Optimal. Leaf size=25 \[ \frac{a x^4}{4}+\frac{b x^6}{6}+\frac{c x^8}{8} \]
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Rubi [A] time = 0.0078675, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {14} \[ \frac{a x^4}{4}+\frac{b x^6}{6}+\frac{c x^8}{8} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x^2 \left (a x+b x^3+c x^5\right ) \, dx &=\int \left (a x^3+b x^5+c x^7\right ) \, dx\\ &=\frac{a x^4}{4}+\frac{b x^6}{6}+\frac{c x^8}{8}\\ \end{align*}
Mathematica [A] time = 0.0019507, size = 25, normalized size = 1. \[ \frac{a x^4}{4}+\frac{b x^6}{6}+\frac{c x^8}{8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 20, normalized size = 0.8 \begin{align*}{\frac{a{x}^{4}}{4}}+{\frac{b{x}^{6}}{6}}+{\frac{c{x}^{8}}{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12666, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{8} \, c x^{8} + \frac{1}{6} \, b x^{6} + \frac{1}{4} \, a x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.0509, size = 47, normalized size = 1.88 \begin{align*} \frac{1}{8} x^{8} c + \frac{1}{6} x^{6} b + \frac{1}{4} x^{4} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.056171, size = 19, normalized size = 0.76 \begin{align*} \frac{a x^{4}}{4} + \frac{b x^{6}}{6} + \frac{c x^{8}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09845, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{8} \, c x^{8} + \frac{1}{6} \, b x^{6} + \frac{1}{4} \, a x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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