Optimal. Leaf size=28 \[ \frac{1}{45} b \log \left (b x^5+3\right )-\frac{1}{9} b \log (x)-\frac{1}{15 x^5} \]
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Rubi [A] time = 0.0185472, antiderivative size = 28, 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, 44} \[ \frac{1}{45} b \log \left (b x^5+3\right )-\frac{1}{9} b \log (x)-\frac{1}{15 x^5} \]
Antiderivative was successfully verified.
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Rule 266
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^6 \left (3+b x^5\right )} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{1}{x^2 (3+b x)} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{1}{3 x^2}-\frac{b}{9 x}+\frac{b^2}{9 (3+b x)}\right ) \, dx,x,x^5\right )\\ &=-\frac{1}{15 x^5}-\frac{1}{9} b \log (x)+\frac{1}{45} b \log \left (3+b x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0044286, size = 28, normalized size = 1. \[ \frac{1}{45} b \log \left (b x^5+3\right )-\frac{1}{9} b \log (x)-\frac{1}{15 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 23, normalized size = 0.8 \begin{align*} -{\frac{1}{15\,{x}^{5}}}-{\frac{b\ln \left ( x \right ) }{9}}+{\frac{b\ln \left ( b{x}^{5}+3 \right ) }{45}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06359, size = 32, normalized size = 1.14 \begin{align*} \frac{1}{45} \, b \log \left (b x^{5} + 3\right ) - \frac{1}{45} \, b \log \left (x^{5}\right ) - \frac{1}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.71815, size = 73, normalized size = 2.61 \begin{align*} \frac{b x^{5} \log \left (b x^{5} + 3\right ) - 5 \, b x^{5} \log \left (x\right ) - 3}{45 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.82268, size = 24, normalized size = 0.86 \begin{align*} - \frac{b \log{\left (x \right )}}{9} + \frac{b \log{\left (x^{5} + \frac{3}{b} \right )}}{45} - \frac{1}{15 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.38326, size = 42, normalized size = 1.5 \begin{align*} \frac{1}{45} \, b \log \left ({\left | b x^{5} + 3 \right |}\right ) - \frac{1}{9} \, b \log \left ({\left | x \right |}\right ) + \frac{b x^{5} - 3}{45 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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