Optimal. Leaf size=17 \[ \frac{b x^2}{2}-\frac{a}{2 x^2} \]
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Rubi [A] time = 0.0046726, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {14} \[ \frac{b x^2}{2}-\frac{a}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+b x^4}{x^3} \, dx &=\int \left (\frac{a}{x^3}+b x\right ) \, dx\\ &=-\frac{a}{2 x^2}+\frac{b x^2}{2}\\ \end{align*}
Mathematica [A] time = 0.000985, size = 17, normalized size = 1. \[ \frac{b x^2}{2}-\frac{a}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.8 \begin{align*} -{\frac{a}{2\,{x}^{2}}}+{\frac{b{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983496, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{2} \, b x^{2} - \frac{a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.37554, size = 28, normalized size = 1.65 \begin{align*} \frac{b x^{4} - a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.229365, size = 12, normalized size = 0.71 \begin{align*} - \frac{a}{2 x^{2}} + \frac{b x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10798, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{2} \, b x^{2} - \frac{a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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