Optimal. Leaf size=18 \[ -\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b} \]
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Rubi [A] time = 0.0058873, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ -\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^4} \, dx &=-\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b}\\ \end{align*}
Mathematica [A] time = 0.0079881, size = 18, normalized size = 1. \[ -\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 29, normalized size = 1.6 \begin{align*} -{\frac{2\,a{x}^{3}+2\,b}{3\,b{x}^{3}}{\frac{1}{\sqrt{{\frac{a{x}^{3}+b}{{x}^{3}}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.980899, size = 19, normalized size = 1.06 \begin{align*} -\frac{2 \, \sqrt{a + \frac{b}{x^{3}}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52495, size = 41, normalized size = 2.28 \begin{align*} -\frac{2 \, \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.74299, size = 29, normalized size = 1.61 \begin{align*} \begin{cases} - \frac{2 \sqrt{a + \frac{b}{x^{3}}}}{3 b} & \text{for}\: b \neq 0 \\- \frac{1}{3 \sqrt{a} x^{3}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11277, size = 19, normalized size = 1.06 \begin{align*} -\frac{2 \, \sqrt{a + \frac{b}{x^{3}}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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