Optimal. Leaf size=29 \[ -\frac {5 x \log (\log (x))}{\left (3 \left (4+e^4\right )^2-x\right ) (-x+\log (5))} \]
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Rubi [F]
time = 1.45, 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 {240 x+120 e^4 x+15 e^8 x-5 x^2+\left (-240-120 e^4-15 e^8+5 x\right ) \log (5)+\left (5 x^2+\left (-240-120 e^4-15 e^8\right ) \log (5)\right ) \log (x) \log (\log (x))}{\left (2304 x^2+144 e^{12} x^2+9 e^{16} x^2-96 x^3+x^4+e^4 \left (2304 x^2-48 x^3\right )+e^8 \left (864 x^2-6 x^3\right )+\left (-4608 x-288 e^{12} x-18 e^{16} x+192 x^2-2 x^3+e^8 \left (-1728 x+12 x^2\right )+e^4 \left (-4608 x+96 x^2\right )\right ) \log (5)+\left (2304+144 e^{12}+9 e^{16}+e^4 (2304-48 x)+e^8 (864-6 x)-96 x+x^2\right ) \log ^2(5)\right ) \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 {240 x+120 e^4 x+15 e^8 x-5 x^2+\left (-240-120 e^4-15 e^8+5 x\right ) \log (5)+\left (5 x^2+\left (-240-120 e^4-15 e^8\right ) \log (5)\right ) \log (x) \log (\log (x))}{\left (9 e^{16} x^2+\left (2304+144 e^{12}\right ) x^2-96 x^3+x^4+e^4 \left (2304 x^2-48 x^3\right )+e^8 \left (864 x^2-6 x^3\right )+\left (-4608 x-288 e^{12} x-18 e^{16} x+192 x^2-2 x^3+e^8 \left (-1728 x+12 x^2\right )+e^4 \left (-4608 x+96 x^2\right )\right ) \log (5)+\left (2304+144 e^{12}+9 e^{16}+e^4 (2304-48 x)+e^8 (864-6 x)-96 x+x^2\right ) \log ^2(5)\right ) \log (x)} \, dx\\ &=\int \frac {240 x+120 e^4 x+15 e^8 x-5 x^2+\left (-240-120 e^4-15 e^8+5 x\right ) \log (5)+\left (5 x^2+\left (-240-120 e^4-15 e^8\right ) \log (5)\right ) \log (x) \log (\log (x))}{\left (\left (2304+144 e^{12}+9 e^{16}\right ) x^2-96 x^3+x^4+e^4 \left (2304 x^2-48 x^3\right )+e^8 \left (864 x^2-6 x^3\right )+\left (-4608 x-288 e^{12} x-18 e^{16} x+192 x^2-2 x^3+e^8 \left (-1728 x+12 x^2\right )+e^4 \left (-4608 x+96 x^2\right )\right ) \log (5)+\left (2304+144 e^{12}+9 e^{16}+e^4 (2304-48 x)+e^8 (864-6 x)-96 x+x^2\right ) \log ^2(5)\right ) \log (x)} \, dx\\ &=\int \frac {15 e^8 x+\left (240+120 e^4\right ) x-5 x^2+\left (-240-120 e^4-15 e^8+5 x\right ) \log (5)+\left (5 x^2+\left (-240-120 e^4-15 e^8\right ) \log (5)\right ) \log (x) \log (\log (x))}{\left (\left (2304+144 e^{12}+9 e^{16}\right ) x^2-96 x^3+x^4+e^4 \left (2304 x^2-48 x^3\right )+e^8 \left (864 x^2-6 x^3\right )+\left (-4608 x-288 e^{12} x-18 e^{16} x+192 x^2-2 x^3+e^8 \left (-1728 x+12 x^2\right )+e^4 \left (-4608 x+96 x^2\right )\right ) \log (5)+\left (2304+144 e^{12}+9 e^{16}+e^4 (2304-48 x)+e^8 (864-6 x)-96 x+x^2\right ) \log ^2(5)\right ) \log (x)} \, dx\\ &=\int \frac {\left (240+120 e^4+15 e^8\right ) x-5 x^2+\left (-240-120 e^4-15 e^8+5 x\right ) \log (5)+\left (5 x^2+\left (-240-120 e^4-15 e^8\right ) \log (5)\right ) \log (x) \log (\log (x))}{\left (\left (2304+144 e^{12}+9 e^{16}\right ) x^2-96 x^3+x^4+e^4 \left (2304 x^2-48 x^3\right )+e^8 \left (864 x^2-6 x^3\right )+\left (-4608 x-288 e^{12} x-18 e^{16} x+192 x^2-2 x^3+e^8 \left (-1728 x+12 x^2\right )+e^4 \left (-4608 x+96 x^2\right )\right ) \log (5)+\left (2304+144 e^{12}+9 e^{16}+e^4 (2304-48 x)+e^8 (864-6 x)-96 x+x^2\right ) \log ^2(5)\right ) \log (x)} \, dx\\ &=\int \frac {5 \left (\left (48+24 e^4+3 e^8-x\right ) (x-\log (5))+\left (x^2-3 \left (4+e^4\right )^2 \log (5)\right ) \log (x) \log (\log (x))\right )}{\left (48+24 e^4+3 e^8-x\right )^2 (x-\log (5))^2 \log (x)} \, dx\\ &=5 \int \frac {\left (48+24 e^4+3 e^8-x\right ) (x-\log (5))+\left (x^2-3 \left (4+e^4\right )^2 \log (5)\right ) \log (x) \log (\log (x))}{\left (48+24 e^4+3 e^8-x\right )^2 (x-\log (5))^2 \log (x)} \, dx\\ &=5 \int \left (\frac {1}{\left (48+24 e^4+3 e^8-x\right ) (x-\log (5)) \log (x)}-\frac {\left (-x^2+48 \log (5)+24 e^4 \log (5)+3 e^8 \log (5)\right ) \log (\log (x))}{\left (48+24 e^4+3 e^8-x\right )^2 (x-\log (5))^2}\right ) \, dx\\ &=5 \int \frac {1}{\left (48+24 e^4+3 e^8-x\right ) (x-\log (5)) \log (x)} \, dx-5 \int \frac {\left (-x^2+48 \log (5)+24 e^4 \log (5)+3 e^8 \log (5)\right ) \log (\log (x))}{\left (48+24 e^4+3 e^8-x\right )^2 (x-\log (5))^2} \, dx\\ &=5 \int \frac {1}{\left (48+24 e^4+3 e^8-x\right ) (x-\log (5)) \log (x)} \, dx-5 \int \frac {\left (-x^2+3 \left (4+e^4\right )^2 \log (5)\right ) \log (\log (x))}{\left (48+24 e^4+3 e^8-x\right )^2 (x-\log (5))^2} \, dx\\ &=5 \int \frac {1}{\left (48+24 e^4+3 e^8-x\right ) (x-\log (5)) \log (x)} \, dx-5 \int \left (-\frac {3 \left (4+e^4\right )^2 \log (\log (x))}{\left (48+24 e^4+3 e^8-x\right )^2 \left (48+24 e^4+3 e^8-\log (5)\right )}+\frac {\log (5) \log (\log (x))}{\left (48+24 e^4+3 e^8-\log (5)\right ) (-x+\log (5))^2}\right ) \, dx\\ &=5 \int \frac {1}{\left (48+24 e^4+3 e^8-x\right ) (x-\log (5)) \log (x)} \, dx+\frac {\left (15 \left (4+e^4\right )^2\right ) \int \frac {\log (\log (x))}{\left (48+24 e^4+3 e^8-x\right )^2} \, dx}{48+24 e^4+3 e^8-\log (5)}-\frac {(5 \log (5)) \int \frac {\log (\log (x))}{(-x+\log (5))^2} \, dx}{48+24 e^4+3 e^8-\log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 31, normalized size = 1.07 \begin {gather*} \frac {5 x \log (\log (x))}{\left (48+24 e^4+3 e^8-x\right ) (x-\log (5))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 29.39, size = 47, normalized size = 1.62
method | result | size |
risch | \(-\frac {5 x \ln \left (\ln \left (x \right )\right )}{3 \ln \left (5\right ) {\mathrm e}^{8}-3 x \,{\mathrm e}^{8}+24 \,{\mathrm e}^{4} \ln \left (5\right )-x \ln \left (5\right )-24 x \,{\mathrm e}^{4}+x^{2}+48 \ln \left (5\right )-48 x}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 43, normalized size = 1.48 \begin {gather*} -\frac {5 \, x \log \left (\log \left (x\right )\right )}{x^{2} - x {\left (3 \, e^{8} + 24 \, e^{4} + \log \left (5\right ) + 48\right )} + 3 \, e^{8} \log \left (5\right ) + 24 \, e^{4} \log \left (5\right ) + 48 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 40, normalized size = 1.38 \begin {gather*} -\frac {5 \, x \log \left (\log \left (x\right )\right )}{x^{2} - 3 \, x e^{8} - 24 \, x e^{4} - {\left (x - 3 \, e^{8} - 24 \, e^{4} - 48\right )} \log \left (5\right ) - 48 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 56 vs.
\(2 (24) = 48\).
time = 0.39, size = 56, normalized size = 1.93 \begin {gather*} - \frac {5 x \log {\left (\log {\left (x \right )} \right )}}{x^{2} - 3 x e^{8} - 24 x e^{4} - 48 x - x \log {\left (5 \right )} + 48 \log {\left (5 \right )} + 24 e^{4} \log {\left (5 \right )} + 3 e^{8} \log {\left (5 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.40, size = 46, normalized size = 1.59 \begin {gather*} -\frac {5 \, x \log \left (\log \left (x\right )\right )}{x^{2} - 3 \, x e^{8} - 24 \, x e^{4} - x \log \left (5\right ) + 3 \, e^{8} \log \left (5\right ) + 24 \, e^{4} \log \left (5\right ) - 48 \, x + 48 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {240\,x+120\,x\,{\mathrm {e}}^4+15\,x\,{\mathrm {e}}^8-\ln \left (5\right )\,\left (120\,{\mathrm {e}}^4-5\,x+15\,{\mathrm {e}}^8+240\right )-5\,x^2-\ln \left (\ln \left (x\right )\right )\,\ln \left (x\right )\,\left (\ln \left (5\right )\,\left (120\,{\mathrm {e}}^4+15\,{\mathrm {e}}^8+240\right )-5\,x^2\right )}{\ln \left (x\right )\,\left ({\mathrm {e}}^8\,\left (864\,x^2-6\,x^3\right )-\ln \left (5\right )\,\left (4608\,x+{\mathrm {e}}^8\,\left (1728\,x-12\,x^2\right )+{\mathrm {e}}^4\,\left (4608\,x-96\,x^2\right )+288\,x\,{\mathrm {e}}^{12}+18\,x\,{\mathrm {e}}^{16}-192\,x^2+2\,x^3\right )+{\mathrm {e}}^4\,\left (2304\,x^2-48\,x^3\right )+144\,x^2\,{\mathrm {e}}^{12}+9\,x^2\,{\mathrm {e}}^{16}+{\ln \left (5\right )}^2\,\left (144\,{\mathrm {e}}^{12}-96\,x+9\,{\mathrm {e}}^{16}+x^2-{\mathrm {e}}^8\,\left (6\,x-864\right )-{\mathrm {e}}^4\,\left (48\,x-2304\right )+2304\right )+2304\,x^2-96\,x^3+x^4\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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