Optimal. Leaf size=41 \[ -\frac {1}{18 x^6}+\frac {4}{27 x^3}-\frac {1}{6} \log \left (x^3+1\right )+\frac {1}{162} \log \left (x^3+3\right )+\frac {13 \log (x)}{27} \]
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Rubi [A] time = 0.04, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {1357, 709, 800} \[ \frac {4}{27 x^3}-\frac {1}{18 x^6}-\frac {1}{6} \log \left (x^3+1\right )+\frac {1}{162} \log \left (x^3+3\right )+\frac {13 \log (x)}{27} \]
Antiderivative was successfully verified.
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Rule 709
Rule 800
Rule 1357
Rubi steps
\begin {align*} \int \frac {1}{x^7 \left (3+4 x^3+x^6\right )} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {1}{x^3 \left (3+4 x+x^2\right )} \, dx,x,x^3\right )\\ &=-\frac {1}{18 x^6}+\frac {1}{9} \operatorname {Subst}\left (\int \frac {-4-x}{x^2 \left (3+4 x+x^2\right )} \, dx,x,x^3\right )\\ &=-\frac {1}{18 x^6}+\frac {1}{9} \operatorname {Subst}\left (\int \left (-\frac {4}{3 x^2}+\frac {13}{9 x}-\frac {3}{2 (1+x)}+\frac {1}{18 (3+x)}\right ) \, dx,x,x^3\right )\\ &=-\frac {1}{18 x^6}+\frac {4}{27 x^3}+\frac {13 \log (x)}{27}-\frac {1}{6} \log \left (1+x^3\right )+\frac {1}{162} \log \left (3+x^3\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 41, normalized size = 1.00 \[ -\frac {1}{18 x^6}+\frac {4}{27 x^3}-\frac {1}{6} \log \left (x^3+1\right )+\frac {1}{162} \log \left (x^3+3\right )+\frac {13 \log (x)}{27} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 40, normalized size = 0.98 \[ \frac {x^{6} \log \left (x^{3} + 3\right ) - 27 \, x^{6} \log \left (x^{3} + 1\right ) + 78 \, x^{6} \log \relax (x) + 24 \, x^{3} - 9}{162 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 41, normalized size = 1.00 \[ -\frac {13 \, x^{6} - 8 \, x^{3} + 3}{54 \, x^{6}} + \frac {1}{162} \, \log \left ({\left | x^{3} + 3 \right |}\right ) - \frac {1}{6} \, \log \left ({\left | x^{3} + 1 \right |}\right ) + \frac {13}{27} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 41, normalized size = 1.00 \[ \frac {13 \ln \relax (x )}{27}-\frac {\ln \left (x +1\right )}{6}+\frac {\ln \left (x^{3}+3\right )}{162}-\frac {\ln \left (x^{2}-x +1\right )}{6}+\frac {4}{27 x^{3}}-\frac {1}{18 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 35, normalized size = 0.85 \[ \frac {8 \, x^{3} - 3}{54 \, x^{6}} + \frac {1}{162} \, \log \left (x^{3} + 3\right ) - \frac {1}{6} \, \log \left (x^{3} + 1\right ) + \frac {13}{81} \, \log \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 32, normalized size = 0.78 \[ \frac {\ln \left (x^3+3\right )}{162}-\frac {\ln \left (x^3+1\right )}{6}+\frac {13\,\ln \relax (x)}{27}+\frac {\frac {4\,x^3}{27}-\frac {1}{18}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 34, normalized size = 0.83 \[ \frac {13 \log {\relax (x )}}{27} - \frac {\log {\left (x^{3} + 1 \right )}}{6} + \frac {\log {\left (x^{3} + 3 \right )}}{162} + \frac {8 x^{3} - 3}{54 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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