Optimal. Leaf size=29 \[ \frac {4 \left (-e^x+2 x+x^4\right )^2 \log ^2(3) \log ^2(x)}{(-3+x)^2} \]
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Rubi [F] time = 12.84, 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 {\left (e^{2 x} (-24+8 x) \log ^2(3)+e^x \left (96 x-32 x^2+48 x^4-16 x^5\right ) \log ^2(3)+\left (-96 x^2+32 x^3-96 x^5+32 x^6-24 x^8+8 x^9\right ) \log ^2(3)\right ) \log (x)+\left (e^{2 x} \left (-32 x+8 x^2\right ) \log ^2(3)+e^x \left (48 x+64 x^2-16 x^3+96 x^4+8 x^5-8 x^6\right ) \log ^2(3)+\left (-96 x^2-240 x^5+48 x^6-96 x^8+24 x^9\right ) \log ^2(3)\right ) \log ^2(x)}{-27 x+27 x^2-9 x^3+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 \left (e^x-x \left (2+x^3\right )\right ) \log ^2(3) \log (x) \left (-\left ((-3+x) \left (e^x-x \left (2+x^3\right )\right )\right )-x \left (6+e^x (-4+x)+12 x^3-3 x^4\right ) \log (x)\right )}{(3-x)^3 x} \, dx\\ &=\left (8 \log ^2(3)\right ) \int \frac {\left (e^x-x \left (2+x^3\right )\right ) \log (x) \left (-\left ((-3+x) \left (e^x-x \left (2+x^3\right )\right )\right )-x \left (6+e^x (-4+x)+12 x^3-3 x^4\right ) \log (x)\right )}{(3-x)^3 x} \, dx\\ &=\left (8 \log ^2(3)\right ) \int \left (\frac {x \left (2+x^3\right )^2 \log (x)}{(-3+x)^2}-\frac {6 x \left (2+x^3\right ) \log ^2(x)}{(-3+x)^3}-\frac {12 x^4 \left (2+x^3\right ) \log ^2(x)}{(-3+x)^3}+\frac {3 x^5 \left (2+x^3\right ) \log ^2(x)}{(-3+x)^3}+\frac {e^{2 x} \log (x) \left (-3+x-4 x \log (x)+x^2 \log (x)\right )}{(-3+x)^3 x}-\frac {e^x \log (x) \left (-12+4 x-6 x^3+2 x^4-6 \log (x)-8 x \log (x)+2 x^2 \log (x)-12 x^3 \log (x)-x^4 \log (x)+x^5 \log (x)\right )}{(-3+x)^3}\right ) \, dx\\ &=\left (8 \log ^2(3)\right ) \int \frac {x \left (2+x^3\right )^2 \log (x)}{(-3+x)^2} \, dx+\left (8 \log ^2(3)\right ) \int \frac {e^{2 x} \log (x) \left (-3+x-4 x \log (x)+x^2 \log (x)\right )}{(-3+x)^3 x} \, dx-\left (8 \log ^2(3)\right ) \int \frac {e^x \log (x) \left (-12+4 x-6 x^3+2 x^4-6 \log (x)-8 x \log (x)+2 x^2 \log (x)-12 x^3 \log (x)-x^4 \log (x)+x^5 \log (x)\right )}{(-3+x)^3} \, dx+\left (24 \log ^2(3)\right ) \int \frac {x^5 \left (2+x^3\right ) \log ^2(x)}{(-3+x)^3} \, dx-\left (48 \log ^2(3)\right ) \int \frac {x \left (2+x^3\right ) \log ^2(x)}{(-3+x)^3} \, dx-\left (96 \log ^2(3)\right ) \int \frac {x^4 \left (2+x^3\right ) \log ^2(x)}{(-3+x)^3} \, dx\\ &=\left (8 \log ^2(3)\right ) \int \left (1566 \log (x)+\frac {2523 \log (x)}{(-3+x)^2}+\frac {5539 \log (x)}{-3+x}+429 x \log (x)+112 x^2 \log (x)+27 x^3 \log (x)+6 x^4 \log (x)+x^5 \log (x)\right ) \, dx+\left (8 \log ^2(3)\right ) \int \left (\frac {e^{2 x} \log (x)}{(-3+x)^2 x}+\frac {e^{2 x} (-4+x) \log ^2(x)}{(-3+x)^3}\right ) \, dx-\left (8 \log ^2(3)\right ) \int \left (\frac {2 e^x \left (2+x^3\right ) \log (x)}{(-3+x)^2}+\frac {e^x \left (-6-8 x+2 x^2-12 x^3-x^4+x^5\right ) \log ^2(x)}{(-3+x)^3}\right ) \, dx+\left (24 \log ^2(3)\right ) \int \left (5211 \log ^2(x)+\frac {7047 \log ^2(x)}{(-3+x)^3}+\frac {18306 \log ^2(x)}{(-3+x)^2}+\frac {20952 \log ^2(x)}{-3+x}+1233 x \log ^2(x)+272 x^2 \log ^2(x)+54 x^3 \log ^2(x)+9 x^4 \log ^2(x)+x^5 \log ^2(x)\right ) \, dx-\left (48 \log ^2(3)\right ) \int \left (9 \log ^2(x)+\frac {87 \log ^2(x)}{(-3+x)^3}+\frac {110 \log ^2(x)}{(-3+x)^2}+\frac {54 \log ^2(x)}{-3+x}+x \log ^2(x)\right ) \, dx-\left (96 \log ^2(3)\right ) \int \left (1233 \log ^2(x)+\frac {2349 \log ^2(x)}{(-3+x)^3}+\frac {5319 \log ^2(x)}{(-3+x)^2}+\frac {5211 \log ^2(x)}{-3+x}+272 x \log ^2(x)+54 x^2 \log ^2(x)+9 x^3 \log ^2(x)+x^4 \log ^2(x)\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 2.23, size = 29, normalized size = 1.00 \begin {gather*} \frac {4 \left (-e^x+2 x+x^4\right )^2 \log ^2(3) \log ^2(x)}{(-3+x)^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.67, size = 62, normalized size = 2.14 \begin {gather*} -\frac {4 \, {\left (2 \, {\left (x^{4} + 2 \, x\right )} e^{x} \log \relax (3)^{2} - {\left (x^{8} + 4 \, x^{5} + 4 \, x^{2}\right )} \log \relax (3)^{2} - e^{\left (2 \, x\right )} \log \relax (3)^{2}\right )} \log \relax (x)^{2}}{x^{2} - 6 \, x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 92, normalized size = 3.17 \begin {gather*} \frac {4 \, {\left (x^{8} \log \relax (3)^{2} \log \relax (x)^{2} + 4 \, x^{5} \log \relax (3)^{2} \log \relax (x)^{2} - 2 \, x^{4} e^{x} \log \relax (3)^{2} \log \relax (x)^{2} + 4 \, x^{2} \log \relax (3)^{2} \log \relax (x)^{2} - 4 \, x e^{x} \log \relax (3)^{2} \log \relax (x)^{2} + e^{\left (2 \, x\right )} \log \relax (3)^{2} \log \relax (x)^{2}\right )}}{x^{2} - 6 \, x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 46, normalized size = 1.59
method | result | size |
risch | \(\frac {4 \left (x^{8}+4 x^{5}-2 \,{\mathrm e}^{x} x^{4}+4 x^{2}-4 \,{\mathrm e}^{x} x +{\mathrm e}^{2 x}\right ) \ln \relax (3)^{2} \ln \relax (x )^{2}}{\left (x -3\right )^{2}}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 160, normalized size = 5.52 \begin {gather*} 16 \, {\left (\frac {3 \, {\left (2 \, x - 3\right )} \log \relax (x)}{x^{2} - 6 \, x + 9} + \frac {3}{x - 3} - \log \left (x - 3\right ) + \log \relax (x)\right )} \log \relax (3)^{2} + 16 \, \log \relax (3)^{2} \log \left (x - 3\right ) - \frac {4 \, {\left (4 \, x^{2} \log \relax (3)^{2} \log \relax (x) - e^{\left (2 \, x\right )} \log \relax (3)^{2} \log \relax (x)^{2} + 2 \, {\left (x^{4} \log \relax (3)^{2} + 2 \, x \log \relax (3)^{2}\right )} e^{x} \log \relax (x)^{2} + 12 \, x \log \relax (3)^{2} - {\left (x^{8} \log \relax (3)^{2} + 4 \, x^{5} \log \relax (3)^{2} + 4 \, x^{2} \log \relax (3)^{2}\right )} \log \relax (x)^{2} - 36 \, \log \relax (3)^{2}\right )}}{x^{2} - 6 \, x + 9} \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 {{\ln \relax (x)}^2\,\left ({\ln \relax (3)}^2\,\left (-24\,x^9+96\,x^8-48\,x^6+240\,x^5+96\,x^2\right )-{\mathrm {e}}^x\,{\ln \relax (3)}^2\,\left (-8\,x^6+8\,x^5+96\,x^4-16\,x^3+64\,x^2+48\,x\right )+{\mathrm {e}}^{2\,x}\,{\ln \relax (3)}^2\,\left (32\,x-8\,x^2\right )\right )-\ln \relax (x)\,\left ({\mathrm {e}}^{2\,x}\,{\ln \relax (3)}^2\,\left (8\,x-24\right )-{\ln \relax (3)}^2\,\left (-8\,x^9+24\,x^8-32\,x^6+96\,x^5-32\,x^3+96\,x^2\right )+{\mathrm {e}}^x\,{\ln \relax (3)}^2\,\left (-16\,x^5+48\,x^4-32\,x^2+96\,x\right )\right )}{-x^4+9\,x^3-27\,x^2+27\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.81, size = 201, normalized size = 6.93 \begin {gather*} \frac {\left (4 x^{2} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} - 24 x \log {\relax (3 )}^{2} \log {\relax (x )}^{2} + 36 \log {\relax (3 )}^{2} \log {\relax (x )}^{2}\right ) e^{2 x} + \left (- 8 x^{6} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} + 48 x^{5} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} - 72 x^{4} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} - 16 x^{3} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} + 96 x^{2} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} - 144 x \log {\relax (3 )}^{2} \log {\relax (x )}^{2}\right ) e^{x}}{x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81} + \frac {\left (4 x^{8} \log {\relax (3 )}^{2} + 16 x^{5} \log {\relax (3 )}^{2} + 16 x^{2} \log {\relax (3 )}^{2}\right ) \log {\relax (x )}^{2}}{x^{2} - 6 x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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