Optimal. Leaf size=19 \[ \frac{\log (x)}{3}-\frac{1}{15} \log \left (b x^5+3\right ) \]
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Rubi [A] time = 0.0094368, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308, Rules used = {266, 36, 29, 31} \[ \frac{\log (x)}{3}-\frac{1}{15} \log \left (b x^5+3\right ) \]
Antiderivative was successfully verified.
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Rule 266
Rule 36
Rule 29
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{x \left (3+b x^5\right )} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{1}{x (3+b x)} \, dx,x,x^5\right )\\ &=\frac{1}{15} \operatorname{Subst}\left (\int \frac{1}{x} \, dx,x,x^5\right )-\frac{1}{15} b \operatorname{Subst}\left (\int \frac{1}{3+b x} \, dx,x,x^5\right )\\ &=\frac{\log (x)}{3}-\frac{1}{15} \log \left (3+b x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0036338, size = 19, normalized size = 1. \[ \frac{\log (x)}{3}-\frac{1}{15} \log \left (b x^5+3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 16, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( x \right ) }{3}}-{\frac{\ln \left ( b{x}^{5}+3 \right ) }{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970603, size = 23, normalized size = 1.21 \begin{align*} -\frac{1}{15} \, \log \left (b x^{5} + 3\right ) + \frac{1}{15} \, \log \left (x^{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68837, size = 47, normalized size = 2.47 \begin{align*} -\frac{1}{15} \, \log \left (b x^{5} + 3\right ) + \frac{1}{3} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.183386, size = 14, normalized size = 0.74 \begin{align*} \frac{\log{\left (x \right )}}{3} - \frac{\log{\left (x^{5} + \frac{3}{b} \right )}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.44475, size = 23, normalized size = 1.21 \begin{align*} -\frac{1}{15} \, \log \left ({\left | b x^{5} + 3 \right |}\right ) + \frac{1}{3} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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