Optimal. Leaf size=22 \[ e^{e^{e^x \left (4+\frac {-1+e^4}{5 x}\right )}} \]
________________________________________________________________________________________
Rubi [F] time = 5.97, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right ) \left (1+e^4 (-1+x)-x+20 x^2\right )}{5 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right ) \left (1+e^4 (-1+x)-x+20 x^2\right )}{x^2} \, dx\\ &=\frac {1}{5} \int \frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right ) \left (1-e^4-\left (1-e^4\right ) x+20 x^2\right )}{x^2} \, dx\\ &=\frac {1}{5} \int \left (20 \exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right )+\frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right ) \left (1-e^4\right )}{x^2}+\frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right ) \left (-1+e^4\right )}{x}\right ) \, dx\\ &=4 \int \exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right ) \, dx+\frac {1}{5} \left (1-e^4\right ) \int \frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right )}{x^2} \, dx+\frac {1}{5} \left (-1+e^4\right ) \int \frac {\exp \left (e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}+x+\frac {e^x \left (-1+e^4+20 x\right )}{5 x}\right )}{x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 4.15, size = 22, normalized size = 1.00 \begin {gather*} e^{e^{\frac {e^x \left (-1+e^4+20 x\right )}{5 x}}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.55, size = 58, normalized size = 2.64 \begin {gather*} e^{\left (-x - \frac {{\left (20 \, x + e^{4} - 1\right )} e^{x}}{5 \, x} + \frac {5 \, x^{2} + {\left (20 \, x + e^{4} - 1\right )} e^{x} + 5 \, x e^{\left (\frac {{\left (20 \, x + e^{4} - 1\right )} e^{x}}{5 \, x}\right )}}{5 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (20 \, x^{2} + {\left (x - 1\right )} e^{4} - x + 1\right )} e^{\left (x + \frac {{\left (20 \, x + e^{4} - 1\right )} e^{x}}{5 \, x} + e^{\left (\frac {{\left (20 \, x + e^{4} - 1\right )} e^{x}}{5 \, x}\right )}\right )}}{5 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.15, size = 17, normalized size = 0.77
method | result | size |
norman | \({\mathrm e}^{{\mathrm e}^{\frac {\left ({\mathrm e}^{4}+20 x -1\right ) {\mathrm e}^{x}}{5 x}}}\) | \(17\) |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {\left ({\mathrm e}^{4}+20 x -1\right ) {\mathrm e}^{x}}{5 x}}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.75, size = 23, normalized size = 1.05 \begin {gather*} e^{\left (e^{\left (\frac {e^{\left (x + 4\right )}}{5 \, x} - \frac {e^{x}}{5 \, x} + 4 \, e^{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 7.55, size = 25, normalized size = 1.14 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-\frac {{\mathrm {e}}^x}{5\,x}}\,{\mathrm {e}}^{4\,{\mathrm {e}}^x}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^4\,{\mathrm {e}}^x}{5\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.25, size = 19, normalized size = 0.86 \begin {gather*} e^{e^{\frac {\left (4 x - \frac {1}{5} + \frac {e^{4}}{5}\right ) e^{x}}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________