Integrand size = 116, antiderivative size = 28 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3-e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x}+3 x \]
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\[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+\exp \left (e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6\right ) \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 3 x+\int e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+\exp \left (e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6\right ) \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right ) \, dx \\ & = 3 x+\int \left (-2 e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}-2 \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \left (2 e^{2 e}+5 e^e x+3 x^2\right )\right ) \, dx \\ & = 3 x-2 \int e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x} \, dx-2 \int \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \left (2 e^{2 e}+5 e^e x+3 x^2\right ) \, dx \\ & = 3 x-2 \int e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x} \, dx-2 \int \left (2 \exp \left (2 e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3+5 \exp \left (e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^4+3 \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^5\right ) \, dx \\ & = 3 x-2 \int e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x} \, dx-4 \int \exp \left (2 e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \, dx-6 \int \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^5 \, dx-10 \int \exp \left (e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^4 \, dx \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=-e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}+3 x \]
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Time = 295.79 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18
method | result | size |
risch | \(-{\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}^{x^{4} \left (2 x \,{\mathrm e}^{{\mathrm e}}+x^{2}+{\mathrm e}^{2 \,{\mathrm e}}\right )}}}+3 x\) | \(33\) |
parallelrisch | \(-{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{4} {\mathrm e}^{2 \,{\mathrm e}}+2 x^{5} {\mathrm e}^{{\mathrm e}}+x^{6}}}+x}+3 x\) | \(35\) |
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Timed out. \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\text {Timed out} \]
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Timed out. \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\text {Timed out} \]
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Time = 0.38 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3 \, x - e^{\left (2 \, x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} \]
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\[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\int { -2 \, {\left ({\left (3 \, x^{5} e^{x} + 5 \, x^{4} e^{\left (x + e\right )} + 2 \, x^{3} e^{\left (x + 2 \, e\right )}\right )} e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )} + e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )} + e^{x}\right )} e^{\left (x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} + 3 \,d x } \]
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Time = 12.76 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3\,x-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x^6}\,{\mathrm {e}}^{2\,x^5\,{\mathrm {e}}^{\mathrm {e}}}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{2\,\mathrm {e}}}}} \]
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