\(\int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} (-16 x+4 x^2)+e^x (-48 x-46 x^2+6 x^3+2 x^4)+e^{2 x} (-40-248 x-28 x^2+14 x^3+2 x^4)+(e^{2 x} (8+88 x-6 x^2-4 x^3)+e^x (8 x+6 x^2-2 x^3)) \log (\frac {-12+3 x}{x})+e^{2 x} (-8 x+2 x^2) \log ^2(\frac {-12+3 x}{x})+e^{e^{2 x}} (-8 x+2 x^2+e^x (-8-48 x+4 x^2+2 x^3)+e^{2 x} (-16 x^2+4 x^3)+e^{3 x} (-80 x+4 x^2+4 x^3)+(e^{3 x} (16 x-4 x^2)+e^x (8 x-2 x^2)) \log (\frac {-12+3 x}{x}))}{-4 x+x^2} \, dx\) [1986]

Optimal result

Integrand size = 284, antiderivative size = 29 \[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=\left (e^{e^{2 x}}+x+e^x \left (5+x-\log \left (\frac {3 (-4+x)}{x}\right )\right )\right )^2 \]

[Out]

((5+x-ln(3*(x-4)/x))*exp(x)+exp(exp(x)^2)+x)^2

Rubi [F(-1)]

Timed out. \[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=\text {\$Aborted} \]

[In]

Int[(-8*x^2 + 2*x^3 + E^(2*E^(2*x) + 2*x)*(-16*x + 4*x^2) + E^x*(-48*x - 46*x^2 + 6*x^3 + 2*x^4) + E^(2*x)*(-4
0 - 248*x - 28*x^2 + 14*x^3 + 2*x^4) + (E^(2*x)*(8 + 88*x - 6*x^2 - 4*x^3) + E^x*(8*x + 6*x^2 - 2*x^3))*Log[(-
12 + 3*x)/x] + E^(2*x)*(-8*x + 2*x^2)*Log[(-12 + 3*x)/x]^2 + E^E^(2*x)*(-8*x + 2*x^2 + E^x*(-8 - 48*x + 4*x^2
+ 2*x^3) + E^(2*x)*(-16*x^2 + 4*x^3) + E^(3*x)*(-80*x + 4*x^2 + 4*x^3) + (E^(3*x)*(16*x - 4*x^2) + E^x*(8*x -
2*x^2))*Log[(-12 + 3*x)/x]))/(-4*x + x^2),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [A] (verified)

Time = 0.32 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=\left (e^{e^{2 x}}+x+e^x (5+x)-e^x \log \left (\frac {3 (-4+x)}{x}\right )\right )^2 \]

[In]

Integrate[(-8*x^2 + 2*x^3 + E^(2*E^(2*x) + 2*x)*(-16*x + 4*x^2) + E^x*(-48*x - 46*x^2 + 6*x^3 + 2*x^4) + E^(2*
x)*(-40 - 248*x - 28*x^2 + 14*x^3 + 2*x^4) + (E^(2*x)*(8 + 88*x - 6*x^2 - 4*x^3) + E^x*(8*x + 6*x^2 - 2*x^3))*
Log[(-12 + 3*x)/x] + E^(2*x)*(-8*x + 2*x^2)*Log[(-12 + 3*x)/x]^2 + E^E^(2*x)*(-8*x + 2*x^2 + E^x*(-8 - 48*x +
4*x^2 + 2*x^3) + E^(2*x)*(-16*x^2 + 4*x^3) + E^(3*x)*(-80*x + 4*x^2 + 4*x^3) + (E^(3*x)*(16*x - 4*x^2) + E^x*(
8*x - 2*x^2))*Log[(-12 + 3*x)/x]))/(-4*x + x^2),x]

[Out]

(E^E^(2*x) + x + E^x*(5 + x) - E^x*Log[(3*(-4 + x))/x])^2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(150\) vs. \(2(26)=52\).

Time = 0.95 (sec) , antiderivative size = 151, normalized size of antiderivative = 5.21

method	result	size
parallelrisch	\({\mathrm e}^{2 x} x^{2}-2 \ln \left (\frac {3 x -12}{x}\right ) {\mathrm e}^{2 x} x +{\mathrm e}^{2 x} \ln \left (\frac {3 x -12}{x}\right )^{2}+2 \,{\mathrm e}^{x} x^{2}+10 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{2 x}} x -2 \,{\mathrm e}^{x} \ln \left (\frac {3 x -12}{x}\right ) x -10 \ln \left (\frac {3 x -12}{x}\right ) {\mathrm e}^{2 x}-2 \ln \left (\frac {3 x -12}{x}\right ) {\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{2 x}}+x^{2}+10 \,{\mathrm e}^{x} x +2 x \,{\mathrm e}^{{\mathrm e}^{2 x}}+25 \,{\mathrm e}^{2 x}+10 \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{2 x}}+{\mathrm e}^{2 \,{\mathrm e}^{2 x}}\)	\(151\)
risch	\(\text {Expression too large to display}\)	\(1246\)

[In]

int(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*ln((3*x-12)/x)+(4*x^3
+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x^2-8*x)
*exp(x)^2*ln((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*ln((3*x-12)/x)+(2*x^4+14
*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x,method=_RETURNVERBOSE
)

[Out]

exp(x)^2*x^2-2*x*exp(x)^2*ln(3*(x-4)/x)+exp(x)^2*ln(3*(x-4)/x)^2+2*exp(x)*x^2+10*x*exp(x)^2+2*exp(x)*exp(exp(x
)^2)*x-2*exp(x)*ln(3*(x-4)/x)*x-10*exp(x)^2*ln(3*(x-4)/x)-2*ln(3*(x-4)/x)*exp(x)*exp(exp(x)^2)+x^2+10*exp(x)*x
+2*x*exp(exp(x)^2)+25*exp(x)^2+10*exp(x)*exp(exp(x)^2)+exp(exp(x)^2)^2

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (26) = 52\).

Time = 0.25 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.55 \[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=e^{\left (2 \, x\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )^{2} + x^{2} + {\left (x^{2} + 10 \, x + 25\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} + 5 \, x\right )} e^{x} + 2 \, {\left ({\left (x + 5\right )} e^{x} - e^{x} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) + x\right )} e^{\left (e^{\left (2 \, x\right )}\right )} - 2 \, {\left ({\left (x + 5\right )} e^{\left (2 \, x\right )} + x e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) + e^{\left (2 \, e^{\left (2 \, x\right )}\right )} \]

[In]

integrate(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*log((3*x-12)/x)
+(4*x^3+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x
^2-8*x)*exp(x)^2*log((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*log((3*x-12)/x)+
(2*x^4+14*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x, algorithm="
fricas")

[Out]

e^(2*x)*log(3*(x - 4)/x)^2 + x^2 + (x^2 + 10*x + 25)*e^(2*x) + 2*(x^2 + 5*x)*e^x + 2*((x + 5)*e^x - e^x*log(3*
(x - 4)/x) + x)*e^(e^(2*x)) - 2*((x + 5)*e^(2*x) + x*e^x)*log(3*(x - 4)/x) + e^(2*e^(2*x))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (24) = 48\).

Time = 44.59 (sec) , antiderivative size = 116, normalized size of antiderivative = 4.00 \[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=x^{2} + \left (2 x^{2} - 2 x \log {\left (\frac {3 x - 12}{x} \right )} + 10 x\right ) e^{x} + \left (2 x e^{x} + 2 x - 2 e^{x} \log {\left (\frac {3 x - 12}{x} \right )} + 10 e^{x}\right ) e^{e^{2 x}} + \left (x^{2} - 2 x \log {\left (\frac {3 x - 12}{x} \right )} + 10 x + \log {\left (\frac {3 x - 12}{x} \right )}^{2} - 10 \log {\left (\frac {3 x - 12}{x} \right )} + 25\right ) e^{2 x} + e^{2 e^{2 x}} \]

[In]

integrate(((4*x**2-16*x)*exp(x)**2*exp(exp(x)**2)**2+(((-4*x**2+16*x)*exp(x)**3+(-2*x**2+8*x)*exp(x))*ln((3*x-
12)/x)+(4*x**3+4*x**2-80*x)*exp(x)**3+(4*x**3-16*x**2)*exp(x)**2+(2*x**3+4*x**2-48*x-8)*exp(x)+2*x**2-8*x)*exp
(exp(x)**2)+(2*x**2-8*x)*exp(x)**2*ln((3*x-12)/x)**2+((-4*x**3-6*x**2+88*x+8)*exp(x)**2+(-2*x**3+6*x**2+8*x)*e
xp(x))*ln((3*x-12)/x)+(2*x**4+14*x**3-28*x**2-248*x-40)*exp(x)**2+(2*x**4+6*x**3-46*x**2-48*x)*exp(x)+2*x**3-8
*x**2)/(x**2-4*x),x)

[Out]

x**2 + (2*x**2 - 2*x*log((3*x - 12)/x) + 10*x)*exp(x) + (2*x*exp(x) + 2*x - 2*exp(x)*log((3*x - 12)/x) + 10*ex
p(x))*exp(exp(2*x)) + (x**2 - 2*x*log((3*x - 12)/x) + 10*x + log((3*x - 12)/x)**2 - 10*log((3*x - 12)/x) + 25)
*exp(2*x) + exp(2*exp(2*x))

Maxima [F]

\[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=\int { \frac {2 \, {\left ({\left (x^{2} - 4 \, x\right )} e^{\left (2 \, x\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )^{2} + x^{3} - 4 \, x^{2} + {\left (x^{4} + 7 \, x^{3} - 14 \, x^{2} - 124 \, x - 20\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{4} + 3 \, x^{3} - 23 \, x^{2} - 24 \, x\right )} e^{x} + {\left (x^{2} + 2 \, {\left (x^{3} + x^{2} - 20 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (2 \, x\right )} + {\left (x^{3} + 2 \, x^{2} - 24 \, x - 4\right )} e^{x} - {\left (2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (3 \, x\right )} + {\left (x^{2} - 4 \, x\right )} e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) - 4 \, x\right )} e^{\left (e^{\left (2 \, x\right )}\right )} - {\left ({\left (2 \, x^{3} + 3 \, x^{2} - 44 \, x - 4\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 3 \, x^{2} - 4 \, x\right )} e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )\right )}}{x^{2} - 4 \, x} \,d x } \]

[In]

integrate(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*log((3*x-12)/x)
+(4*x^3+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x
^2-8*x)*exp(x)^2*log((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*log((3*x-12)/x)+
(2*x^4+14*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x, algorithm="
maxima")

[Out]

e^(2*x)*log(x - 4)^2 + 2*x*e^x*log(x) + x^2 + (x^2 - 2*x*(log(3) - 5) + log(3)^2 + 2*(x - log(3) + 5)*log(x) +
log(x)^2 - 10*log(3) + 25)*e^(2*x) + 2*((x - log(3) + log(x) + 5)*e^x - e^x*log(x - 4) + x)*e^(e^(2*x)) + 48*
e^4*exp_integral_e(1, -x + 4) - 2*((x - log(3) + log(x) + 5)*e^(2*x) + x*e^x)*log(x - 4) + e^(2*e^(2*x)) + 2*i
ntegrate((x^3 - x^2*(log(3) - 3) + x*(3*log(3) - 23) + 4*log(3) + 4)*e^x/(x - 4), x)

Giac [F]

\[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=\int { \frac {2 \, {\left ({\left (x^{2} - 4 \, x\right )} e^{\left (2 \, x\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )^{2} + x^{3} - 4 \, x^{2} + {\left (x^{4} + 7 \, x^{3} - 14 \, x^{2} - 124 \, x - 20\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{4} + 3 \, x^{3} - 23 \, x^{2} - 24 \, x\right )} e^{x} + {\left (x^{2} + 2 \, {\left (x^{3} + x^{2} - 20 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (2 \, x\right )} + {\left (x^{3} + 2 \, x^{2} - 24 \, x - 4\right )} e^{x} - {\left (2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (3 \, x\right )} + {\left (x^{2} - 4 \, x\right )} e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) - 4 \, x\right )} e^{\left (e^{\left (2 \, x\right )}\right )} - {\left ({\left (2 \, x^{3} + 3 \, x^{2} - 44 \, x - 4\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 3 \, x^{2} - 4 \, x\right )} e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )\right )}}{x^{2} - 4 \, x} \,d x } \]

[In]

integrate(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*log((3*x-12)/x)
+(4*x^3+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x
^2-8*x)*exp(x)^2*log((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*log((3*x-12)/x)+
(2*x^4+14*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x, algorithm="
giac")

[Out]

integrate(2*((x^2 - 4*x)*e^(2*x)*log(3*(x - 4)/x)^2 + x^3 - 4*x^2 + (x^4 + 7*x^3 - 14*x^2 - 124*x - 20)*e^(2*x
) + 2*(x^2 - 4*x)*e^(2*x + 2*e^(2*x)) + (x^4 + 3*x^3 - 23*x^2 - 24*x)*e^x + (x^2 + 2*(x^3 + x^2 - 20*x)*e^(3*x
) + 2*(x^3 - 4*x^2)*e^(2*x) + (x^3 + 2*x^2 - 24*x - 4)*e^x - (2*(x^2 - 4*x)*e^(3*x) + (x^2 - 4*x)*e^x)*log(3*(
x - 4)/x) - 4*x)*e^(e^(2*x)) - ((2*x^3 + 3*x^2 - 44*x - 4)*e^(2*x) + (x^3 - 3*x^2 - 4*x)*e^x)*log(3*(x - 4)/x)
)/(x^2 - 4*x), x)

Mupad [F(-1)]

Timed out. \[ \int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} \left (-16 x+4 x^2\right )+e^x \left (-48 x-46 x^2+6 x^3+2 x^4\right )+e^{2 x} \left (-40-248 x-28 x^2+14 x^3+2 x^4\right )+\left (e^{2 x} \left (8+88 x-6 x^2-4 x^3\right )+e^x \left (8 x+6 x^2-2 x^3\right )\right ) \log \left (\frac {-12+3 x}{x}\right )+e^{2 x} \left (-8 x+2 x^2\right ) \log ^2\left (\frac {-12+3 x}{x}\right )+e^{e^{2 x}} \left (-8 x+2 x^2+e^x \left (-8-48 x+4 x^2+2 x^3\right )+e^{2 x} \left (-16 x^2+4 x^3\right )+e^{3 x} \left (-80 x+4 x^2+4 x^3\right )+\left (e^{3 x} \left (16 x-4 x^2\right )+e^x \left (8 x-2 x^2\right )\right ) \log \left (\frac {-12+3 x}{x}\right )\right )}{-4 x+x^2} \, dx=\int \frac {{\mathrm {e}}^x\,\left (-2\,x^4-6\,x^3+46\,x^2+48\,x\right )+{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\left (8\,x-{\mathrm {e}}^{3\,x}\,\left (4\,x^3+4\,x^2-80\,x\right )-\ln \left (\frac {3\,x-12}{x}\right )\,\left ({\mathrm {e}}^{3\,x}\,\left (16\,x-4\,x^2\right )+{\mathrm {e}}^x\,\left (8\,x-2\,x^2\right )\right )+{\mathrm {e}}^{2\,x}\,\left (16\,x^2-4\,x^3\right )-2\,x^2+{\mathrm {e}}^x\,\left (-2\,x^3-4\,x^2+48\,x+8\right )\right )+{\mathrm {e}}^{2\,x}\,\left (-2\,x^4-14\,x^3+28\,x^2+248\,x+40\right )-\ln \left (\frac {3\,x-12}{x}\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (-4\,x^3-6\,x^2+88\,x+8\right )+{\mathrm {e}}^x\,\left (-2\,x^3+6\,x^2+8\,x\right )\right )+8\,x^2-2\,x^3+{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{2\,x}\,\left (16\,x-4\,x^2\right )+{\mathrm {e}}^{2\,x}\,{\ln \left (\frac {3\,x-12}{x}\right )}^2\,\left (8\,x-2\,x^2\right )}{4\,x-x^2} \,d x \]

[In]

int((exp(x)*(48*x + 46*x^2 - 6*x^3 - 2*x^4) + exp(exp(2*x))*(8*x - exp(3*x)*(4*x^2 - 80*x + 4*x^3) - log((3*x
- 12)/x)*(exp(3*x)*(16*x - 4*x^2) + exp(x)*(8*x - 2*x^2)) + exp(2*x)*(16*x^2 - 4*x^3) - 2*x^2 + exp(x)*(48*x -
4*x^2 - 2*x^3 + 8)) + exp(2*x)*(248*x + 28*x^2 - 14*x^3 - 2*x^4 + 40) - log((3*x - 12)/x)*(exp(2*x)*(88*x - 6
*x^2 - 4*x^3 + 8) + exp(x)*(8*x + 6*x^2 - 2*x^3)) + 8*x^2 - 2*x^3 + exp(2*exp(2*x))*exp(2*x)*(16*x - 4*x^2) +
exp(2*x)*log((3*x - 12)/x)^2*(8*x - 2*x^2))/(4*x - x^2),x)

[Out]

int((exp(x)*(48*x + 46*x^2 - 6*x^3 - 2*x^4) + exp(exp(2*x))*(8*x - exp(3*x)*(4*x^2 - 80*x + 4*x^3) - log((3*x
- 12)/x)*(exp(3*x)*(16*x - 4*x^2) + exp(x)*(8*x - 2*x^2)) + exp(2*x)*(16*x^2 - 4*x^3) - 2*x^2 + exp(x)*(48*x -
4*x^2 - 2*x^3 + 8)) + exp(2*x)*(248*x + 28*x^2 - 14*x^3 - 2*x^4 + 40) - log((3*x - 12)/x)*(exp(2*x)*(88*x - 6
*x^2 - 4*x^3 + 8) + exp(x)*(8*x + 6*x^2 - 2*x^3)) + 8*x^2 - 2*x^3 + exp(2*exp(2*x))*exp(2*x)*(16*x - 4*x^2) +
exp(2*x)*log((3*x - 12)/x)^2*(8*x - 2*x^2))/(4*x - x^2), x)