Optimal. Leaf size=16 \[ -\frac {3 \left (x^5+1\right )^{5/3}}{5 x^{10}} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {446, 74} \begin {gather*} -\frac {3 \left (x^5+1\right )^{5/3}}{5 x^{10}} \end {gather*}
Antiderivative was successfully verified.
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Rule 74
Rule 446
Rubi steps
\begin {align*} \int \frac {\left (1+x^5\right )^{2/3} \left (6+x^5\right )}{x^{11}} \, dx &=\frac {1}{5} \operatorname {Subst}\left (\int \frac {(1+x)^{2/3} (6+x)}{x^3} \, dx,x,x^5\right )\\ &=-\frac {3 \left (1+x^5\right )^{5/3}}{5 x^{10}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3 \left (x^5+1\right )^{5/3}}{5 x^{10}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.08, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3 \left (x^5+1\right )^{5/3}}{5 x^{10}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 12, normalized size = 0.75 \begin {gather*} -\frac {3 \, {\left (x^{5} + 1\right )}^{\frac {5}{3}}}{5 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.74, size = 12, normalized size = 0.75 \begin {gather*} -\frac {3 \, {\left (x^{5} + 1\right )}^{\frac {5}{3}}}{5 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 32, normalized size = 2.00 \begin {gather*} -\frac {3 \left (1+x \right ) \left (x^{4}-x^{3}+x^{2}-x +1\right ) \left (x^{5}+1\right )^{\frac {2}{3}}}{5 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.57, size = 50, normalized size = 3.12 \begin {gather*} \frac {2 \, {\left (x^{5} + 1\right )}^{\frac {5}{3}} + {\left (x^{5} + 1\right )}^{\frac {2}{3}}}{5 \, {\left (2 \, x^{5} - {\left (x^{5} + 1\right )}^{2} + 1\right )}} - \frac {{\left (x^{5} + 1\right )}^{\frac {2}{3}}}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 12, normalized size = 0.75 \begin {gather*} -\frac {3\,{\left (x^5+1\right )}^{5/3}}{5\,x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 3.95, size = 70, normalized size = 4.38 \begin {gather*} - \frac {\Gamma \left (\frac {1}{3}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {2}{3}, \frac {1}{3} \\ \frac {4}{3} \end {matrix}\middle | {\frac {e^{i \pi }}{x^{5}}} \right )}}{5 x^{\frac {5}{3}} \Gamma \left (\frac {4}{3}\right )} - \frac {6 \Gamma \left (\frac {4}{3}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {2}{3}, \frac {4}{3} \\ \frac {7}{3} \end {matrix}\middle | {\frac {e^{i \pi }}{x^{5}}} \right )}}{5 x^{\frac {20}{3}} \Gamma \left (\frac {7}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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