Optimal. Leaf size=35 \[ \frac {1-x}{3-x-\frac {e^{2-e^5}+e^x-\log (x)}{e^3}} \]
________________________________________________________________________________________
Rubi [F] time = 6.61, 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 {e^{1+e^5} x+e^{-4+2 e^5} \left (e^3 (-1+x)-2 e^6 x+e^{3+x} \left (2 x-x^2\right )\right )-e^{-1+2 e^5} x \log (x)}{x+e^{-2+e^5} \left (2 e^x x+e^3 \left (-6 x+2 x^2\right )\right )+e^{-4+2 e^5} \left (e^{2 x} x+e^{3+x} \left (-6 x+2 x^2\right )+e^6 \left (9 x-6 x^2+x^3\right )\right )+\left (-2 e^{-2+e^5} x+e^{-4+2 e^5} \left (-2 e^x x+e^3 \left (6 x-2 x^2\right )\right )\right ) \log (x)+e^{-4+2 e^5} x \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3+e^5} \left (e^{e^5} (-1+x)+e^2 \left (1-2 e^{1+e^5}\right ) x-e^{e^5+x} (-2+x) x-e^{e^5} x \log (x)\right )}{x \left (e^2+e^{e^5+x}+e^{3+e^5} (-3+x)-e^{e^5} \log (x)\right )^2} \, dx\\ &=e^{3+e^5} \int \frac {e^{e^5} (-1+x)+e^2 \left (1-2 e^{1+e^5}\right ) x-e^{e^5+x} (-2+x) x-e^{e^5} x \log (x)}{x \left (e^2+e^{e^5+x}+e^{3+e^5} (-3+x)-e^{e^5} \log (x)\right )^2} \, dx\\ &=e^{3+e^5} \int \left (\frac {2-x}{e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)}+\frac {(1-x) \left (-e^{e^5}-e^2 \left (1-4 e^{1+e^5}\right ) x-e^{3+e^5} x^2+e^{e^5} x \log (x)\right )}{x \left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}\right ) \, dx\\ &=e^{3+e^5} \int \frac {2-x}{e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)} \, dx+e^{3+e^5} \int \frac {(1-x) \left (-e^{e^5}-e^2 \left (1-4 e^{1+e^5}\right ) x-e^{3+e^5} x^2+e^{e^5} x \log (x)\right )}{x \left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx\\ &=e^{3+e^5} \int \left (\frac {2}{e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)}+\frac {x}{-e^{e^5+x}-e^2 \left (1-3 e^{1+e^5}\right )-e^{3+e^5} x+e^{e^5} \log (x)}\right ) \, dx+e^{3+e^5} \int \left (\frac {e^{e^5}+e^2 \left (1-4 e^{1+e^5}\right ) x+e^{3+e^5} x^2-e^{e^5} x \log (x)}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}+\frac {-e^{e^5}-e^2 \left (1-4 e^{1+e^5}\right ) x-e^{3+e^5} x^2+e^{e^5} x \log (x)}{x \left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}\right ) \, dx\\ &=e^{3+e^5} \int \frac {x}{-e^{e^5+x}-e^2 \left (1-3 e^{1+e^5}\right )-e^{3+e^5} x+e^{e^5} \log (x)} \, dx+e^{3+e^5} \int \frac {e^{e^5}+e^2 \left (1-4 e^{1+e^5}\right ) x+e^{3+e^5} x^2-e^{e^5} x \log (x)}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx+e^{3+e^5} \int \frac {-e^{e^5}-e^2 \left (1-4 e^{1+e^5}\right ) x-e^{3+e^5} x^2+e^{e^5} x \log (x)}{x \left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx+\left (2 e^{3+e^5}\right ) \int \frac {1}{e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)} \, dx\\ &=e^{3+e^5} \int \frac {x}{-e^{e^5+x}-e^2 \left (1-3 e^{1+e^5}\right )-e^{3+e^5} x+e^{e^5} \log (x)} \, dx+e^{3+e^5} \int \left (\frac {e^2 \left (-1+4 e^{1+e^5}\right )}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}-\frac {e^{e^5}}{x \left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}-\frac {e^{3+e^5} x}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}+\frac {e^{e^5} \log (x)}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}\right ) \, dx+e^{3+e^5} \int \left (\frac {e^{e^5}}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}+\frac {e^2 \left (1-4 e^{1+e^5}\right ) x}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}+\frac {e^{3+e^5} x^2}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}-\frac {e^{e^5} x \log (x)}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2}\right ) \, dx+\left (2 e^{3+e^5}\right ) \int \frac {1}{e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)} \, dx\\ &=e^{3+e^5} \int \frac {x}{-e^{e^5+x}-e^2 \left (1-3 e^{1+e^5}\right )-e^{3+e^5} x+e^{e^5} \log (x)} \, dx+\left (2 e^{3+e^5}\right ) \int \frac {1}{e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)} \, dx+e^{3+2 e^5} \int \frac {1}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx-e^{3+2 e^5} \int \frac {1}{x \left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx+e^{3+2 e^5} \int \frac {\log (x)}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx-e^{3+2 e^5} \int \frac {x \log (x)}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx-e^{6+2 e^5} \int \frac {x}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx+e^{6+2 e^5} \int \frac {x^2}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx-\left (e^{5+e^5} \left (1-4 e^{1+e^5}\right )\right ) \int \frac {1}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx+\left (e^{5+e^5} \left (1-4 e^{1+e^5}\right )\right ) \int \frac {x}{\left (e^{e^5+x}+e^2 \left (1-3 e^{1+e^5}\right )+e^{3+e^5} x-e^{e^5} \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 44, normalized size = 1.26 \begin {gather*} \frac {e^{3+e^5} (-1+x)}{e^2+e^{e^5+x}+e^{3+e^5} (-3+x)-e^{e^5} \log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 40, normalized size = 1.14 \begin {gather*} \frac {{\left (x - 1\right )} e^{\left (e^{5} + 7\right )}}{{\left ({\left (x - 3\right )} e^{6} + e^{\left (x + 3\right )}\right )} e^{\left (e^{5} + 1\right )} - e^{\left (e^{5} + 4\right )} \log \relax (x) + e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 38, normalized size = 1.09
method | result | size |
risch | \(\frac {\left (x -1\right ) {\mathrm e}^{{\mathrm e}^{5}}}{{\mathrm e}^{{\mathrm e}^{5}-3+x}-\ln \relax (x ) {\mathrm e}^{{\mathrm e}^{5}-3}+x \,{\mathrm e}^{{\mathrm e}^{5}}+{\mathrm e}^{-1}-3 \,{\mathrm e}^{{\mathrm e}^{5}}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.42, size = 47, normalized size = 1.34 \begin {gather*} \frac {x e^{\left (e^{5} + 3\right )} - e^{\left (e^{5} + 3\right )}}{x e^{\left (e^{5} + 3\right )} - e^{\left (e^{5}\right )} \log \relax (x) + e^{2} + e^{\left (x + e^{5}\right )} - 3 \, e^{\left (e^{5} + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^5-4}\,\left ({\mathrm {e}}^3\,\left (x-1\right )-2\,x\,{\mathrm {e}}^6+{\mathrm {e}}^3\,{\mathrm {e}}^x\,\left (2\,x-x^2\right )\right )+x\,{\mathrm {e}}^{{\mathrm {e}}^5-2}\,{\mathrm {e}}^3-x\,{\mathrm {e}}^3\,{\mathrm {e}}^{2\,{\mathrm {e}}^5-4}\,\ln \relax (x)}{x\,{\mathrm {e}}^{2\,{\mathrm {e}}^5-4}\,{\ln \relax (x)}^2+\left ({\mathrm {e}}^{2\,{\mathrm {e}}^5-4}\,\left ({\mathrm {e}}^3\,\left (6\,x-2\,x^2\right )-2\,x\,{\mathrm {e}}^x\right )-2\,x\,{\mathrm {e}}^{{\mathrm {e}}^5-2}\right )\,\ln \relax (x)+x+{\mathrm {e}}^{2\,{\mathrm {e}}^5-4}\,\left ({\mathrm {e}}^6\,\left (x^3-6\,x^2+9\,x\right )+x\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^3\,{\mathrm {e}}^x\,\left (6\,x-2\,x^2\right )\right )-{\mathrm {e}}^{{\mathrm {e}}^5-2}\,\left ({\mathrm {e}}^3\,\left (6\,x-2\,x^2\right )-2\,x\,{\mathrm {e}}^x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.44, size = 58, normalized size = 1.66 \begin {gather*} \frac {x e^{3} e^{e^{5}} - e^{3} e^{e^{5}}}{x e^{3} e^{e^{5}} + e^{x} e^{e^{5}} - e^{e^{5}} \log {\relax (x )} - 3 e^{3} e^{e^{5}} + e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________