Optimal. Leaf size=43 \[ \frac{1}{3} a^2 b x^9+\frac{a^3 x^5}{5}+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17} \]
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Rubi [A] time = 0.0144689, antiderivative size = 43, 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} \[ \frac{1}{3} a^2 b x^9+\frac{a^3 x^5}{5}+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int x^4 \left (a+b x^4\right )^3 \, dx &=\int \left (a^3 x^4+3 a^2 b x^8+3 a b^2 x^{12}+b^3 x^{16}\right ) \, dx\\ &=\frac{a^3 x^5}{5}+\frac{1}{3} a^2 b x^9+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17}\\ \end{align*}
Mathematica [A] time = 0.0019542, size = 43, normalized size = 1. \[ \frac{1}{3} a^2 b x^9+\frac{a^3 x^5}{5}+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17} \]
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}^{5}}{5}}+{\frac{{a}^{2}b{x}^{9}}{3}}+{\frac{3\,a{b}^{2}{x}^{13}}{13}}+{\frac{{b}^{3}{x}^{17}}{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.954608, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{17} \, b^{3} x^{17} + \frac{3}{13} \, a b^{2} x^{13} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{5} \, a^{3} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.23005, size = 85, normalized size = 1.98 \begin{align*} \frac{1}{17} x^{17} b^{3} + \frac{3}{13} x^{13} b^{2} a + \frac{1}{3} x^{9} b a^{2} + \frac{1}{5} x^{5} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096962, size = 37, normalized size = 0.86 \begin{align*} \frac{a^{3} x^{5}}{5} + \frac{a^{2} b x^{9}}{3} + \frac{3 a b^{2} x^{13}}{13} + \frac{b^{3} x^{17}}{17} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12421, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{17} \, b^{3} x^{17} + \frac{3}{13} \, a b^{2} x^{13} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{5} \, a^{3} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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