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 = 0.06, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3 \left (1+x^5\right )^{5/3}}{5 x^{10}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, 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 [A] time = 0.11, size = 13, normalized size = 0.81
method | result | size |
trager | \(-\frac {3 \left (x^{5}+1\right )^{\frac {5}{3}}}{5 x^{10}}\) | \(13\) |
risch | \(-\frac {3 \left (x^{10}+2 x^{5}+1\right )}{5 x^{10} \left (x^{5}+1\right )^{\frac {1}{3}}}\) | \(23\) |
gosper | \(-\frac {3 \left (1+x \right ) \left (x^{4}-x^{3}+x^{2}-x +1\right ) \left (x^{5}+1\right )^{\frac {2}{3}}}{5 x^{10}}\) | \(32\) |
meijerg | \(-\frac {\Gamma \left (\frac {2}{3}\right ) \sqrt {3}\, \left (\frac {\pi \sqrt {3}}{\Gamma \left (\frac {2}{3}\right ) x^{5}}-\frac {2 \left (-\frac {\pi \sqrt {3}}{6}-\frac {3 \ln \relax (3)}{2}-1+5 \ln \relax (x )\right ) \pi \sqrt {3}}{3 \Gamma \left (\frac {2}{3}\right )}+\frac {\hypergeom \left (\left [1, 1, \frac {4}{3}\right ], \left [2, 3\right ], -x^{5}\right ) \pi \sqrt {3}\, x^{5}}{9 \Gamma \left (\frac {2}{3}\right )}\right )}{15 \pi }-\frac {2 \Gamma \left (\frac {2}{3}\right ) \sqrt {3}\, \left (\frac {\pi \sqrt {3}}{2 \Gamma \left (\frac {2}{3}\right ) x^{10}}+\frac {2 \pi \sqrt {3}}{3 \Gamma \left (\frac {2}{3}\right ) x^{5}}+\frac {\left (\frac {3}{2}-\frac {\pi \sqrt {3}}{6}-\frac {3 \ln \relax (3)}{2}+5 \ln \relax (x )\right ) \pi \sqrt {3}}{9 \Gamma \left (\frac {2}{3}\right )}-\frac {4 \hypergeom \left (\left [1, 1, \frac {7}{3}\right ], \left [2, 4\right ], -x^{5}\right ) \pi \sqrt {3}\, x^{5}}{81 \Gamma \left (\frac {2}{3}\right )}\right )}{5 \pi }\) | \(166\) |
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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