Integrand size = 161, antiderivative size = 36 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=2+e^{3-e^{3-e^{x^2 (-x+\log (4+x))^2}-x}-x} \]
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Time = 4.20 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.19, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {6838} \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=\exp \left (-\exp \left ((x+4)^{-2 x^3} \left (-e^{x^4+x^2 \log ^2(x+4)}\right )-x+3\right )-x+3\right ) \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = \exp \left (3-\exp \left (3-x-e^{x^4+x^2 \log ^2(4+x)} (4+x)^{-2 x^3}\right )-x\right ) \\ \end{align*}
Time = 0.40 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.19 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=e^{3-e^{3-x-e^{x^4+x^2 \log ^2(4+x)} (4+x)^{-2 x^3}}-x} \]
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Time = 4.73 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.14
method | result | size |
risch | \({\mathrm e}^{-{\mathrm e}^{-\left (4+x \right )^{-2 x^{3}} {\mathrm e}^{x^{2} \left (\ln \left (4+x \right )^{2}+x^{2}\right )}+3-x}+3-x}\) | \(41\) |
parallelrisch | \({\mathrm e}^{-{\mathrm e}^{-{\mathrm e}^{x^{2} \ln \left (4+x \right )^{2}-2 x^{3} \ln \left (4+x \right )+x^{4}}+3-x}+3-x}\) | \(41\) |
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Time = 0.38 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.11 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=e^{\left (-x - e^{\left (-x - e^{\left (x^{4} - 2 \, x^{3} \log \left (x + 4\right ) + x^{2} \log \left (x + 4\right )^{2}\right )} + 3\right )} + 3\right )} \]
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Time = 166.79 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.94 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=e^{- x - e^{- x - e^{x^{4} - 2 x^{3} \log {\left (x + 4 \right )} + x^{2} \log {\left (x + 4 \right )}^{2}} + 3} + 3} \]
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Time = 0.53 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.11 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=e^{\left (-x - e^{\left (-x - e^{\left (x^{4} - 2 \, x^{3} \log \left (x + 4\right ) + x^{2} \log \left (x + 4\right )^{2}\right )} + 3\right )} + 3\right )} \]
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Time = 23.50 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.11 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx=e^{\left (-x - e^{\left (-x - e^{\left (x^{4} - 2 \, x^{3} \log \left (x + 4\right ) + x^{2} \log \left (x + 4\right )^{2}\right )} + 3\right )} + 3\right )} \]
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Time = 14.80 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.25 \[ \int \frac {e^{3-e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x}-x} \left (-4-x+e^{3-e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)}-x} \left (4+x+e^{x^4-2 x^3 \log (4+x)+x^2 \log ^2(4+x)} \left (14 x^3+4 x^4+\left (-22 x^2-6 x^3\right ) \log (4+x)+\left (8 x+2 x^2\right ) \log ^2(4+x)\right )\right )\right )}{4+x} \, dx={\mathrm {e}}^{-{\mathrm {e}}^{-x}\,{\mathrm {e}}^3\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{x^2\,{\ln \left (x+4\right )}^2}}{{\left (x+4\right )}^{2\,x^3}}}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^3 \]
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