Optimal. Leaf size=24 \[ \log \left (x+\left (3-x^2 \left (x+e^4 x\right )\right ) \log (5)-\log (x)\right ) \]
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Rubi [F] time = 0.48, 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 {1-x+\left (3 x^3+3 e^4 x^3\right ) \log (5)}{-x^2+\left (-3 x+x^4+e^4 x^4\right ) \log (5)+x \log (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 {-1+x-3 \left (1+e^4\right ) x^3 \log (5)}{x^2-\left (-3 x+x^4+e^4 x^4\right ) \log (5)-x \log (x)} \, dx\\ &=\int \left (\frac {3 \left (-1-e^4\right ) x^2 \log (5)}{x+3 \log (5)-\left (1+e^4\right ) x^3 \log (5)-\log (x)}+\frac {1}{x-\left (1+e^4\right ) x^3 \log (5)+\log (125)-\log (x)}+\frac {1}{x \left (-x-3 \log (5)+\left (1+e^4\right ) x^3 \log (5)+\log (x)\right )}\right ) \, dx\\ &=-\left (\left (3 \left (1+e^4\right ) \log (5)\right ) \int \frac {x^2}{x+3 \log (5)-\left (1+e^4\right ) x^3 \log (5)-\log (x)} \, dx\right )+\int \frac {1}{x-\left (1+e^4\right ) x^3 \log (5)+\log (125)-\log (x)} \, dx+\int \frac {1}{x \left (-x-3 \log (5)+\left (1+e^4\right ) x^3 \log (5)+\log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.48, size = 26, normalized size = 1.08 \begin {gather*} \log \left (-x-3 \log (5)+x^3 \log (5)+e^4 x^3 \log (5)+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 21, normalized size = 0.88 \begin {gather*} \log \left ({\left (x^{3} e^{4} + x^{3} - 3\right )} \log \relax (5) - x + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 27, normalized size = 1.12 \begin {gather*} \log \left (-x^{3} e^{4} \log \relax (5) - x^{3} \log \relax (5) + x + 3 \, \log \relax (5) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 26, normalized size = 1.08
method | result | size |
norman | \(\ln \left (\ln \relax (5) {\mathrm e}^{4} x^{3}+x^{3} \ln \relax (5)+\ln \relax (x )-3 \ln \relax (5)-x \right )\) | \(26\) |
risch | \(\ln \left (\ln \relax (5) {\mathrm e}^{4} x^{3}+x^{3} \ln \relax (5)+\ln \relax (x )-3 \ln \relax (5)-x \right )\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 23, normalized size = 0.96 \begin {gather*} \log \left ({\left (e^{4} \log \relax (5) + \log \relax (5)\right )} x^{3} - x - 3 \, \log \relax (5) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.76, size = 21, normalized size = 0.88 \begin {gather*} \ln \left (\ln \relax (x)-3\,\ln \relax (5)-x+x^3\,\ln \relax (5)\,\left ({\mathrm {e}}^4+1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 27, normalized size = 1.12 \begin {gather*} \log {\left (x^{3} \log {\relax (5 )} + x^{3} e^{4} \log {\relax (5 )} - x + \log {\relax (x )} - 3 \log {\relax (5 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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