Integrand size = 114, antiderivative size = 20 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{\frac {2 x}{5 \left (-12+e^x+x+x^2+\log (x)\right )}} \]
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Time = 1.13 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.40, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6820, 12, 6838} \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{-\frac {2 x}{5 \left (-x^2-x-e^x-\log (x)+12\right )}} \]
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Rule 12
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 e^{\frac {2 x}{5 \left (-12+e^x+x+x^2+\log (x)\right )}} \left (-13-e^x (-1+x)-x^2+\log (x)\right )}{5 \left (12-e^x-x-x^2-\log (x)\right )^2} \, dx \\ & = \frac {2}{5} \int \frac {e^{\frac {2 x}{5 \left (-12+e^x+x+x^2+\log (x)\right )}} \left (-13-e^x (-1+x)-x^2+\log (x)\right )}{\left (12-e^x-x-x^2-\log (x)\right )^2} \, dx \\ & = e^{-\frac {2 x}{5 \left (12-e^x-x-x^2-\log (x)\right )}} \\ \end{align*}
Time = 1.79 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{\frac {2 x}{5 \left (-12+e^x+x+x^2+\log (x)\right )}} \]
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Time = 13.45 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85
method | result | size |
risch | \({\mathrm e}^{\frac {2 x}{5 \left (x^{2}+\ln \left (x \right )+{\mathrm e}^{x}+x -12\right )}}\) | \(17\) |
parallelrisch | \({\mathrm e}^{\frac {2 x}{5 \left (x^{2}+\ln \left (x \right )+{\mathrm e}^{x}+x -12\right )}}\) | \(17\) |
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Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{\left (\frac {2 \, x}{5 \, {\left (x^{2} + x + e^{x} + \log \left (x\right ) - 12\right )}}\right )} \]
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Time = 1.69 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{\frac {2 x}{5 x^{2} + 5 x + 5 e^{x} + 5 \log {\left (x \right )} - 60}} \]
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Time = 0.31 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{\left (\frac {2 \, x}{5 \, {\left (x^{2} + x + e^{x} + \log \left (x\right ) - 12\right )}}\right )} \]
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Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx=e^{\left (\frac {2 \, x}{5 \, {\left (x^{2} + x + e^{x} + \log \left (x\right ) - 12\right )}}\right )} \]
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Time = 8.81 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {2 x}{-60+5 e^x+5 x+5 x^2+5 \log (x)}} \left (-26+e^x (2-2 x)-2 x^2+2 \log (x)\right )}{720+5 e^{2 x}-120 x-115 x^2+10 x^3+5 x^4+e^x \left (-120+10 x+10 x^2\right )+\left (-120+10 e^x+10 x+10 x^2\right ) \log (x)+5 \log ^2(x)} \, dx={\mathrm {e}}^{\frac {2\,x}{5\,\left (x+{\mathrm {e}}^x+\ln \left (x\right )+x^2-12\right )}} \]
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