Optimal. Leaf size=30 \[ \frac{a^2 x^5}{5}+\frac{2}{9} a b x^9+\frac{b^2 x^{13}}{13} \]
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Rubi [A] time = 0.0100323, 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} \[ \frac{a^2 x^5}{5}+\frac{2}{9} a b x^9+\frac{b^2 x^{13}}{13} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int x^4 \left (a+b x^4\right )^2 \, dx &=\int \left (a^2 x^4+2 a b x^8+b^2 x^{12}\right ) \, dx\\ &=\frac{a^2 x^5}{5}+\frac{2}{9} a b x^9+\frac{b^2 x^{13}}{13}\\ \end{align*}
Mathematica [A] time = 0.0007075, size = 30, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{2}{9} a b x^9+\frac{b^2 x^{13}}{13} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 25, normalized size = 0.8 \begin{align*}{\frac{{x}^{5}{a}^{2}}{5}}+{\frac{2\,ab{x}^{9}}{9}}+{\frac{{b}^{2}{x}^{13}}{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967404, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{13} \, b^{2} x^{13} + \frac{2}{9} \, a b x^{9} + \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 = 1.28108, size = 58, normalized size = 1.93 \begin{align*} \frac{1}{13} x^{13} b^{2} + \frac{2}{9} x^{9} 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 = 0.060751, size = 26, normalized size = 0.87 \begin{align*} \frac{a^{2} x^{5}}{5} + \frac{2 a b x^{9}}{9} + \frac{b^{2} x^{13}}{13} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08971, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{13} \, b^{2} x^{13} + \frac{2}{9} \, a b x^{9} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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