Integrand size = 158, antiderivative size = 30 \[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=e^{1+e^{-2 x+2 e^{2 x} x^2 (9+\log (x))^2} x^4} \]
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\[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=\int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (4 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3-2 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (10+9 x)+4 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (19+18 x) \log (x)+4 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (1+x) \log ^2(x)\right ) \, dx \\ & = -\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (19+18 x) \log (x) \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (1+x) \log ^2(x) \, dx+36 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (10+9 x) \, dx \\ & = -\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \left (19 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log (x)+18 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log (x)\right ) \, dx+4 \int \left (\exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log ^2(x)+\exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log ^2(x)\right ) \, dx+36 \int \left (10 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5+9 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6\right ) \, dx \\ & = -\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log ^2(x) \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log ^2(x) \, dx+72 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log (x) \, dx+76 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log (x) \, dx+324 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \, dx+360 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \, dx \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=e^{1+e^{2 x \left (-1+e^{2 x} x \left (81+\log ^2(x)\right )\right )} x^{4+36 e^{2 x} x^2}} \]
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Time = 114.70 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.47
method | result | size |
risch | \({\mathrm e}^{x^{4} x^{36 \,{\mathrm e}^{2 x} x^{2}} {\mathrm e}^{2 x \left ({\mathrm e}^{2 x} \ln \left (x \right )^{2} x +81 x \,{\mathrm e}^{2 x}-1\right )}+1}\) | \(44\) |
parallelrisch | \({\mathrm e}^{x^{4} {\mathrm e}^{2 \,{\mathrm e}^{2 x} \ln \left (x \right )^{2} x^{2}+36 x^{2} {\mathrm e}^{2 x} \ln \left (x \right )+162 \,{\mathrm e}^{2 x} x^{2}-2 x}+1}\) | \(47\) |
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Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.50 \[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 1\right )} \]
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Time = 22.97 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=e^{x^{4} e^{2 x^{2} e^{2 x} \log {\left (x \right )}^{2} + 36 x^{2} e^{2 x} \log {\left (x \right )} + 162 x^{2} e^{2 x} - 2 x} + 1} \]
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Time = 0.60 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.50 \[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 1\right )} \]
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\[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=\int { -2 \, {\left (x^{4} - 2 \, {\left (x^{6} + x^{5}\right )} e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 2 \, x^{3} - 2 \, {\left (18 \, x^{6} + 19 \, x^{5}\right )} e^{\left (2 \, x\right )} \log \left (x\right ) - 18 \, {\left (9 \, x^{6} + 10 \, x^{5}\right )} e^{\left (2 \, x\right )}\right )} e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x + 1\right )} \,d x } \]
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Time = 8.28 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.53 \[ \int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx=\mathrm {e}\,{\mathrm {e}}^{x^{36\,x^2\,{\mathrm {e}}^{2\,x}+4}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{162\,x^2\,{\mathrm {e}}^{2\,x}}} \]
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