Optimal. Leaf size=28 \[ -\frac{a \log \left (a-b x^3\right )}{3 b^2}-\frac{x^3}{3 b} \]
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Rubi [A] time = 0.0193602, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {266, 43} \[ -\frac{a \log \left (a-b x^3\right )}{3 b^2}-\frac{x^3}{3 b} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^5}{a-b x^3} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{x}{a-b x} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (-\frac{1}{b}-\frac{a}{b (-a+b x)}\right ) \, dx,x,x^3\right )\\ &=-\frac{x^3}{3 b}-\frac{a \log \left (a-b x^3\right )}{3 b^2}\\ \end{align*}
Mathematica [A] time = 0.0049251, size = 28, normalized size = 1. \[ -\frac{a \log \left (a-b x^3\right )}{3 b^2}-\frac{x^3}{3 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 26, normalized size = 0.9 \begin{align*} -{\frac{{x}^{3}}{3\,b}}-{\frac{a\ln \left ( b{x}^{3}-a \right ) }{3\,{b}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959788, size = 34, normalized size = 1.21 \begin{align*} -\frac{x^{3}}{3 \, b} - \frac{a \log \left (b x^{3} - a\right )}{3 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50801, size = 50, normalized size = 1.79 \begin{align*} -\frac{b x^{3} + a \log \left (b x^{3} - a\right )}{3 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.426014, size = 22, normalized size = 0.79 \begin{align*} - \frac{a \log{\left (- a + b x^{3} \right )}}{3 b^{2}} - \frac{x^{3}}{3 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13149, size = 35, normalized size = 1.25 \begin{align*} -\frac{x^{3}}{3 \, b} - \frac{a \log \left ({\left | b x^{3} - a \right |}\right )}{3 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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