Integrand size = 59, antiderivative size = 18 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{7+e^2+e^{e^{e^{1+x}}}} \]
[Out]
Time = 0.13 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.085, Rules used = {12, 2320, 2279, 2278, 32} \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{e^{e^{e^{x+1}}}+7+e^2} \]
[In]
[Out]
Rule 12
Rule 32
Rule 2278
Rule 2279
Rule 2320
Rubi steps \begin{align*} \text {integral}& = -\left (20 \int \frac {e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx\right ) \\ & = -\left (20 \text {Subst}\left (\int \frac {e^{1+e^{e x}+e x}}{\left (e^{e^{e x}}+7 \left (1+\frac {e^2}{7}\right )\right )^2} \, dx,x,e^x\right )\right ) \\ & = -\frac {20 \text {Subst}\left (\int \frac {e^{1+x}}{\left (e^x+7 \left (1+\frac {e^2}{7}\right )\right )^2} \, dx,x,e^{e^{1+x}}\right )}{e} \\ & = -\left (20 \text {Subst}\left (\int \frac {e^x}{\left (e^x+7 \left (1+\frac {e^2}{7}\right )\right )^2} \, dx,x,e^{e^{1+x}}\right )\right ) \\ & = -\left (20 \text {Subst}\left (\int \frac {1}{\left (7 \left (1+\frac {e^2}{7}\right )+x\right )^2} \, dx,x,e^{e^{e^{1+x}}}\right )\right ) \\ & = \frac {20}{7+e^2+e^{e^{e^{1+x}}}} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{7+e^2+e^{e^{e^{1+x}}}} \]
[In]
[Out]
Time = 0.94 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83
method | result | size |
norman | \(\frac {20}{7+{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{1+x}}}+{\mathrm e}^{2}}\) | \(15\) |
risch | \(\frac {20}{7+{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{1+x}}}+{\mathrm e}^{2}}\) | \(15\) |
parallelrisch | \(\frac {20}{7+{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{1+x}}}+{\mathrm e}^{2}}\) | \(15\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 39 vs. \(2 (14) = 28\).
Time = 0.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 2.17 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20 \, e^{\left (x + e^{\left (x + 1\right )} + 1\right )}}{{\left (e^{2} + 7\right )} e^{\left (x + e^{\left (x + 1\right )} + 1\right )} + e^{\left (x + e^{\left (x + 1\right )} + e^{\left (e^{\left (x + 1\right )}\right )} + 1\right )}} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{e^{e^{e^{x + 1}}} + 7 + e^{2}} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{e^{2} + e^{\left (e^{\left (e^{\left (x + 1\right )}\right )}\right )} + 7} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{e^{2} + e^{\left (e^{\left (e^{\left (x + 1\right )}\right )}\right )} + 7} \]
[In]
[Out]
Time = 9.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int -\frac {20 e^{1+e^{e^{1+x}}+e^{1+x}+x}}{49+14 e^2+e^4+e^{2 e^{e^{1+x}}}+e^{e^{e^{1+x}}} \left (14+2 e^2\right )} \, dx=\frac {20}{{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x+1}}}+{\mathrm {e}}^2+7} \]
[In]
[Out]