Integrand size = 52, antiderivative size = 29 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=e^{-e^{2+e^4}-x+4 \log (x) \left (x-2 e^2 x \log (x)\right )} \]
[Out]
Time = 0.09 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6838} \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=x^{4 x} e^{-x-8 e^2 x \log ^2(x)-e^{2+e^4}} \]
[In]
[Out]
Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{-e^{2+e^4}-x-8 e^2 x \log ^2(x)} x^{4 x} \\ \end{align*}
Time = 1.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \]
[In]
[Out]
Time = 0.12 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93
method | result | size |
norman | \({\mathrm e}^{-8 x \,{\mathrm e}^{2} \ln \left (x \right )^{2}+4 x \ln \left (x \right )-{\mathrm e}^{2+{\mathrm e}^{4}}-x}\) | \(27\) |
parallelrisch | \({\mathrm e}^{-8 x \,{\mathrm e}^{2} \ln \left (x \right )^{2}+4 x \ln \left (x \right )-{\mathrm e}^{2+{\mathrm e}^{4}}-x}\) | \(27\) |
risch | \(x^{4 x} {\mathrm e}^{-8 x \,{\mathrm e}^{2} \ln \left (x \right )^{2}-{\mathrm e}^{2+{\mathrm e}^{4}}-x}\) | \(28\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=e^{\left (-8 \, x e^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right ) - x - e^{\left (e^{4} + 2\right )}\right )} \]
[In]
[Out]
Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=e^{- 8 x e^{2} \log {\left (x \right )}^{2} + 4 x \log {\left (x \right )} - x - e^{2 + e^{4}}} \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=e^{\left (-8 \, x e^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right ) - x - e^{\left (e^{4} + 2\right )}\right )} \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=e^{\left (-8 \, x e^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right ) - x - e^{\left (e^{4} + 2\right )}\right )} \]
[In]
[Out]
Time = 9.36 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int e^{-e^{2+e^4}-x+4 x \log (x)-8 e^2 x \log ^2(x)} \left (3+\left (4-16 e^2\right ) \log (x)-8 e^2 \log ^2(x)\right ) \, dx=x^{4\,x}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-8\,x\,{\mathrm {e}}^2\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^4}} \]
[In]
[Out]