Optimal. Leaf size=18 \[ -\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b} \]
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Rubi [A] time = 0.0059425, 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} \[ -\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\sqrt{a+\frac{b}{x^3}}}{x^4} \, dx &=-\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b}\\ \end{align*}
Mathematica [A] time = 0.0111442, size = 18, normalized size = 1. \[ -\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b} \]
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}{9\,b{x}^{3}}\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 = 0.957996, size = 19, normalized size = 1.06 \begin{align*} -\frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50823, size = 65, normalized size = 3.61 \begin{align*} -\frac{2 \,{\left (a x^{3} + b\right )} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, b x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.13011, size = 46, normalized size = 2.56 \begin{align*} - \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{3}}}}{9 b} - \frac{2 \sqrt{a} \sqrt{1 + \frac{b}{a x^{3}}}}{9 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.59336, size = 19, normalized size = 1.06 \begin{align*} -\frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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