Optimal. Leaf size=29 \[ e^{-2 e^{e^x}} x \left (e^{\frac {4}{-1+x}}-\log (-1+x)\right )^2 \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(95\) vs. \(2(29)=58\).
time = 1.13, antiderivative size = 95, normalized size of antiderivative = 3.28, number of steps
used = 2, number of rules used = 2, integrand size = 194, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {27, 2326}
\begin {gather*} \frac {e^{-x-2 e^{e^x}} \left (e^{x-\frac {8}{1-x}} \left (x^3-2 x^2+x\right )+e^x \left (x^3-2 x^2+x\right ) \log ^2(x-1)-2 e^{x-\frac {4}{1-x}} \left (x^3-2 x^2+x\right ) \log (x-1)\right )}{(1-x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-2 e^{e^x}} \left (e^{\frac {4}{-1+x}} \left (2 x-2 x^2\right )+e^{\frac {8}{-1+x}} \left (1-10 x+x^2\right )+\left (-2 x+2 x^2+e^{\frac {4}{-1+x}} \left (-2+12 x-2 x^2\right )\right ) \log (-1+x)+\left (1-2 x+x^2\right ) \log ^2(-1+x)+e^{e^x} \left (e^{\frac {8}{-1+x}+x} \left (-2 x+4 x^2-2 x^3\right )+e^{\frac {4}{-1+x}+x} \left (4 x-8 x^2+4 x^3\right ) \log (-1+x)+e^x \left (-2 x+4 x^2-2 x^3\right ) \log ^2(-1+x)\right )\right )}{(-1+x)^2} \, dx\\ &=\frac {e^{-2 e^{e^x}-x} \left (e^{-\frac {8}{1-x}+x} \left (x-2 x^2+x^3\right )-2 e^{-\frac {4}{1-x}+x} \left (x-2 x^2+x^3\right ) \log (-1+x)+e^x \left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )}{(1-x)^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.41, size = 29, normalized size = 1.00 \begin {gather*} e^{-2 e^{e^x}} x \left (e^{\frac {4}{-1+x}}-\log (-1+x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 2.79, size = 38, normalized size = 1.31
method | result | size |
risch | \(\left ({\mathrm e}^{\frac {8}{x -1}}-2 \,{\mathrm e}^{\frac {4}{x -1}} \ln \left (x -1\right )+\ln \left (x -1\right )^{2}\right ) x \,{\mathrm e}^{-2 \,{\mathrm e}^{{\mathrm e}^{x}}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.36, size = 44, normalized size = 1.52 \begin {gather*} -{\left (2 \, x e^{\left (\frac {4}{x - 1}\right )} \log \left (x - 1\right ) - x \log \left (x - 1\right )^{2} - x e^{\left (\frac {8}{x - 1}\right )}\right )} e^{\left (-2 \, e^{\left (e^{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 133 vs.
\(2 (25) = 50\).
time = 0.38, size = 133, normalized size = 4.59 \begin {gather*} {\left (x e^{\left (\frac {2 \, {\left (x^{2} - x + 4\right )}}{x - 1}\right )} \log \left (x - 1\right )^{2} - 2 \, x e^{\left (\frac {x^{2} - x + 8}{x - 1} + \frac {x^{2} - x + 4}{x - 1}\right )} \log \left (x - 1\right ) + x e^{\left (\frac {2 \, {\left (x^{2} - x + 8\right )}}{x - 1}\right )}\right )} e^{\left (-\frac {2 \, {\left (x^{2} - x + 4\right )}}{x - 1} - 2 \, e^{\left (e^{\left (-\frac {x^{2} - x + 8}{x - 1} + \frac {2 \, {\left (x^{2} - x + 4\right )}}{x - 1}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
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]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.67, size = 41, normalized size = 1.41 \begin {gather*} {\mathrm {e}}^{-2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,\left (x\,{\ln \left (x-1\right )}^2-2\,x\,{\mathrm {e}}^{\frac {4}{x-1}}\,\ln \left (x-1\right )+x\,{\mathrm {e}}^{\frac {8}{x-1}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________