Optimal. Leaf size=12 \[ b x+\frac{c x^3}{3} \]
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Rubi [A] time = 0.0044172, antiderivative size = 12, 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} \[ b x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{b x^2+c x^4}{x^2} \, dx &=\int \left (b+c x^2\right ) \, dx\\ &=b x+\frac{c x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0003584, size = 12, normalized size = 1. \[ b x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 11, normalized size = 0.9 \begin{align*} bx+{\frac{c{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96898, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, c x^{3} + b x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.11098, size = 23, normalized size = 1.92 \begin{align*} \frac{1}{3} \, c x^{3} + b x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062623, size = 8, normalized size = 0.67 \begin{align*} b x + \frac{c x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25198, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, c x^{3} + b x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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