Optimal. Leaf size=31 \[ -e^{\frac {5}{x (3+x) \left (-4+\frac {1}{-3+x}+x\right ) \log (x)}}+\log (2) \]
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Rubi [F] time = 13.34, 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 {\exp \left (\frac {-15+5 x}{\left (39 x-8 x^2-4 x^3+x^4\right ) \log (x)}\right ) \left (-585+315 x+20 x^2-35 x^3+5 x^4+\left (-585+240 x+140 x^2-100 x^3+15 x^4\right ) \log (x)\right )}{\left (1521 x^2-624 x^3-248 x^4+142 x^5-8 x^7+x^8\right ) \log ^2(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 {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} \left (-585+315 x+20 x^2-35 x^3+5 x^4+\left (-585+240 x+140 x^2-100 x^3+15 x^4\right ) \log (x)\right )}{x^2 \left (39-8 x-4 x^2+x^3\right )^2 \log ^2(x)} \, dx\\ &=\int \left (\frac {5 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} (-3+x)}{x^2 (3+x) \left (13-7 x+x^2\right ) \log ^2(x)}+\frac {5 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} \left (-117+48 x+28 x^2-20 x^3+3 x^4\right )}{x^2 (3+x)^2 \left (13-7 x+x^2\right )^2 \log (x)}\right ) \, dx\\ &=5 \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} (-3+x)}{x^2 (3+x) \left (13-7 x+x^2\right ) \log ^2(x)} \, dx+5 \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} \left (-117+48 x+28 x^2-20 x^3+3 x^4\right )}{x^2 (3+x)^2 \left (13-7 x+x^2\right )^2 \log (x)} \, dx\\ &=5 \int \left (-\frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{13 x^2 \log ^2(x)}+\frac {5 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{507 x \log ^2(x)}-\frac {2 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{129 (3+x) \log ^2(x)}+\frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} (-66+41 x)}{7267 \left (13-7 x+x^2\right ) \log ^2(x)}\right ) \, dx+5 \int \left (-\frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{13 x^2 \log (x)}+\frac {2 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{43 (3+x)^2 \log (x)}+\frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} (-155+37 x)}{559 \left (13-7 x+x^2\right )^2 \log (x)}+\frac {17 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{559 \left (13-7 x+x^2\right ) \log (x)}\right ) \, dx\\ &=\frac {5 \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} (-66+41 x)}{\left (13-7 x+x^2\right ) \log ^2(x)} \, dx}{7267}+\frac {5}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} (-155+37 x)}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx+\frac {25}{507} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x \log ^2(x)} \, dx-\frac {10}{129} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x) \log ^2(x)} \, dx+\frac {85}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right ) \log (x)} \, dx+\frac {10}{43} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x)^2 \log (x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log ^2(x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log (x)} \, dx\\ &=\frac {5 \int \left (-\frac {66 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right ) \log ^2(x)}+\frac {41 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} x}{\left (13-7 x+x^2\right ) \log ^2(x)}\right ) \, dx}{7267}+\frac {5}{559} \int \left (-\frac {155 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right )^2 \log (x)}+\frac {37 e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} x}{\left (13-7 x+x^2\right )^2 \log (x)}\right ) \, dx+\frac {25}{507} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x \log ^2(x)} \, dx-\frac {10}{129} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x) \log ^2(x)} \, dx+\frac {85}{559} \int \left (\frac {2 i e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\sqrt {3} \left (7+i \sqrt {3}-2 x\right ) \log (x)}+\frac {2 i e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\sqrt {3} \left (-7+i \sqrt {3}+2 x\right ) \log (x)}\right ) \, dx+\frac {10}{43} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x)^2 \log (x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log ^2(x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log (x)} \, dx\\ &=\frac {205 \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} x}{\left (13-7 x+x^2\right ) \log ^2(x)} \, dx}{7267}-\frac {330 \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right ) \log ^2(x)} \, dx}{7267}+\frac {25}{507} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x \log ^2(x)} \, dx-\frac {10}{129} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x) \log ^2(x)} \, dx+\frac {10}{43} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x)^2 \log (x)} \, dx+\frac {185}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} x}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log ^2(x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log (x)} \, dx-\frac {775}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx+\frac {(170 i) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (7+i \sqrt {3}-2 x\right ) \log (x)} \, dx}{559 \sqrt {3}}+\frac {(170 i) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7+i \sqrt {3}+2 x\right ) \log (x)} \, dx}{559 \sqrt {3}}\\ &=\frac {205 \int \left (\frac {\left (1-\frac {7 i}{\sqrt {3}}\right ) e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7-i \sqrt {3}+2 x\right ) \log ^2(x)}+\frac {\left (1+\frac {7 i}{\sqrt {3}}\right ) e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7+i \sqrt {3}+2 x\right ) \log ^2(x)}\right ) \, dx}{7267}-\frac {330 \int \left (\frac {2 i e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\sqrt {3} \left (7+i \sqrt {3}-2 x\right ) \log ^2(x)}+\frac {2 i e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\sqrt {3} \left (-7+i \sqrt {3}+2 x\right ) \log ^2(x)}\right ) \, dx}{7267}+\frac {25}{507} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x \log ^2(x)} \, dx-\frac {10}{129} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x) \log ^2(x)} \, dx+\frac {10}{43} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x)^2 \log (x)} \, dx+\frac {185}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} x}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log ^2(x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log (x)} \, dx-\frac {775}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx+\frac {(170 i) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (7+i \sqrt {3}-2 x\right ) \log (x)} \, dx}{559 \sqrt {3}}+\frac {(170 i) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7+i \sqrt {3}+2 x\right ) \log (x)} \, dx}{559 \sqrt {3}}\\ &=\frac {25}{507} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x \log ^2(x)} \, dx-\frac {10}{129} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x) \log ^2(x)} \, dx+\frac {10}{43} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{(3+x)^2 \log (x)} \, dx+\frac {185}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} x}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log ^2(x)} \, dx-\frac {5}{13} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{x^2 \log (x)} \, dx-\frac {775}{559} \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (13-7 x+x^2\right )^2 \log (x)} \, dx+\frac {(170 i) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (7+i \sqrt {3}-2 x\right ) \log (x)} \, dx}{559 \sqrt {3}}+\frac {(170 i) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7+i \sqrt {3}+2 x\right ) \log (x)} \, dx}{559 \sqrt {3}}-\frac {\left (220 i \sqrt {3}\right ) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (7+i \sqrt {3}-2 x\right ) \log ^2(x)} \, dx}{7267}-\frac {\left (220 i \sqrt {3}\right ) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7+i \sqrt {3}+2 x\right ) \log ^2(x)} \, dx}{7267}+\frac {\left (205 \left (3-7 i \sqrt {3}\right )\right ) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7-i \sqrt {3}+2 x\right ) \log ^2(x)} \, dx}{21801}+\frac {\left (205 \left (3+7 i \sqrt {3}\right )\right ) \int \frac {e^{\frac {-15+5 x}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}}}{\left (-7+i \sqrt {3}+2 x\right ) \log ^2(x)} \, dx}{21801}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 31, normalized size = 1.00 \begin {gather*} -e^{\frac {5 (-3+x)}{x \left (39-8 x-4 x^2+x^3\right ) \log (x)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 31, normalized size = 1.00 \begin {gather*} -e^{\left (\frac {5 \, {\left (x - 3\right )}}{{\left (x^{4} - 4 \, x^{3} - 8 \, x^{2} + 39 \, x\right )} \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.55, size = 65, normalized size = 2.10 \begin {gather*} -e^{\left (\frac {5 \, x}{x^{4} \log \relax (x) - 4 \, x^{3} \log \relax (x) - 8 \, x^{2} \log \relax (x) + 39 \, x \log \relax (x)} - \frac {15}{x^{4} \log \relax (x) - 4 \, x^{3} \log \relax (x) - 8 \, x^{2} \log \relax (x) + 39 \, x \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 31, normalized size = 1.00
method | result | size |
risch | \(-{\mathrm e}^{\frac {5 x -15}{x \left (3+x \right ) \left (x^{2}-7 x +13\right ) \ln \relax (x )}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.78, size = 62, normalized size = 2.00 \begin {gather*} -{\mathrm {e}}^{\frac {15}{8\,x^2\,\ln \relax (x)+4\,x^3\,\ln \relax (x)-x^4\,\ln \relax (x)-39\,x\,\ln \relax (x)}}\,{\mathrm {e}}^{\frac {5}{39\,\ln \relax (x)-4\,x^2\,\ln \relax (x)+x^3\,\ln \relax (x)-8\,x\,\ln \relax (x)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.85, size = 27, normalized size = 0.87 \begin {gather*} - e^{\frac {5 x - 15}{\left (x^{4} - 4 x^{3} - 8 x^{2} + 39 x\right ) \log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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