Optimal. Leaf size=43 \[ \frac{1}{6} a^2 b x^{18}+\frac{a^3 x^{15}}{15}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24} \]
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Rubi [A] time = 0.0273662, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{1}{6} a^2 b x^{18}+\frac{a^3 x^{15}}{15}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^{14} \left (a+b x^3\right )^3 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^4 (a+b x)^3 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (a^3 x^4+3 a^2 b x^5+3 a b^2 x^6+b^3 x^7\right ) \, dx,x,x^3\right )\\ &=\frac{a^3 x^{15}}{15}+\frac{1}{6} a^2 b x^{18}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24}\\ \end{align*}
Mathematica [A] time = 0.0021191, size = 43, normalized size = 1. \[ \frac{1}{6} a^2 b x^{18}+\frac{a^3 x^{15}}{15}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 36, normalized size = 0.8 \begin{align*}{\frac{{a}^{3}{x}^{15}}{15}}+{\frac{{a}^{2}b{x}^{18}}{6}}+{\frac{a{b}^{2}{x}^{21}}{7}}+{\frac{{b}^{3}{x}^{24}}{24}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956449, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{24} \, b^{3} x^{24} + \frac{1}{7} \, a b^{2} x^{21} + \frac{1}{6} \, a^{2} b x^{18} + \frac{1}{15} \, a^{3} x^{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54668, size = 88, normalized size = 2.05 \begin{align*} \frac{1}{24} x^{24} b^{3} + \frac{1}{7} x^{21} b^{2} a + \frac{1}{6} x^{18} b a^{2} + \frac{1}{15} x^{15} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.07106, size = 36, normalized size = 0.84 \begin{align*} \frac{a^{3} x^{15}}{15} + \frac{a^{2} b x^{18}}{6} + \frac{a b^{2} x^{21}}{7} + \frac{b^{3} x^{24}}{24} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17303, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{24} \, b^{3} x^{24} + \frac{1}{7} \, a b^{2} x^{21} + \frac{1}{6} \, a^{2} b x^{18} + \frac{1}{15} \, a^{3} x^{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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