Optimal. Leaf size=18 \[ \frac {4 \left (x^4-x\right )^{5/4}}{15 x^5} \]
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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 )^{5/4}}{15 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{-x+x^4}}{x^5} \, dx &=\frac {4 \left (-x+x^4\right )^{5/4}}{15 x^5}\\ \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 )^{5/4}}{15 x^5} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.18, size = 18, normalized size = 1.00 \begin {gather*} \frac {4 \left (-x+x^4\right )^{5/4}}{15 x^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 19, normalized size = 1.06 \begin {gather*} \frac {4 \, {\left (x^{4} - x\right )}^{\frac {1}{4}} {\left (x^{3} - 1\right )}}{15 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.51, size = 11, normalized size = 0.61 \begin {gather*} -\frac {4}{15} \, {\left (-\frac {1}{x^{3}} + 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 20, normalized size = 1.11
method | result | size |
trager | \(\frac {4 \left (x^{3}-1\right ) \left (x^{4}-x \right )^{\frac {1}{4}}}{15 x^{4}}\) | \(20\) |
gosper | \(\frac {4 \left (-1+x \right ) \left (x^{2}+x +1\right ) \left (x^{4}-x \right )^{\frac {1}{4}}}{15 x^{4}}\) | \(24\) |
risch | \(\frac {4 \left (x \left (x^{3}-1\right )\right )^{\frac {1}{4}} \left (x^{6}-2 x^{3}+1\right )}{15 x^{4} \left (x^{3}-1\right )}\) | \(32\) |
meijerg | \(-\frac {4 \mathrm {signum}\left (x^{3}-1\right )^{\frac {1}{4}} \left (-x^{3}+1\right )^{\frac {5}{4}}}{15 \left (-\mathrm {signum}\left (x^{3}-1\right )\right )^{\frac {1}{4}} x^{\frac {15}{4}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 25, normalized size = 1.39 \begin {gather*} \frac {4 \, {\left (x^{4} - x\right )} {\left (x^{2} + x + 1\right )}^{\frac {1}{4}} {\left (x - 1\right )}^{\frac {1}{4}}}{15 \, x^{\frac {19}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 31, normalized size = 1.72 \begin {gather*} -\frac {4\,{\left (x^4-x\right )}^{1/4}-4\,x^3\,{\left (x^4-x\right )}^{1/4}}{15\,x^4} \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 {\sqrt [4]{x \left (x - 1\right ) \left (x^{2} + x + 1\right )}}{x^{5}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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