Optimal. Leaf size=30 \[ \frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11} \]
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Rubi [A] time = 0.0097121, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {270} \[ \frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int x^4 \left (a+b x^3\right )^2 \, dx &=\int \left (a^2 x^4+2 a b x^7+b^2 x^{10}\right ) \, dx\\ &=\frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11}\\ \end{align*}
Mathematica [A] time = 0.0009039, size = 30, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \begin{align*}{\frac{{x}^{5}{a}^{2}}{5}}+{\frac{ab{x}^{8}}{4}}+{\frac{{b}^{2}{x}^{11}}{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956217, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{11} \, b^{2} x^{11} + \frac{1}{4} \, a b x^{8} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40215, size = 58, normalized size = 1.93 \begin{align*} \frac{1}{11} x^{11} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{5} x^{5} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.09073, size = 24, normalized size = 0.8 \begin{align*} \frac{a^{2} x^{5}}{5} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11998, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{11} \, b^{2} x^{11} + \frac{1}{4} \, a b x^{8} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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