Integrand size = 111, antiderivative size = 32 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=e^{\frac {-\frac {2}{x}+\log (x)+(-x+\log (-x+3 (2+2 x)))^2}{x}} \]
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Time = 1.81 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.19, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {1607, 6838} \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=\frac {x^{\frac {1}{x}} e^{-\frac {-x^3-x \log ^2(5 x+6)+2}{x^2}}}{(5 x+6)^2} \]
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Rule 1607
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}\right ) \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{x^3 (6+5 x)} \, dx \\ & = \frac {e^{-\frac {2-x^3-x \log ^2(6+5 x)}{x^2}} x^{\frac {1}{x}}}{(6+5 x)^2} \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=\frac {e^{\frac {-2+x^3+x \log ^2(6+5 x)}{x^2}} x^{\frac {1}{x}}}{(6+5 x)^2} \]
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Time = 14.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06
method | result | size |
risch | \(\frac {x^{\frac {1}{x}} {\mathrm e}^{\frac {x \ln \left (5 x +6\right )^{2}+x^{3}-2}{x^{2}}}}{\left (5 x +6\right )^{2}}\) | \(34\) |
parallelrisch | \({\mathrm e}^{\frac {x \ln \left (5 x +6\right )^{2}-2 x^{2} \ln \left (5 x +6\right )+x \ln \left (x \right )+x^{3}-2}{x^{2}}}\) | \(36\) |
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Time = 0.26 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.09 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=e^{\left (\frac {x^{3} - 2 \, x^{2} \log \left (5 \, x + 6\right ) + x \log \left (5 \, x + 6\right )^{2} + x \log \left (x\right ) - 2}{x^{2}}\right )} \]
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Time = 0.48 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=e^{\frac {x^{3} - 2 x^{2} \log {\left (5 x + 6 \right )} + x \log {\left (x \right )} + x \log {\left (5 x + 6 \right )}^{2} - 2}{x^{2}}} \]
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Time = 0.28 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.22 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=\frac {e^{\left (x + \frac {\log \left (5 \, x + 6\right )^{2}}{x} + \frac {\log \left (x\right )}{x} - \frac {2}{x^{2}}\right )}}{25 \, x^{2} + 60 \, x + 36} \]
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Time = 0.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=e^{\left (x + \frac {\log \left (5 \, x + 6\right )^{2}}{x} + \frac {\log \left (x\right )}{x} - \frac {2}{x^{2}} - 2 \, \log \left (5 \, x + 6\right )\right )} \]
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Time = 9.37 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {-2+x^3+x \log (x)-2 x^2 \log (6+5 x)+x \log ^2(6+5 x)}{x^2}} \left (24+26 x+5 x^2-4 x^3+5 x^4+\left (-6 x-5 x^2\right ) \log (x)+10 x^2 \log (6+5 x)+\left (-6 x-5 x^2\right ) \log ^2(6+5 x)\right )}{6 x^3+5 x^4} \, dx=\frac {x^{1/x}\,{\mathrm {e}}^{-\frac {2}{x^2}}\,{\mathrm {e}}^{\frac {{\ln \left (5\,x+6\right )}^2}{x}}\,{\mathrm {e}}^x}{{\left (5\,x+6\right )}^2} \]
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