Optimal. Leaf size=17 \[ \frac{b x^2}{2}+\frac{c x^4}{4} \]
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Rubi [A] time = 0.0049654, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {14} \[ \frac{b x^2}{2}+\frac{c x^4}{4} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{b x^2+c x^4}{x} \, dx &=\int \left (b x+c x^3\right ) \, dx\\ &=\frac{b x^2}{2}+\frac{c x^4}{4}\\ \end{align*}
Mathematica [A] time = 0.0012194, size = 17, normalized size = 1. \[ \frac{b x^2}{2}+\frac{c x^4}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 14, normalized size = 0.8 \begin{align*}{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963044, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20785, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058903, size = 12, normalized size = 0.71 \begin{align*} \frac{b x^{2}}{2} + \frac{c x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26469, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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