Integrand size = 34, antiderivative size = 19 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{e^4-e^{e^x}+x-x^2} \]
[Out]
Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6838} \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{-x^2+x-e^{e^x}+e^4} \]
[In]
[Out]
Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{e^4-e^{e^x}+x-x^2} \\ \end{align*}
Time = 0.15 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{e^4-e^{e^x}+x-x^2} \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84
method | result | size |
derivativedivides | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\) | \(16\) |
default | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\) | \(16\) |
norman | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\) | \(16\) |
risch | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\) | \(16\) |
parallelrisch | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\) | \(16\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.42 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{\left (-{\left ({\left (x^{2} - x - e^{4}\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )} \]
[In]
[Out]
Time = 0.12 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{- x^{2} + x - e^{e^{x}} + e^{4}} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{\left (-x^{2} + x + e^{4} - e^{\left (e^{x}\right )}\right )} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{\left (-x^{2} + x + e^{4} - e^{\left (e^{x}\right )}\right )} \]
[In]
[Out]
Time = 0.15 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx={\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{{\mathrm {e}}^4}\,{\mathrm {e}}^x \]
[In]
[Out]