Optimal. Leaf size=80 \[ \frac{3 a^2 \left (a+b x^3\right )^{7/3}}{7 b^4}-\frac{a^3 \left (a+b x^3\right )^{4/3}}{4 b^4}+\frac{\left (a+b x^3\right )^{13/3}}{13 b^4}-\frac{3 a \left (a+b x^3\right )^{10/3}}{10 b^4} \]
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Rubi [A] time = 0.04404, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac{3 a^2 \left (a+b x^3\right )^{7/3}}{7 b^4}-\frac{a^3 \left (a+b x^3\right )^{4/3}}{4 b^4}+\frac{\left (a+b x^3\right )^{13/3}}{13 b^4}-\frac{3 a \left (a+b x^3\right )^{10/3}}{10 b^4} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^{11} \sqrt [3]{a+b x^3} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^3 \sqrt [3]{a+b x} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (-\frac{a^3 \sqrt [3]{a+b x}}{b^3}+\frac{3 a^2 (a+b x)^{4/3}}{b^3}-\frac{3 a (a+b x)^{7/3}}{b^3}+\frac{(a+b x)^{10/3}}{b^3}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^3 \left (a+b x^3\right )^{4/3}}{4 b^4}+\frac{3 a^2 \left (a+b x^3\right )^{7/3}}{7 b^4}-\frac{3 a \left (a+b x^3\right )^{10/3}}{10 b^4}+\frac{\left (a+b x^3\right )^{13/3}}{13 b^4}\\ \end{align*}
Mathematica [A] time = 0.0257377, size = 50, normalized size = 0.62 \[ \frac{\left (a+b x^3\right )^{4/3} \left (108 a^2 b x^3-81 a^3-126 a b^2 x^6+140 b^3 x^9\right )}{1820 b^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 47, normalized size = 0.6 \begin{align*} -{\frac{-140\,{b}^{3}{x}^{9}+126\,a{b}^{2}{x}^{6}-108\,{a}^{2}b{x}^{3}+81\,{a}^{3}}{1820\,{b}^{4}} \left ( b{x}^{3}+a \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.976842, size = 86, normalized size = 1.08 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{\frac{13}{3}}}{13 \, b^{4}} - \frac{3 \,{\left (b x^{3} + a\right )}^{\frac{10}{3}} a}{10 \, b^{4}} + \frac{3 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}} a^{2}}{7 \, b^{4}} - \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}} a^{3}}{4 \, b^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70515, size = 136, normalized size = 1.7 \begin{align*} \frac{{\left (140 \, b^{4} x^{12} + 14 \, a b^{3} x^{9} - 18 \, a^{2} b^{2} x^{6} + 27 \, a^{3} b x^{3} - 81 \, a^{4}\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{1820 \, b^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.97147, size = 110, normalized size = 1.38 \begin{align*} \begin{cases} - \frac{81 a^{4} \sqrt [3]{a + b x^{3}}}{1820 b^{4}} + \frac{27 a^{3} x^{3} \sqrt [3]{a + b x^{3}}}{1820 b^{3}} - \frac{9 a^{2} x^{6} \sqrt [3]{a + b x^{3}}}{910 b^{2}} + \frac{a x^{9} \sqrt [3]{a + b x^{3}}}{130 b} + \frac{x^{12} \sqrt [3]{a + b x^{3}}}{13} & \text{for}\: b \neq 0 \\\frac{\sqrt [3]{a} x^{12}}{12} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10155, size = 77, normalized size = 0.96 \begin{align*} \frac{140 \,{\left (b x^{3} + a\right )}^{\frac{13}{3}} - 546 \,{\left (b x^{3} + a\right )}^{\frac{10}{3}} a + 780 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}} a^{2} - 455 \,{\left (b x^{3} + a\right )}^{\frac{4}{3}} a^{3}}{1820 \, b^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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