Optimal. Leaf size=18 \[ -\frac{a}{x}+b x+\frac{c x^3}{3} \]
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Rubi [A] time = 0.0068819, antiderivative size = 18, 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} \[ -\frac{a}{x}+b x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a x+b x^3+c x^5}{x^3} \, dx &=\int \left (b+\frac{a}{x^2}+c x^2\right ) \, dx\\ &=-\frac{a}{x}+b x+\frac{c x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0020158, size = 18, normalized size = 1. \[ -\frac{a}{x}+b x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 17, normalized size = 0.9 \begin{align*} -{\frac{a}{x}}+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 = 1.11163, size = 22, normalized size = 1.22 \begin{align*} \frac{1}{3} \, c x^{3} + b x - \frac{a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19098, size = 42, normalized size = 2.33 \begin{align*} \frac{c x^{4} + 3 \, b x^{2} - 3 \, a}{3 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.247622, size = 12, normalized size = 0.67 \begin{align*} - \frac{a}{x} + 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 = 1.09081, size = 22, normalized size = 1.22 \begin{align*} \frac{1}{3} \, c x^{3} + b x - \frac{a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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