Optimal. Leaf size=33 \[ \frac {\left (x^3+1\right )^{2/3} \left (-227 x^9-142 x^6+45 x^3-40\right )}{440 x^{11}} \]
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Rubi [A] time = 0.03, antiderivative size = 49, normalized size of antiderivative = 1.48, number of steps used = 4, number of rules used = 4, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.160, Rules used = {1486, 453, 271, 264} \begin {gather*} -\frac {\left (x^3+1\right )^{5/3}}{11 x^{11}}+\frac {17 \left (x^3+1\right )^{5/3}}{88 x^8}-\frac {227 \left (x^3+1\right )^{5/3}}{440 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rule 271
Rule 453
Rule 1486
Rubi steps
\begin {align*} \int \frac {\left (1+x^3\right )^{2/3} \left (1-x^3+2 x^6\right )}{x^{12}} \, dx &=-\frac {2 \left (1+x^3\right )^{5/3}}{3 x^8}-\frac {1}{3} \int \frac {\left (1+x^3\right )^{2/3} \left (-3+19 x^3\right )}{x^{12}} \, dx\\ &=-\frac {\left (1+x^3\right )^{5/3}}{11 x^{11}}-\frac {2 \left (1+x^3\right )^{5/3}}{3 x^8}-\frac {227}{33} \int \frac {\left (1+x^3\right )^{2/3}}{x^9} \, dx\\ &=-\frac {\left (1+x^3\right )^{5/3}}{11 x^{11}}+\frac {17 \left (1+x^3\right )^{5/3}}{88 x^8}+\frac {227}{88} \int \frac {\left (1+x^3\right )^{2/3}}{x^6} \, dx\\ &=-\frac {\left (1+x^3\right )^{5/3}}{11 x^{11}}+\frac {17 \left (1+x^3\right )^{5/3}}{88 x^8}-\frac {227 \left (1+x^3\right )^{5/3}}{440 x^5}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 1.00 \begin {gather*} -\frac {\left (x^3+1\right )^{2/3} \left (227 x^9+142 x^6-45 x^3+40\right )}{440 x^{11}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.13, size = 33, normalized size = 1.00 \begin {gather*} \frac {\left (x^3+1\right )^{2/3} \left (-227 x^9-142 x^6+45 x^3-40\right )}{440 x^{11}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 29, normalized size = 0.88 \begin {gather*} -\frac {{\left (227 \, x^{9} + 142 \, x^{6} - 45 \, x^{3} + 40\right )} {\left (x^{3} + 1\right )}^{\frac {2}{3}}}{440 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, x^{6} - x^{3} + 1\right )} {\left (x^{3} + 1\right )}^{\frac {2}{3}}}{x^{12}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 1.09 \begin {gather*} -\frac {\left (1+x \right ) \left (x^{2}-x +1\right ) \left (227 x^{6}-85 x^{3}+40\right ) \left (x^{3}+1\right )^{\frac {2}{3}}}{440 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 37, normalized size = 1.12 \begin {gather*} -\frac {4 \, {\left (x^{3} + 1\right )}^{\frac {5}{3}}}{5 \, x^{5}} + \frac {3 \, {\left (x^{3} + 1\right )}^{\frac {8}{3}}}{8 \, x^{8}} - \frac {{\left (x^{3} + 1\right )}^{\frac {11}{3}}}{11 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.41, size = 49, normalized size = 1.48 \begin {gather*} \frac {9\,{\left (x^3+1\right )}^{2/3}}{88\,x^8}-\frac {71\,{\left (x^3+1\right )}^{2/3}}{220\,x^5}-\frac {227\,{\left (x^3+1\right )}^{2/3}}{440\,x^2}-\frac {{\left (x^3+1\right )}^{2/3}}{11\,x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.94, size = 260, normalized size = 7.88 \begin {gather*} \frac {2 \left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {5}{3}\right )}{3 \Gamma \left (- \frac {2}{3}\right )} + \frac {2 \left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {11}{3}\right )}{3 \Gamma \left (- \frac {2}{3}\right )} - \frac {\left (x^{3} + 1\right )^{\frac {2}{3}} \Gamma \left (- \frac {8}{3}\right )}{3 x^{2} \Gamma \left (- \frac {2}{3}\right )} + \frac {2 \left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {5}{3}\right )}{3 x^{3} \Gamma \left (- \frac {2}{3}\right )} - \frac {4 \left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {11}{3}\right )}{9 x^{3} \Gamma \left (- \frac {2}{3}\right )} + \frac {2 \left (x^{3} + 1\right )^{\frac {2}{3}} \Gamma \left (- \frac {8}{3}\right )}{9 x^{5} \Gamma \left (- \frac {2}{3}\right )} + \frac {10 \left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {11}{3}\right )}{27 x^{6} \Gamma \left (- \frac {2}{3}\right )} + \frac {5 \left (x^{3} + 1\right )^{\frac {2}{3}} \Gamma \left (- \frac {8}{3}\right )}{9 x^{8} \Gamma \left (- \frac {2}{3}\right )} + \frac {40 \left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {11}{3}\right )}{27 x^{9} \Gamma \left (- \frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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