\(\int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} (20 x \log (3)+e^{3-e^x} (-x \log (3)-e^x x^2 \log (3)))+(-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3))) \log (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x)}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} (400+e^{6-2 e^x}-40 e^{3-e^x})-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx\) [6793]

Optimal result

Integrand size = 320, antiderivative size = 30 \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=x \log (3) \log \left (e^{4+\frac {x}{20-e^{3-e^x}}}-x\right ) \]

[Out]

ln(3)*x*ln(exp(x/(20-exp(-exp(x)+3))+4)-x)

Rubi [F(-1)]

Timed out. \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=\text {\$Aborted} \]

[In]

Int[(-400*x*Log[3] - E^(6 - 2*E^x)*x*Log[3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^
(3 - E^x)))*(20*x*Log[3] + E^(3 - E^x)*(-(x*Log[3]) - E^x*x^2*Log[3])) + (-400*x*Log[3] - E^(6 - 2*E^x)*x*Log[
3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x)))*(400*Log[3] + E^(6 - 2*E^x)*L
og[3] - 40*E^(3 - E^x)*Log[3]))*Log[E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x))) - x])/(E^((-80 + 4*E^(3
- E^x) - x)/(-20 + E^(3 - E^x)))*(400 + E^(6 - 2*E^x) - 40*E^(3 - E^x)) - 400*x - E^(6 - 2*E^x)*x + 40*E^(3 -
E^x)*x),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [A] (verified)

Time = 3.96 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=x \log (3) \log \left (e^{\frac {1}{20} \left (80+x-\frac {e^3 x}{e^3-20 e^{e^x}}\right )}-x\right ) \]

[In]

Integrate[(-400*x*Log[3] - E^(6 - 2*E^x)*x*Log[3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-2
0 + E^(3 - E^x)))*(20*x*Log[3] + E^(3 - E^x)*(-(x*Log[3]) - E^x*x^2*Log[3])) + (-400*x*Log[3] - E^(6 - 2*E^x)*
x*Log[3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x)))*(400*Log[3] + E^(6 - 2*
E^x)*Log[3] - 40*E^(3 - E^x)*Log[3]))*Log[E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x))) - x])/(E^((-80 + 4
*E^(3 - E^x) - x)/(-20 + E^(3 - E^x)))*(400 + E^(6 - 2*E^x) - 40*E^(3 - E^x)) - 400*x - E^(6 - 2*E^x)*x + 40*E
^(3 - E^x)*x),x]

[Out]

x*Log[3]*Log[E^((80 + x - (E^3*x)/(E^3 - 20*E^E^x))/20) - x]

Maple [A] (verified)

Time = 157.76 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20

method	result	size
risch	\(\ln \left (3\right ) \ln \left ({\mathrm e}^{-\frac {-4 \,{\mathrm e}^{-{\mathrm e}^{x}+3}+x +80}{{\mathrm e}^{-{\mathrm e}^{x}+3}-20}}-x \right ) x\)	\(36\)
parallelrisch	\(\ln \left (3\right ) x \ln \left ({\mathrm e}^{\frac {4 \,{\mathrm e}^{-{\mathrm e}^{x}+3}-x -80}{{\mathrm e}^{-{\mathrm e}^{x}+3}-20}}-x \right )\)	\(37\)

[In]

int((((ln(3)*exp(-exp(x)+3)^2-40*ln(3)*exp(-exp(x)+3)+400*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-2
0))-x*ln(3)*exp(-exp(x)+3)^2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))*ln(exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x
)+3)-20))-x)+((-x^2*ln(3)*exp(x)-x*ln(3))*exp(-exp(x)+3)+20*x*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+
3)-20))-x*ln(3)*exp(-exp(x)+3)^2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))/((exp(-exp(x)+3)^2-40*exp(-exp(x)+3)+4
00)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)-400*x),x,method=_R
ETURNVERBOSE)

[Out]

ln(3)*ln(exp(-(-4*exp(-exp(x)+3)+x+80)/(exp(-exp(x)+3)-20))-x)*x

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=x \log \left (3\right ) \log \left (-x + e^{\left (-\frac {x - 4 \, e^{\left (-e^{x} + 3\right )} + 80}{e^{\left (-e^{x} + 3\right )} - 20}\right )}\right ) \]

[In]

integrate((((log(3)*exp(-exp(x)+3)^2-40*log(3)*exp(-exp(x)+3)+400*log(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-ex
p(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))*log(exp((4*exp(-exp(x)+3)-x-80
)/(exp(-exp(x)+3)-20))-x)+((-x^2*log(3)*exp(x)-x*log(3))*exp(-exp(x)+3)+20*x*log(3))*exp((4*exp(-exp(x)+3)-x-8
0)/(exp(-exp(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))/((exp(-exp(x)+3)^2-
40*exp(-exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)
-400*x),x, algorithm="fricas")

[Out]

x*log(3)*log(-x + e^(-(x - 4*e^(-e^x + 3) + 80)/(e^(-e^x + 3) - 20)))

Sympy [F(-1)]

Timed out. \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=\text {Timed out} \]

[In]

integrate((((ln(3)*exp(-exp(x)+3)**2-40*ln(3)*exp(-exp(x)+3)+400*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(
x)+3)-20))-x*ln(3)*exp(-exp(x)+3)**2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))*ln(exp((4*exp(-exp(x)+3)-x-80)/(ex
p(-exp(x)+3)-20))-x)+((-x**2*ln(3)*exp(x)-x*ln(3))*exp(-exp(x)+3)+20*x*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp
(-exp(x)+3)-20))-x*ln(3)*exp(-exp(x)+3)**2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))/((exp(-exp(x)+3)**2-40*exp(-
exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)**2+40*x*exp(-exp(x)+3)-400*x)
,x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (26) = 52\).

Time = 0.63 (sec) , antiderivative size = 88, normalized size of antiderivative = 2.93 \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=\frac {4 \, x e^{3} \log \left (3\right ) + {\left (x e^{3} \log \left (3\right ) - 20 \, x e^{\left (e^{x}\right )} \log \left (3\right )\right )} \log \left (-x e^{\left (-\frac {4 \, e^{3}}{e^{3} - 20 \, e^{\left (e^{x}\right )}}\right )} + e^{\left (-\frac {x e^{\left (e^{x}\right )}}{e^{3} - 20 \, e^{\left (e^{x}\right )}} - \frac {80 \, e^{\left (e^{x}\right )}}{e^{3} - 20 \, e^{\left (e^{x}\right )}}\right )}\right )}{e^{3} - 20 \, e^{\left (e^{x}\right )}} \]

[In]

integrate((((log(3)*exp(-exp(x)+3)^2-40*log(3)*exp(-exp(x)+3)+400*log(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-ex
p(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))*log(exp((4*exp(-exp(x)+3)-x-80
)/(exp(-exp(x)+3)-20))-x)+((-x^2*log(3)*exp(x)-x*log(3))*exp(-exp(x)+3)+20*x*log(3))*exp((4*exp(-exp(x)+3)-x-8
0)/(exp(-exp(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))/((exp(-exp(x)+3)^2-
40*exp(-exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)
-400*x),x, algorithm="maxima")

[Out]

(4*x*e^3*log(3) + (x*e^3*log(3) - 20*x*e^(e^x)*log(3))*log(-x*e^(-4*e^3/(e^3 - 20*e^(e^x))) + e^(-x*e^(e^x)/(e
^3 - 20*e^(e^x)) - 80*e^(e^x)/(e^3 - 20*e^(e^x)))))/(e^3 - 20*e^(e^x))

Giac [F(-1)]

Timed out. \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=\text {Timed out} \]

[In]

integrate((((log(3)*exp(-exp(x)+3)^2-40*log(3)*exp(-exp(x)+3)+400*log(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-ex
p(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))*log(exp((4*exp(-exp(x)+3)-x-80
)/(exp(-exp(x)+3)-20))-x)+((-x^2*log(3)*exp(x)-x*log(3))*exp(-exp(x)+3)+20*x*log(3))*exp((4*exp(-exp(x)+3)-x-8
0)/(exp(-exp(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))/((exp(-exp(x)+3)^2-
40*exp(-exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)
-400*x),x, algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 12.74 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.10 \[ \int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (20 x \log (3)+e^{3-e^x} \left (-x \log (3)-e^x x^2 \log (3)\right )\right )+\left (-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3)\right )\right ) \log \left (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x\right )}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} \left (400+e^{6-2 e^x}-40 e^{3-e^x}\right )-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx=x\,\ln \left ({\mathrm {e}}^{-\frac {x}{{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}-20}}\,{\mathrm {e}}^{-\frac {80}{{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}-20}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}}{{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}-20}}-x\right )\,\ln \left (3\right ) \]

[In]

int((400*x*log(3) - exp(-(x - 4*exp(3 - exp(x)) + 80)/(exp(3 - exp(x)) - 20))*(20*x*log(3) - exp(3 - exp(x))*(
x*log(3) + x^2*exp(x)*log(3))) + log(exp(-(x - 4*exp(3 - exp(x)) + 80)/(exp(3 - exp(x)) - 20)) - x)*(400*x*log
(3) - exp(-(x - 4*exp(3 - exp(x)) + 80)/(exp(3 - exp(x)) - 20))*(400*log(3) - 40*exp(3 - exp(x))*log(3) + exp(
6 - 2*exp(x))*log(3)) - 40*x*exp(3 - exp(x))*log(3) + x*exp(6 - 2*exp(x))*log(3)) - 40*x*exp(3 - exp(x))*log(3
) + x*exp(6 - 2*exp(x))*log(3))/(400*x - 40*x*exp(3 - exp(x)) + x*exp(6 - 2*exp(x)) - exp(-(x - 4*exp(3 - exp(
x)) + 80)/(exp(3 - exp(x)) - 20))*(exp(6 - 2*exp(x)) - 40*exp(3 - exp(x)) + 400)),x)

[Out]

x*log(exp(-x/(exp(3)*exp(-exp(x)) - 20))*exp(-80/(exp(3)*exp(-exp(x)) - 20))*exp((4*exp(3)*exp(-exp(x)))/(exp(
3)*exp(-exp(x)) - 20)) - x)*log(3)