Optimal. Leaf size=20 \[ \frac {2 \left (x^4-x^2\right )^{5/4}}{5 x^5} \]
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Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2014} \begin {gather*} \frac {2 \left (x^4-x^2\right )^{5/4}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{-x^2+x^4}}{x^4} \, dx &=\frac {2 \left (-x^2+x^4\right )^{5/4}}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 \left (x^2 \left (x^2-1\right )\right )^{5/4}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.11, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 \left (x^4-x^2\right )^{5/4}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 21, normalized size = 1.05 \begin {gather*} \frac {2 \, {\left (x^{4} - x^{2}\right )}^{\frac {1}{4}} {\left (x^{2} - 1\right )}}{5 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 11, normalized size = 0.55 \begin {gather*} -\frac {2}{5} \, {\left (-\frac {1}{x^{2}} + 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 1.15 \begin {gather*} \frac {2 \left (-1+x \right ) \left (1+x \right ) \left (x^{4}-x^{2}\right )^{\frac {1}{4}}}{5 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 22, normalized size = 1.10 \begin {gather*} \frac {2 \, {\left (x^{3} - x\right )} {\left (x + 1\right )}^{\frac {1}{4}} {\left (x - 1\right )}^{\frac {1}{4}}}{5 \, x^{\frac {7}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 33, normalized size = 1.65 \begin {gather*} \frac {2\,{\left (x^4-x^2\right )}^{1/4}}{5\,x}-\frac {2\,{\left (x^4-x^2\right )}^{1/4}}{5\,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 {\sqrt [4]{x^{2} \left (x - 1\right ) \left (x + 1\right )}}{x^{4}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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