Optimal. Leaf size=27 \[ \frac{x^3}{3 b}-\frac{a \log \left (a+b x^3\right )}{3 b^2} \]
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Rubi [A] time = 0.0169171, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{x^3}{3 b}-\frac{a \log \left (a+b x^3\right )}{3 b^2} \]
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 = 0.0040328, size = 27, normalized size = 1. \[ \frac{x^3}{3 b}-\frac{a \log \left (a+b x^3\right )}{3 b^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 24, 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 = 0.984372, size = 31, normalized size = 1.15 \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 = 1.40539, size = 49, normalized size = 1.81 \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 = 0.357183, size = 20, normalized size = 0.74 \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 = 1.12267, size = 32, normalized size = 1.19 \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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