Integrand size = 63, antiderivative size = 19 \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=e^{e^{x+e^{-x} (1+x)} x} x \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(105\) vs. \(2(19)=38\).
Time = 0.20 (sec) , antiderivative size = 105, normalized size of antiderivative = 5.53, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2326} \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=\frac {\left (-e^{-x} (x+1) x^3+x^3+2 x^2+x\right ) \exp \left (e^{x+e^{-x} (x+1)} x+x+e^{-x} (x+1)\right )}{(x+1) \left (e^{x+e^{-x} (x+1)} x \left (-e^{-x} (x+1)+e^{-x}+1\right )+e^{x+e^{-x} (x+1)}\right )} \]
[In]
[Out]
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {\exp \left (x+e^{x+e^{-x} (1+x)} x+e^{-x} (1+x)\right ) \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )}{(1+x) \left (e^{x+e^{-x} (1+x)}+e^{x+e^{-x} (1+x)} x \left (1+e^{-x}-e^{-x} (1+x)\right )\right )} \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16 \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=e^{e^{e^{-x} \left (1+x+e^x x\right )} x} x \]
[In]
[Out]
Time = 0.64 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95
method | result | size |
parallelrisch | \({\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{\ln \left (1+x \right )-x}+x}} x\) | \(18\) |
risch | \(x \,{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{-x}+{\mathrm e}^{-x}+x} x}\) | \(19\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=x e^{\left (x e^{\left (x + e^{\left (-x + \log \left (x + 1\right )\right )}\right )}\right )} \]
[In]
[Out]
Time = 2.40 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=x e^{x e^{x + \left (x + 1\right ) e^{- x}}} \]
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=x e^{\left (x e^{\left (x e^{\left (-x\right )} + x + e^{\left (-x\right )}\right )}\right )} \]
[In]
[Out]
\[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=\int { -\frac {{\left ({\left (x^{3} e^{\left (-x + \log \left (x + 1\right )\right )} - x^{3} - 2 \, x^{2} - x\right )} e^{\left (x + e^{\left (-x + \log \left (x + 1\right )\right )}\right )} - x - 1\right )} e^{\left (x e^{\left (x + e^{\left (-x + \log \left (x + 1\right )\right )}\right )}\right )}}{x + 1} \,d x } \]
[In]
[Out]
Time = 0.18 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{x+e^{-x} (1+x)} x} \left (1+x+e^{x+e^{-x} (1+x)} \left (x+2 x^2+x^3-e^{-x} x^3 (1+x)\right )\right )}{1+x} \, dx=x\,{\mathrm {e}}^{x\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{{\mathrm {e}}^{-x}}\,{\mathrm {e}}^x} \]
[In]
[Out]