Optimal. Leaf size=27 \[ \frac {3 \left (3 x^4+2\right ) \left (x^6-x^2\right )^{2/3}}{40 x^8} \]
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Rubi [A] time = 0.06, antiderivative size = 41, normalized size of antiderivative = 1.52, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {2016, 2014} \begin {gather*} \frac {3 \left (x^6-x^2\right )^{2/3}}{20 x^8}+\frac {9 \left (x^6-x^2\right )^{2/3}}{40 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rule 2016
Rubi steps
\begin {align*} \int \frac {1}{x^7 \sqrt [3]{-x^2+x^6}} \, dx &=\frac {3 \left (-x^2+x^6\right )^{2/3}}{20 x^8}+\frac {3}{5} \int \frac {1}{x^3 \sqrt [3]{-x^2+x^6}} \, dx\\ &=\frac {3 \left (-x^2+x^6\right )^{2/3}}{20 x^8}+\frac {9 \left (-x^2+x^6\right )^{2/3}}{40 x^4}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \begin {gather*} \frac {3 \left (x^2 \left (x^4-1\right )\right )^{2/3} \left (3 x^4+2\right )}{40 x^8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.44, size = 27, normalized size = 1.00 \begin {gather*} \frac {3 \left (3 x^4+2\right ) \left (x^6-x^2\right )^{2/3}}{40 x^8} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 23, normalized size = 0.85 \begin {gather*} \frac {3 \, {\left (x^{6} - x^{2}\right )}^{\frac {2}{3}} {\left (3 \, x^{4} + 2\right )}}{40 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 23, normalized size = 0.85 \begin {gather*} -\frac {3}{20} \, {\left (-\frac {1}{x^{4}} + 1\right )}^{\frac {5}{3}} + \frac {3}{8} \, {\left (-\frac {1}{x^{4}} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 1.30 \begin {gather*} \frac {3 \left (-1+x \right ) \left (1+x \right ) \left (x^{2}+1\right ) \left (3 x^{4}+2\right )}{40 x^{6} \left (x^{6}-x^{2}\right )^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 37, normalized size = 1.37 \begin {gather*} \frac {3 \, {\left (3 \, x^{10} - x^{6} - 2 \, x^{2}\right )}}{40 \, {\left (x^{2} + 1\right )}^{\frac {1}{3}} {\left (x^{2} - 1\right )}^{\frac {1}{3}} {\left (x^{2}\right )}^{\frac {13}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 35, normalized size = 1.30 \begin {gather*} \frac {9\,x^4\,{\left (x^6-x^2\right )}^{2/3}+6\,{\left (x^6-x^2\right )}^{2/3}}{40\,x^8} \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^{7} \sqrt [3]{x^{2} \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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