) | \(20\) |
gosper | \(\frac {4 \left (-1+x \right ) \left (x^{2}+x +1\right )}{9 x^{2} \left (x^{4}-x \right )^{\frac {1}{4}}}\) | \(24\) |
meijerg | \(-\frac {4 \left (-\mathrm {signum}\left (x^{3}-1\right )\right )^{\frac {1}{4}} \left (-x^{3}+1\right )^{\frac {3}{4}}}{9 \mathrm {signum}\left (x^{3}-1\right )^{\frac {1}{4}} x^{\frac {9}{4}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 25, normalized size = 1.39 \begin {gather*} \frac {4 \, {\left (x^{4} - x\right )}}{9 \, {\left (x^{2} + x + 1\right )}^{\frac {1}{4}} {\left (x - 1\right )}^{\frac {1}{4}} x^{\frac {13}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 14, normalized size = 0.78 \begin {gather*} \frac {4\,{\left (x^4-x\right )}^{3/4}}{9\,x^3} \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}{x^{3} \sqrt [4]{x \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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