Optimal. Leaf size=17 \[ \frac{a x^2}{2}+\frac{b x^6}{6} \]
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Rubi [A] time = 0.0047628, antiderivative size = 17, 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 = {14} \[ \frac{a x^2}{2}+\frac{b x^6}{6} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x \left (a+b x^4\right ) \, dx &=\int \left (a x+b x^5\right ) \, dx\\ &=\frac{a x^2}{2}+\frac{b x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.000922, size = 17, normalized size = 1. \[ \frac{a x^2}{2}+\frac{b x^6}{6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.8 \begin{align*}{\frac{a{x}^{2}}{2}}+{\frac{b{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963845, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{6} \, b x^{6} + \frac{1}{2} \, a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24332, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{6} x^{6} b + \frac{1}{2} x^{2} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074177, size = 12, normalized size = 0.71 \begin{align*} \frac{a x^{2}}{2} + \frac{b x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1063, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{6} \, b x^{6} + \frac{1}{2} \, a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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