Optimal. Leaf size=17 \[ 4 \log (x)-\frac {9}{10} \log \left (2-x^{10}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {1593, 446, 72} \begin {gather*} 4 \log (x)-\frac {9}{10} \log \left (2-x^{10}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 72
Rule 446
Rule 1593
Rubi steps
\begin {align*} \int \frac {8+5 x^{10}}{2 x-x^{11}} \, dx &=\int \frac {8+5 x^{10}}{x \left (2-x^{10}\right )} \, dx\\ &=\frac {1}{10} \operatorname {Subst}\left (\int \frac {8+5 x}{(2-x) x} \, dx,x,x^{10}\right )\\ &=\frac {1}{10} \operatorname {Subst}\left (\int \left (-\frac {9}{-2+x}+\frac {4}{x}\right ) \, dx,x,x^{10}\right )\\ &=4 \log (x)-\frac {9}{10} \log \left (2-x^{10}\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} 4 \log (x)-\frac {9}{10} \log \left (2-x^{10}\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {8+5 x^{10}}{2 x-x^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9}{10} \, \log \left (x^{10} - 2\right ) + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 16, normalized size = 0.94 \begin {gather*} \frac {2}{5} \, \log \left (x^{10}\right ) - \frac {9}{10} \, \log \left ({\left | x^{10} - 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 14, normalized size = 0.82 \begin {gather*} 4 \ln \relax (x )-\frac {9 \ln \left (x^{10}-2\right )}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.94, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9}{10} \, \log \left (x^{10} - 2\right ) + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 13, normalized size = 0.76 \begin {gather*} 4\,\ln \relax (x)-\frac {9\,\ln \left (x^{10}-2\right )}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 14, normalized size = 0.82 \begin {gather*} 4 \log {\relax (x )} - \frac {9 \log {\left (x^{10} - 2 \right )}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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