Optimal. Leaf size=92 \[ \frac{81 b^3 \left (a+b x^3\right )^{4/3}}{1820 a^4 x^4}-\frac{27 b^2 \left (a+b x^3\right )^{4/3}}{455 a^3 x^7}+\frac{9 b \left (a+b x^3\right )^{4/3}}{130 a^2 x^{10}}-\frac{\left (a+b x^3\right )^{4/3}}{13 a x^{13}} \]
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Rubi [A] time = 0.0304313, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {271, 264} \[ \frac{81 b^3 \left (a+b x^3\right )^{4/3}}{1820 a^4 x^4}-\frac{27 b^2 \left (a+b x^3\right )^{4/3}}{455 a^3 x^7}+\frac{9 b \left (a+b x^3\right )^{4/3}}{130 a^2 x^{10}}-\frac{\left (a+b x^3\right )^{4/3}}{13 a x^{13}} \]
Antiderivative was successfully verified.
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Rule 271
Rule 264
Rubi steps
\begin{align*} \int \frac{\sqrt [3]{a+b x^3}}{x^{14}} \, dx &=-\frac{\left (a+b x^3\right )^{4/3}}{13 a x^{13}}-\frac{(9 b) \int \frac{\sqrt [3]{a+b x^3}}{x^{11}} \, dx}{13 a}\\ &=-\frac{\left (a+b x^3\right )^{4/3}}{13 a x^{13}}+\frac{9 b \left (a+b x^3\right )^{4/3}}{130 a^2 x^{10}}+\frac{\left (27 b^2\right ) \int \frac{\sqrt [3]{a+b x^3}}{x^8} \, dx}{65 a^2}\\ &=-\frac{\left (a+b x^3\right )^{4/3}}{13 a x^{13}}+\frac{9 b \left (a+b x^3\right )^{4/3}}{130 a^2 x^{10}}-\frac{27 b^2 \left (a+b x^3\right )^{4/3}}{455 a^3 x^7}-\frac{\left (81 b^3\right ) \int \frac{\sqrt [3]{a+b x^3}}{x^5} \, dx}{455 a^3}\\ &=-\frac{\left (a+b x^3\right )^{4/3}}{13 a x^{13}}+\frac{9 b \left (a+b x^3\right )^{4/3}}{130 a^2 x^{10}}-\frac{27 b^2 \left (a+b x^3\right )^{4/3}}{455 a^3 x^7}+\frac{81 b^3 \left (a+b x^3\right )^{4/3}}{1820 a^4 x^4}\\ \end{align*}
Mathematica [A] time = 0.0120998, size = 53, normalized size = 0.58 \[ \frac{\left (a+b x^3\right )^{4/3} \left (126 a^2 b x^3-140 a^3-108 a b^2 x^6+81 b^3 x^9\right )}{1820 a^4 x^{13}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 50, normalized size = 0.5 \begin{align*} -{\frac{-81\,{b}^{3}{x}^{9}+108\,a{b}^{2}{x}^{6}-126\,{a}^{2}b{x}^{3}+140\,{a}^{3}}{1820\,{x}^{13}{a}^{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 = 1.00406, size = 93, normalized size = 1.01 \begin{align*} \frac{\frac{455 \,{\left (b x^{3} + a\right )}^{\frac{4}{3}} b^{3}}{x^{4}} - \frac{780 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}} b^{2}}{x^{7}} + \frac{546 \,{\left (b x^{3} + a\right )}^{\frac{10}{3}} b}{x^{10}} - \frac{140 \,{\left (b x^{3} + a\right )}^{\frac{13}{3}}}{x^{13}}}{1820 \, a^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.98513, size = 146, normalized size = 1.59 \begin{align*} \frac{{\left (81 \, b^{4} x^{12} - 27 \, a b^{3} x^{9} + 18 \, a^{2} b^{2} x^{6} - 14 \, a^{3} b x^{3} - 140 \, a^{4}\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{1820 \, a^{4} x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 4.30894, size = 847, normalized size = 9.21 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{x^{14}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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