Optimal. Leaf size=27 \[ \frac {1}{5} \left (x+\frac {5 x \left (x+x^4+\log (4)\right )}{(1+x) \log (-x)}\right ) \]
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Rubi [F] time = 0.24, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-5 x-5 x^2-5 x^4-5 x^5+(-5-5 x) \log (4)+\left (10 x+5 x^2+25 x^4+20 x^5+5 \log (4)\right ) \log (-x)+\left (1+2 x+x^2\right ) \log ^2(-x)}{\left (5+10 x+5 x^2\right ) \log ^2(-x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-5 x-5 x^2-5 x^4-5 x^5+(-5-5 x) \log (4)+\left (10 x+5 x^2+25 x^4+20 x^5+5 \log (4)\right ) \log (-x)+\left (1+2 x+x^2\right ) \log ^2(-x)}{5 (1+x)^2 \log ^2(-x)} \, dx\\ &=\frac {1}{5} \int \frac {-5 x-5 x^2-5 x^4-5 x^5+(-5-5 x) \log (4)+\left (10 x+5 x^2+25 x^4+20 x^5+5 \log (4)\right ) \log (-x)+\left (1+2 x+x^2\right ) \log ^2(-x)}{(1+x)^2 \log ^2(-x)} \, dx\\ &=\frac {1}{5} \int \left (1-\frac {5 \left (x+x^4+\log (4)\right )}{(1+x) \log ^2(-x)}+\frac {5 \left (2 x+x^2+5 x^4+4 x^5+\log (4)\right )}{(1+x)^2 \log (-x)}\right ) \, dx\\ &=\frac {x}{5}-\int \frac {x+x^4+\log (4)}{(1+x) \log ^2(-x)} \, dx+\int \frac {2 x+x^2+5 x^4+4 x^5+\log (4)}{(1+x)^2 \log (-x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.68, size = 26, normalized size = 0.96 \begin {gather*} \frac {x}{5}+\frac {x \left (x+x^4+\log (4)\right )}{(1+x) \log (-x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 39, normalized size = 1.44 \begin {gather*} \frac {5 \, x^{5} + 5 \, x^{2} + 10 \, x \log \relax (2) + {\left (x^{2} + x\right )} \log \left (-x\right )}{5 \, {\left (x + 1\right )} \log \left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 30, normalized size = 1.11 \begin {gather*} \frac {1}{5} \, x + \frac {x^{5} + x^{2} + 2 \, x \log \relax (2)}{x \log \left (-x\right ) + \log \left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 27, normalized size = 1.00
method | result | size |
risch | \(\frac {x \left (2 \ln \relax (2)+x^{4}+x \right )}{\left (x +1\right ) \ln \left (-x \right )}+\frac {x}{5}\) | \(27\) |
norman | \(\frac {x^{2}+x^{5}-\frac {\ln \left (-x \right )}{5}+2 x \ln \relax (2)+\frac {\ln \left (-x \right ) x^{2}}{5}}{\left (x +1\right ) \ln \left (-x \right )}\) | \(40\) |
derivativedivides | \(\frac {x}{5}-\frac {-10 x \ln \relax (2)-10 x^{2} \ln \relax (2)}{5 \left (-x -1\right )^{2} \ln \left (-x \right )}+\frac {x^{4}}{\ln \left (-x \right )}-\frac {x^{3}}{\ln \left (-x \right )}+\frac {x^{2}}{\ln \left (-x \right )}\) | \(64\) |
default | \(\frac {x}{5}-\frac {-10 x \ln \relax (2)-10 x^{2} \ln \relax (2)}{5 \left (-x -1\right )^{2} \ln \left (-x \right )}+\frac {x^{4}}{\ln \left (-x \right )}-\frac {x^{3}}{\ln \left (-x \right )}+\frac {x^{2}}{\ln \left (-x \right )}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 39, normalized size = 1.44 \begin {gather*} \frac {5 \, x^{5} + 5 \, x^{2} + 10 \, x \log \relax (2) + {\left (x^{2} + x\right )} \log \left (-x\right )}{5 \, {\left (x + 1\right )} \log \left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.23, size = 31, normalized size = 1.15 \begin {gather*} \frac {x}{5}+\frac {x\,\left (5\,x^4+5\,x+10\,\ln \relax (2)\right )}{5\,\ln \left (-x\right )\,\left (x+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 24, normalized size = 0.89 \begin {gather*} \frac {x}{5} + \frac {x^{5} + x^{2} + 2 x \log {\relax (2 )}}{\left (x + 1\right ) \log {\left (- x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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