Optimal. Leaf size=33 \[ -\frac{1}{10 b x^5}+\frac{\log \left (x^5+2\right )}{20 b}-\frac{\log (x)}{4 b} \]
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Rubi [A] time = 0.0181239, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 44} \[ -\frac{1}{10 b x^5}+\frac{\log \left (x^5+2\right )}{20 b}-\frac{\log (x)}{4 b} \]
Antiderivative was successfully verified.
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Rule 266
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^6 \left (2 b+b x^5\right )} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{1}{x^2 (2 b+b x)} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{1}{2 b x^2}-\frac{1}{4 b x}+\frac{1}{4 b (2+x)}\right ) \, dx,x,x^5\right )\\ &=-\frac{1}{10 b x^5}-\frac{\log (x)}{4 b}+\frac{\log \left (2+x^5\right )}{20 b}\\ \end{align*}
Mathematica [A] time = 0.004133, size = 33, normalized size = 1. \[ -\frac{1}{10 b x^5}+\frac{\log \left (x^5+2\right )}{20 b}-\frac{\log (x)}{4 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \begin{align*} -{\frac{1}{10\,b{x}^{5}}}-{\frac{\ln \left ( x \right ) }{4\,b}}+{\frac{\ln \left ({x}^{5}+2 \right ) }{20\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02313, size = 39, normalized size = 1.18 \begin{align*} \frac{\log \left (x^{5} + 2\right )}{20 \, b} - \frac{\log \left (x^{5}\right )}{20 \, b} - \frac{1}{10 \, b x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.71003, size = 70, normalized size = 2.12 \begin{align*} \frac{x^{5} \log \left (x^{5} + 2\right ) - 5 \, x^{5} \log \left (x\right ) - 2}{20 \, b x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.801041, size = 24, normalized size = 0.73 \begin{align*} - \frac{\log{\left (x \right )}}{4 b} + \frac{\log{\left (x^{5} + 2 \right )}}{20 b} - \frac{1}{10 b x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18481, size = 46, normalized size = 1.39 \begin{align*} \frac{\log \left ({\left | x^{5} + 2 \right |}\right )}{20 \, b} - \frac{\log \left ({\left | x \right |}\right )}{4 \, b} + \frac{x^{5} - 2}{20 \, b x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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