Optimal. Leaf size=15 \[ -\frac{\log \left (a+\frac{b}{x^3}\right )}{3 b} \]
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Rubi [A] time = 0.0041136, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {260} \[ -\frac{\log \left (a+\frac{b}{x^3}\right )}{3 b} \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x^3}\right ) x^4} \, dx &=-\frac{\log \left (a+\frac{b}{x^3}\right )}{3 b}\\ \end{align*}
Mathematica [A] time = 0.0052636, size = 22, normalized size = 1.47 \[ \frac{\log (x)}{b}-\frac{\log \left (a x^3+b\right )}{3 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 21, normalized size = 1.4 \begin{align*}{\frac{\ln \left ( x \right ) }{b}}-{\frac{\ln \left ( a{x}^{3}+b \right ) }{3\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.968656, size = 18, normalized size = 1.2 \begin{align*} -\frac{\log \left (a + \frac{b}{x^{3}}\right )}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45597, size = 49, normalized size = 3.27 \begin{align*} -\frac{\log \left (a x^{3} + b\right ) - 3 \, \log \left (x\right )}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.276183, size = 15, normalized size = 1. \begin{align*} \frac{\log{\left (x \right )}}{b} - \frac{\log{\left (x^{3} + \frac{b}{a} \right )}}{3 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18581, size = 30, normalized size = 2. \begin{align*} -\frac{\log \left ({\left | a x^{3} + b \right |}\right )}{3 \, b} + \frac{\log \left ({\left | x \right |}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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