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 = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, 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 44
Rule 266
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*}
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Mathematica [A] time = 0.00, size = 33, normalized size = 1.00 \[ -\frac {1}{10 b x^5}+\frac {\log \left (x^5+2\right )}{20 b}-\frac {\log (x)}{4 b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 27, normalized size = 0.82 \[ \frac {x^{5} \log \left (x^{5} + 2\right ) - 5 \, x^{5} \log \relax (x) - 2}{20 \, b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 34, normalized size = 1.03 \[ \frac {\log \left ({\left | x^{5} + 2 \right |}\right )}{20 \, b} - \frac {\log \left ({\left | x \right |}\right )}{4 \, b} + \frac {x^{5} - 2}{20 \, b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 0.85 \[ -\frac {\ln \relax (x )}{4 b}+\frac {\ln \left (x^{5}+2\right )}{20 b}-\frac {1}{10 b \,x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.07, size = 29, normalized size = 0.88 \[ \frac {\log \left (x^{5} + 2\right )}{20 \, b} - \frac {\log \left (x^{5}\right )}{20 \, b} - \frac {1}{10 \, b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 27, normalized size = 0.82 \[ \frac {\ln \left (x^5+2\right )}{20\,b}-\frac {\ln \relax (x)}{4\,b}-\frac {1}{10\,b\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.42, size = 24, normalized size = 0.73 \[ - \frac {\log {\relax (x )}}{4 b} + \frac {\log {\left (x^{5} + 2 \right )}}{20 b} - \frac {1}{10 b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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