Optimal. Leaf size=20 \[ -x+\frac {x}{e^4}+\frac {\log \left (\log \left (x^2\right )\right )}{-4+x} \]
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Rubi [F] time = 0.36, 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 {e^4 (-8+2 x)+\left (16 x-8 x^2+x^3+e^4 \left (-16 x+8 x^2-x^3\right )\right ) \log \left (x^2\right )-e^4 x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{e^4 \left (16 x-8 x^2+x^3\right ) \log \left (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} &=\frac {\int \frac {e^4 (-8+2 x)+\left (16 x-8 x^2+x^3+e^4 \left (-16 x+8 x^2-x^3\right )\right ) \log \left (x^2\right )-e^4 x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{\left (16 x-8 x^2+x^3\right ) \log \left (x^2\right )} \, dx}{e^4}\\ &=\frac {\int \frac {e^4 (-8+2 x)+\left (16 x-8 x^2+x^3+e^4 \left (-16 x+8 x^2-x^3\right )\right ) \log \left (x^2\right )-e^4 x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{x \left (16-8 x+x^2\right ) \log \left (x^2\right )} \, dx}{e^4}\\ &=\frac {\int \frac {e^4 (-8+2 x)+\left (16 x-8 x^2+x^3+e^4 \left (-16 x+8 x^2-x^3\right )\right ) \log \left (x^2\right )-e^4 x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{(-4+x)^2 x \log \left (x^2\right )} \, dx}{e^4}\\ &=\frac {\int \left (1-e^4+\frac {2 e^4}{(-4+x) x \log \left (x^2\right )}-\frac {e^4 \log \left (\log \left (x^2\right )\right )}{(-4+x)^2}\right ) \, dx}{e^4}\\ &=-\left (\left (1-\frac {1}{e^4}\right ) x\right )+2 \int \frac {1}{(-4+x) x \log \left (x^2\right )} \, dx-\int \frac {\log \left (\log \left (x^2\right )\right )}{(-4+x)^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 19, normalized size = 0.95 \begin {gather*} \left (-1+\frac {1}{e^4}\right ) x+\frac {\log \left (\log \left (x^2\right )\right )}{-4+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 34, normalized size = 1.70 \begin {gather*} \frac {{\left (x^{2} - {\left (x^{2} - 4 \, x\right )} e^{4} + e^{4} \log \left (\log \left (x^{2}\right )\right ) - 4 \, x\right )} e^{\left (-4\right )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 38, normalized size = 1.90 \begin {gather*} -\frac {{\left (x^{2} e^{4} - x^{2} - 4 \, x e^{4} - e^{4} \log \left (\log \left (x^{2}\right )\right ) + 4 \, x\right )} e^{\left (-4\right )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\left (-x \,{\mathrm e}^{4} \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )+\left (\left (-x^{3}+8 x^{2}-16 x \right ) {\mathrm e}^{4}+x^{3}-8 x^{2}+16 x \right ) \ln \left (x^{2}\right )+\left (2 x -8\right ) {\mathrm e}^{4}\right ) {\mathrm e}^{-4}}{\left (x^{3}-8 x^{2}+16 x \right ) \ln \left (x^{2}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 38, normalized size = 1.90 \begin {gather*} -\frac {{\left (x^{2} {\left (e^{4} - 1\right )} - 4 \, x {\left (e^{4} - 1\right )} - e^{4} \log \relax (2) - e^{4} \log \left (\log \relax (x)\right )\right )} e^{\left (-4\right )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.29, size = 18, normalized size = 0.90 \begin {gather*} \frac {\ln \left (\ln \left (x^2\right )\right )}{x-4}+x\,\left ({\mathrm {e}}^{-4}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 19, normalized size = 0.95 \begin {gather*} \frac {x \left (1 - e^{4}\right )}{e^{4}} + \frac {\log {\left (\log {\left (x^{2} \right )} \right )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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