Optimal. Leaf size=27 \[ e^3-\frac {3 x^2}{\log \left (5+4 (256-x)^2\right )}-\log (x) \]
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Rubi [F] time = 1.16, 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 {-6144 x^3+24 x^4+\left (-1572894 x^2+12288 x^3-24 x^4\right ) \log \left (262149-2048 x+4 x^2\right )+\left (-262149+2048 x-4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )}{\left (262149 x-2048 x^2+4 x^3\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-6144 x^3+24 x^4+\left (-1572894 x^2+12288 x^3-24 x^4\right ) \log \left (262149-2048 x+4 x^2\right )+\left (-262149+2048 x-4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )}{x \left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx\\ &=\int \left (-\frac {1}{x}+\frac {24 (-256+x) x^2}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )}-\frac {6 x}{\log \left (262149-2048 x+4 x^2\right )}\right ) \, dx\\ &=-\log (x)-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+24 \int \frac {(-256+x) x^2}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx\\ &=-\log (x)-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+24 \int \left (\frac {64}{\log ^2\left (262149-2048 x+4 x^2\right )}+\frac {x}{4 \log ^2\left (262149-2048 x+4 x^2\right )}+\frac {-67110144+262139 x}{4 \left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )}\right ) \, dx\\ &=-\log (x)+6 \int \frac {x}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx+6 \int \frac {-67110144+262139 x}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+1536 \int \frac {1}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx\\ &=-\log (x)+6 \int \left (-\frac {67110144}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )}+\frac {262139 x}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )}\right ) \, dx+6 \int \frac {x}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+1536 \int \frac {1}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx\\ &=-\log (x)+6 \int \frac {x}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+1536 \int \frac {1}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx+1572834 \int \frac {x}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx-402660864 \int \frac {1}{\left (262149-2048 x+4 x^2\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx\\ &=-\log (x)+6 \int \frac {x}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+1536 \int \frac {1}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx+1572834 \int \left (\frac {1-\frac {512 i}{\sqrt {5}}}{\left (-2048-4 i \sqrt {5}+8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )}+\frac {1+\frac {512 i}{\sqrt {5}}}{\left (-2048+4 i \sqrt {5}+8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )}\right ) \, dx-402660864 \int \left (\frac {2 i}{\sqrt {5} \left (2048+4 i \sqrt {5}-8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )}+\frac {2 i}{\sqrt {5} \left (-2048+4 i \sqrt {5}+8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )}\right ) \, dx\\ &=-\log (x)+6 \int \frac {x}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx-6 \int \frac {x}{\log \left (262149-2048 x+4 x^2\right )} \, dx+1536 \int \frac {1}{\log ^2\left (262149-2048 x+4 x^2\right )} \, dx-\frac {(805321728 i) \int \frac {1}{\left (2048+4 i \sqrt {5}-8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx}{\sqrt {5}}-\frac {(805321728 i) \int \frac {1}{\left (-2048+4 i \sqrt {5}+8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx}{\sqrt {5}}+\frac {1}{5} \left (1572834 \left (5-512 i \sqrt {5}\right )\right ) \int \frac {1}{\left (-2048-4 i \sqrt {5}+8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx+\frac {1}{5} \left (1572834 \left (5+512 i \sqrt {5}\right )\right ) \int \frac {1}{\left (-2048+4 i \sqrt {5}+8 x\right ) \log ^2\left (262149-2048 x+4 x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.30, size = 23, normalized size = 0.85 \begin {gather*} -\log (x)-\frac {3 x^2}{\log \left (262149-2048 x+4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 35, normalized size = 1.30 \begin {gather*} -\frac {3 \, x^{2} + \log \left (4 \, x^{2} - 2048 \, x + 262149\right ) \log \relax (x)}{\log \left (4 \, x^{2} - 2048 \, x + 262149\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 23, normalized size = 0.85 \begin {gather*} -\frac {3 \, x^{2}}{\log \left (4 \, x^{2} - 2048 \, x + 262149\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 0.89
method | result | size |
norman | \(-\frac {3 x^{2}}{\ln \left (4 x^{2}-2048 x +262149\right )}-\ln \relax (x )\) | \(24\) |
risch | \(-\frac {3 x^{2}}{\ln \left (4 x^{2}-2048 x +262149\right )}-\ln \relax (x )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 23, normalized size = 0.85 \begin {gather*} -\frac {3 \, x^{2}}{\log \left (4 \, x^{2} - 2048 \, x + 262149\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.61, size = 72, normalized size = 2.67 \begin {gather*} 768\,x-\ln \relax (x)-\frac {960}{x-256}-\frac {3\,x^2-\frac {3\,x\,\ln \left (4\,x^2-2048\,x+262149\right )\,\left (4\,x^2-2048\,x+262149\right )}{4\,\left (x-256\right )}}{\ln \left (4\,x^2-2048\,x+262149\right )}-3\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 20, normalized size = 0.74 \begin {gather*} - \frac {3 x^{2}}{\log {\left (4 x^{2} - 2048 x + 262149 \right )}} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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