Optimal. Leaf size=38 \[ \frac{3}{4} a^2 b x^4+a^3 x+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10} \]
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Rubi [A] time = 0.0108652, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {194} \[ \frac{3}{4} a^2 b x^4+a^3 x+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10} \]
Antiderivative was successfully verified.
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Rule 194
Rubi steps
\begin{align*} \int \left (a+b x^3\right )^3 \, dx &=\int \left (a^3+3 a^2 b x^3+3 a b^2 x^6+b^3 x^9\right ) \, dx\\ &=a^3 x+\frac{3}{4} a^2 b x^4+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10}\\ \end{align*}
Mathematica [A] time = 0.0008571, size = 38, normalized size = 1. \[ \frac{3}{4} a^2 b x^4+a^3 x+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 33, normalized size = 0.9 \begin{align*}{a}^{3}x+{\frac{3\,{a}^{2}b{x}^{4}}{4}}+{\frac{3\,a{b}^{2}{x}^{7}}{7}}+{\frac{{b}^{3}{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.990554, size = 43, normalized size = 1.13 \begin{align*} \frac{1}{10} \, b^{3} x^{10} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.56653, size = 74, normalized size = 1.95 \begin{align*} \frac{1}{10} x^{10} b^{3} + \frac{3}{7} x^{7} b^{2} a + \frac{3}{4} x^{4} b a^{2} + x a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.087112, size = 36, normalized size = 0.95 \begin{align*} a^{3} x + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{10}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13089, size = 43, normalized size = 1.13 \begin{align*} \frac{1}{10} \, b^{3} x^{10} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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