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 = 0.02, antiderivative size = 28, normalized size of antiderivative = 1.00, 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 44
Rule 266
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*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.00 \[ \frac {1}{45} b \log \left (b x^5+3\right )-\frac {1}{9} b \log (x)-\frac {1}{15 x^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 28, normalized size = 1.00 \[ \frac {b x^{5} \log \left (b x^{5} + 3\right ) - 5 \, b x^{5} \log \relax (x) - 3}{45 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.52, size = 31, normalized size = 1.11 \[ \frac {1}{45} \, b \log \left ({\left | b x^{5} + 3 \right |}\right ) - \frac {1}{9} \, b \log \left ({\left | x \right |}\right ) + \frac {b x^{5} - 3}{45 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 23, normalized size = 0.82 \[ -\frac {b \ln \relax (x )}{9}+\frac {b \ln \left (b \,x^{5}+3\right )}{45}-\frac {1}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 24, normalized size = 0.86 \[ \frac {1}{45} \, b \log \left (b x^{5} + 3\right ) - \frac {1}{45} \, b \log \left (x^{5}\right ) - \frac {1}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 22, normalized size = 0.79 \[ \frac {b\,\ln \left (b\,x^5+3\right )}{45}-\frac {b\,\ln \relax (x)}{9}-\frac {1}{15\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.88, size = 24, normalized size = 0.86 \[ - \frac {b \log {\relax (x )}}{9} + \frac {b \log {\left (x^{5} + \frac {3}{b} \right )}}{45} - \frac {1}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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