Optimal. Leaf size=17 \[ \frac{b x^4}{4}+\frac{c x^6}{6} \]
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Rubi [A] time = 0.0056222, antiderivative size = 17, 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 = {14} \[ \frac{b x^4}{4}+\frac{c x^6}{6} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x \left (b x^2+c x^4\right ) \, dx &=\int \left (b x^3+c x^5\right ) \, dx\\ &=\frac{b x^4}{4}+\frac{c x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.0012668, size = 17, normalized size = 1. \[ \frac{b x^4}{4}+\frac{c x^6}{6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 14, normalized size = 0.8 \begin{align*}{\frac{b{x}^{4}}{4}}+{\frac{c{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.944011, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{6} \, c x^{6} + \frac{1}{4} \, b x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.00956, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{6} x^{6} c + \frac{1}{4} x^{4} b \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.064077, size = 12, normalized size = 0.71 \begin{align*} \frac{b x^{4}}{4} + \frac{c x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.29331, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{6} \, c x^{6} + \frac{1}{4} \, b x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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