\(\int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) (2700+864 x-756 x^2+e^{2 x} (5400-5400 x+216 x^2-216 x^3))+e^{4-2 e^{2 x}} (-1+x)^2 (2700+432 x-324 x^2+e^{2 x} (5400-5400 x+216 x^2-216 x^3))+e^{6-3 e^{2 x}} (-1+x)^3 (900+96 x-60 x^2+e^{2 x} (1800-1800 x+72 x^2-72 x^3))+e^{8-4 e^{2 x}} (-1+x)^4 (100+8 x-4 x^2+e^{2 x} (200-200 x+8 x^2-8 x^3)))}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx\) [9783]

Optimal result

Integrand size = 351, antiderivative size = 29 \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=e^{\frac {\left (3+e^{2-e^{2 x}} (-1+x)\right )^4}{\left (25+x^2\right )^4}} \]

[Out]

exp((exp(ln(-1+x)-exp(x)^2+2)+3)^4/(x^2+25)^4)

Rubi [F(-1)]

Timed out. \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=\text {\$Aborted} \]

[In]

Int[(E^((81 + 108*E^(2 - E^(2*x))*(-1 + x) + 54*E^(4 - 2*E^(2*x))*(-1 + x)^2 + 12*E^(6 - 3*E^(2*x))*(-1 + x)^3
+ E^(8 - 4*E^(2*x))*(-1 + x)^4)/(390625 + 62500*x^2 + 3750*x^4 + 100*x^6 + x^8))*(648*x - 648*x^2 + E^(2 - E^
(2*x))*(-1 + x)*(2700 + 864*x - 756*x^2 + E^(2*x)*(5400 - 5400*x + 216*x^2 - 216*x^3)) + E^(4 - 2*E^(2*x))*(-1
+ x)^2*(2700 + 432*x - 324*x^2 + E^(2*x)*(5400 - 5400*x + 216*x^2 - 216*x^3)) + E^(6 - 3*E^(2*x))*(-1 + x)^3*
(900 + 96*x - 60*x^2 + E^(2*x)*(1800 - 1800*x + 72*x^2 - 72*x^3)) + E^(8 - 4*E^(2*x))*(-1 + x)^4*(100 + 8*x -
4*x^2 + E^(2*x)*(200 - 200*x + 8*x^2 - 8*x^3))))/(-9765625 + 9765625*x - 1953125*x^2 + 1953125*x^3 - 156250*x^
4 + 156250*x^5 - 6250*x^6 + 6250*x^7 - 125*x^8 + 125*x^9 - x^10 + x^11),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [A] (verified)

Time = 1.05 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=e^{\frac {e^{-4 e^{2 x}} \left (3 e^{e^{2 x}}+e^2 (-1+x)\right )^4}{\left (25+x^2\right )^4}} \]

[In]

Integrate[(E^((81 + 108*E^(2 - E^(2*x))*(-1 + x) + 54*E^(4 - 2*E^(2*x))*(-1 + x)^2 + 12*E^(6 - 3*E^(2*x))*(-1
+ x)^3 + E^(8 - 4*E^(2*x))*(-1 + x)^4)/(390625 + 62500*x^2 + 3750*x^4 + 100*x^6 + x^8))*(648*x - 648*x^2 + E^(
2 - E^(2*x))*(-1 + x)*(2700 + 864*x - 756*x^2 + E^(2*x)*(5400 - 5400*x + 216*x^2 - 216*x^3)) + E^(4 - 2*E^(2*x
))*(-1 + x)^2*(2700 + 432*x - 324*x^2 + E^(2*x)*(5400 - 5400*x + 216*x^2 - 216*x^3)) + E^(6 - 3*E^(2*x))*(-1 +
x)^3*(900 + 96*x - 60*x^2 + E^(2*x)*(1800 - 1800*x + 72*x^2 - 72*x^3)) + E^(8 - 4*E^(2*x))*(-1 + x)^4*(100 +
8*x - 4*x^2 + E^(2*x)*(200 - 200*x + 8*x^2 - 8*x^3))))/(-9765625 + 9765625*x - 1953125*x^2 + 1953125*x^3 - 156
250*x^4 + 156250*x^5 - 6250*x^6 + 6250*x^7 - 125*x^8 + 125*x^9 - x^10 + x^11),x]

[Out]

E^((3*E^E^(2*x) + E^2*(-1 + x))^4/(E^(4*E^(2*x))*(25 + x^2)^4))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(184\) vs. \(2(26)=52\).

Time = 12.65 (sec) , antiderivative size = 185, normalized size of antiderivative = 6.38

\[{\mathrm e}^{\frac {{\mathrm e}^{8-4 \,{\mathrm e}^{2 x}} x^{4}-4 \,{\mathrm e}^{8-4 \,{\mathrm e}^{2 x}} x^{3}+12 \,{\mathrm e}^{6-3 \,{\mathrm e}^{2 x}} x^{3}+6 \,{\mathrm e}^{8-4 \,{\mathrm e}^{2 x}} x^{2}-36 \,{\mathrm e}^{6-3 \,{\mathrm e}^{2 x}} x^{2}+54 \,{\mathrm e}^{-2 \,{\mathrm e}^{2 x}+4} x^{2}-4 \,{\mathrm e}^{8-4 \,{\mathrm e}^{2 x}} x +36 \,{\mathrm e}^{6-3 \,{\mathrm e}^{2 x}} x -108 \,{\mathrm e}^{-2 \,{\mathrm e}^{2 x}+4} x +108 \,{\mathrm e}^{2-{\mathrm e}^{2 x}} x +{\mathrm e}^{8-4 \,{\mathrm e}^{2 x}}-12 \,{\mathrm e}^{6-3 \,{\mathrm e}^{2 x}}+54 \,{\mathrm e}^{-2 \,{\mathrm e}^{2 x}+4}-108 \,{\mathrm e}^{2-{\mathrm e}^{2 x}}+81}{\left (x^{2}+25\right )^{4}}}\]

[In]

int((((-8*x^3+8*x^2-200*x+200)*exp(x)^2-4*x^2+8*x+100)*exp(ln(-1+x)-exp(x)^2+2)^4+((-72*x^3+72*x^2-1800*x+1800
)*exp(x)^2-60*x^2+96*x+900)*exp(ln(-1+x)-exp(x)^2+2)^3+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-324*x^2+432*x+
2700)*exp(ln(-1+x)-exp(x)^2+2)^2+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-756*x^2+864*x+2700)*exp(ln(-1+x)-exp
(x)^2+2)-648*x^2+648*x)*exp((exp(ln(-1+x)-exp(x)^2+2)^4+12*exp(ln(-1+x)-exp(x)^2+2)^3+54*exp(ln(-1+x)-exp(x)^2
+2)^2+108*exp(ln(-1+x)-exp(x)^2+2)+81)/(x^8+100*x^6+3750*x^4+62500*x^2+390625))/(x^11-x^10+125*x^9-125*x^8+625
0*x^7-6250*x^6+156250*x^5-156250*x^4+1953125*x^3-1953125*x^2+9765625*x-9765625),x)

[Out]

exp((exp(8-4*exp(2*x))*x^4-4*exp(8-4*exp(2*x))*x^3+12*exp(6-3*exp(2*x))*x^3+6*exp(8-4*exp(2*x))*x^2-36*exp(6-3
*exp(2*x))*x^2+54*exp(-2*exp(2*x)+4)*x^2-4*exp(8-4*exp(2*x))*x+36*exp(6-3*exp(2*x))*x-108*exp(-2*exp(2*x)+4)*x
+108*exp(2-exp(2*x))*x+exp(8-4*exp(2*x))-12*exp(6-3*exp(2*x))+54*exp(-2*exp(2*x)+4)-108*exp(2-exp(2*x))+81)/(x
^2+25)^4)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (26) = 52\).

Time = 0.28 (sec) , antiderivative size = 90, normalized size of antiderivative = 3.10 \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=e^{\left (\frac {108 \, e^{\left (-e^{\left (2 \, x\right )} + \log \left (x - 1\right ) + 2\right )} + 54 \, e^{\left (-2 \, e^{\left (2 \, x\right )} + 2 \, \log \left (x - 1\right ) + 4\right )} + 12 \, e^{\left (-3 \, e^{\left (2 \, x\right )} + 3 \, \log \left (x - 1\right ) + 6\right )} + e^{\left (-4 \, e^{\left (2 \, x\right )} + 4 \, \log \left (x - 1\right ) + 8\right )} + 81}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625}\right )} \]

[In]

integrate((((-8*x^3+8*x^2-200*x+200)*exp(x)^2-4*x^2+8*x+100)*exp(log(-1+x)-exp(x)^2+2)^4+((-72*x^3+72*x^2-1800
*x+1800)*exp(x)^2-60*x^2+96*x+900)*exp(log(-1+x)-exp(x)^2+2)^3+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-324*x^
2+432*x+2700)*exp(log(-1+x)-exp(x)^2+2)^2+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-756*x^2+864*x+2700)*exp(log
(-1+x)-exp(x)^2+2)-648*x^2+648*x)*exp((exp(log(-1+x)-exp(x)^2+2)^4+12*exp(log(-1+x)-exp(x)^2+2)^3+54*exp(log(-
1+x)-exp(x)^2+2)^2+108*exp(log(-1+x)-exp(x)^2+2)+81)/(x^8+100*x^6+3750*x^4+62500*x^2+390625))/(x^11-x^10+125*x
^9-125*x^8+6250*x^7-6250*x^6+156250*x^5-156250*x^4+1953125*x^3-1953125*x^2+9765625*x-9765625),x, algorithm="fr
icas")

[Out]

e^((108*e^(-e^(2*x) + log(x - 1) + 2) + 54*e^(-2*e^(2*x) + 2*log(x - 1) + 4) + 12*e^(-3*e^(2*x) + 3*log(x - 1)
+ 6) + e^(-4*e^(2*x) + 4*log(x - 1) + 8) + 81)/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 390625))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (22) = 44\).

Time = 7.14 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.93 \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=e^{\frac {\left (x - 1\right )^{4} e^{8 - 4 e^{2 x}} + 12 \left (x - 1\right )^{3} e^{6 - 3 e^{2 x}} + 54 \left (x - 1\right )^{2} e^{4 - 2 e^{2 x}} + 108 \left (x - 1\right ) e^{2 - e^{2 x}} + 81}{x^{8} + 100 x^{6} + 3750 x^{4} + 62500 x^{2} + 390625}} \]

[In]

integrate((((-8*x**3+8*x**2-200*x+200)*exp(x)**2-4*x**2+8*x+100)*exp(ln(-1+x)-exp(x)**2+2)**4+((-72*x**3+72*x*
*2-1800*x+1800)*exp(x)**2-60*x**2+96*x+900)*exp(ln(-1+x)-exp(x)**2+2)**3+((-216*x**3+216*x**2-5400*x+5400)*exp
(x)**2-324*x**2+432*x+2700)*exp(ln(-1+x)-exp(x)**2+2)**2+((-216*x**3+216*x**2-5400*x+5400)*exp(x)**2-756*x**2+
864*x+2700)*exp(ln(-1+x)-exp(x)**2+2)-648*x**2+648*x)*exp((exp(ln(-1+x)-exp(x)**2+2)**4+12*exp(ln(-1+x)-exp(x)
**2+2)**3+54*exp(ln(-1+x)-exp(x)**2+2)**2+108*exp(ln(-1+x)-exp(x)**2+2)+81)/(x**8+100*x**6+3750*x**4+62500*x**
2+390625))/(x**11-x**10+125*x**9-125*x**8+6250*x**7-6250*x**6+156250*x**5-156250*x**4+1953125*x**3-1953125*x**
2+9765625*x-9765625),x)

[Out]

exp(((x - 1)**4*exp(8 - 4*exp(2*x)) + 12*(x - 1)**3*exp(6 - 3*exp(2*x)) + 54*(x - 1)**2*exp(4 - 2*exp(2*x)) +
108*(x - 1)*exp(2 - exp(2*x)) + 81)/(x**8 + 100*x**6 + 3750*x**4 + 62500*x**2 + 390625))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 458 vs. \(2 (26) = 52\).

Time = 2.61 (sec) , antiderivative size = 458, normalized size of antiderivative = 15.79 \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=e^{\left (\frac {108 \, x e^{\left (-e^{\left (2 \, x\right )} + 2\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} - \frac {108 \, x e^{\left (-2 \, e^{\left (2 \, x\right )} + 4\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} - \frac {264 \, x e^{\left (-3 \, e^{\left (2 \, x\right )} + 6\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} + \frac {12 \, x e^{\left (-3 \, e^{\left (2 \, x\right )} + 6\right )}}{x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625} + \frac {96 \, x e^{\left (-4 \, e^{\left (2 \, x\right )} + 8\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} - \frac {4 \, x e^{\left (-4 \, e^{\left (2 \, x\right )} + 8\right )}}{x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625} - \frac {108 \, e^{\left (-e^{\left (2 \, x\right )} + 2\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} - \frac {1296 \, e^{\left (-2 \, e^{\left (2 \, x\right )} + 4\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} + \frac {54 \, e^{\left (-2 \, e^{\left (2 \, x\right )} + 4\right )}}{x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625} + \frac {888 \, e^{\left (-3 \, e^{\left (2 \, x\right )} + 6\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} - \frac {36 \, e^{\left (-3 \, e^{\left (2 \, x\right )} + 6\right )}}{x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625} + \frac {476 \, e^{\left (-4 \, e^{\left (2 \, x\right )} + 8\right )}}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625} - \frac {44 \, e^{\left (-4 \, e^{\left (2 \, x\right )} + 8\right )}}{x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625} + \frac {e^{\left (-4 \, e^{\left (2 \, x\right )} + 8\right )}}{x^{4} + 50 \, x^{2} + 625} + \frac {81}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625}\right )} \]

[In]

integrate((((-8*x^3+8*x^2-200*x+200)*exp(x)^2-4*x^2+8*x+100)*exp(log(-1+x)-exp(x)^2+2)^4+((-72*x^3+72*x^2-1800
*x+1800)*exp(x)^2-60*x^2+96*x+900)*exp(log(-1+x)-exp(x)^2+2)^3+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-324*x^
2+432*x+2700)*exp(log(-1+x)-exp(x)^2+2)^2+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-756*x^2+864*x+2700)*exp(log
(-1+x)-exp(x)^2+2)-648*x^2+648*x)*exp((exp(log(-1+x)-exp(x)^2+2)^4+12*exp(log(-1+x)-exp(x)^2+2)^3+54*exp(log(-
1+x)-exp(x)^2+2)^2+108*exp(log(-1+x)-exp(x)^2+2)+81)/(x^8+100*x^6+3750*x^4+62500*x^2+390625))/(x^11-x^10+125*x
^9-125*x^8+6250*x^7-6250*x^6+156250*x^5-156250*x^4+1953125*x^3-1953125*x^2+9765625*x-9765625),x, algorithm="ma
xima")

[Out]

e^(108*x*e^(-e^(2*x) + 2)/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 390625) - 108*x*e^(-2*e^(2*x) + 4)/(x^8 + 10
0*x^6 + 3750*x^4 + 62500*x^2 + 390625) - 264*x*e^(-3*e^(2*x) + 6)/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 3906
25) + 12*x*e^(-3*e^(2*x) + 6)/(x^6 + 75*x^4 + 1875*x^2 + 15625) + 96*x*e^(-4*e^(2*x) + 8)/(x^8 + 100*x^6 + 375
0*x^4 + 62500*x^2 + 390625) - 4*x*e^(-4*e^(2*x) + 8)/(x^6 + 75*x^4 + 1875*x^2 + 15625) - 108*e^(-e^(2*x) + 2)/
(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 390625) - 1296*e^(-2*e^(2*x) + 4)/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^
2 + 390625) + 54*e^(-2*e^(2*x) + 4)/(x^6 + 75*x^4 + 1875*x^2 + 15625) + 888*e^(-3*e^(2*x) + 6)/(x^8 + 100*x^6
+ 3750*x^4 + 62500*x^2 + 390625) - 36*e^(-3*e^(2*x) + 6)/(x^6 + 75*x^4 + 1875*x^2 + 15625) + 476*e^(-4*e^(2*x)
+ 8)/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 390625) - 44*e^(-4*e^(2*x) + 8)/(x^6 + 75*x^4 + 1875*x^2 + 15625
) + e^(-4*e^(2*x) + 8)/(x^4 + 50*x^2 + 625) + 81/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 390625))

Giac [F]

\[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx=\int { -\frac {4 \, {\left (162 \, x^{2} + 27 \, {\left (7 \, x^{2} + 2 \, {\left (x^{3} - x^{2} + 25 \, x - 25\right )} e^{\left (2 \, x\right )} - 8 \, x - 25\right )} e^{\left (-e^{\left (2 \, x\right )} + \log \left (x - 1\right ) + 2\right )} + 27 \, {\left (3 \, x^{2} + 2 \, {\left (x^{3} - x^{2} + 25 \, x - 25\right )} e^{\left (2 \, x\right )} - 4 \, x - 25\right )} e^{\left (-2 \, e^{\left (2 \, x\right )} + 2 \, \log \left (x - 1\right ) + 4\right )} + 3 \, {\left (5 \, x^{2} + 6 \, {\left (x^{3} - x^{2} + 25 \, x - 25\right )} e^{\left (2 \, x\right )} - 8 \, x - 75\right )} e^{\left (-3 \, e^{\left (2 \, x\right )} + 3 \, \log \left (x - 1\right ) + 6\right )} + {\left (x^{2} + 2 \, {\left (x^{3} - x^{2} + 25 \, x - 25\right )} e^{\left (2 \, x\right )} - 2 \, x - 25\right )} e^{\left (-4 \, e^{\left (2 \, x\right )} + 4 \, \log \left (x - 1\right ) + 8\right )} - 162 \, x\right )} e^{\left (\frac {108 \, e^{\left (-e^{\left (2 \, x\right )} + \log \left (x - 1\right ) + 2\right )} + 54 \, e^{\left (-2 \, e^{\left (2 \, x\right )} + 2 \, \log \left (x - 1\right ) + 4\right )} + 12 \, e^{\left (-3 \, e^{\left (2 \, x\right )} + 3 \, \log \left (x - 1\right ) + 6\right )} + e^{\left (-4 \, e^{\left (2 \, x\right )} + 4 \, \log \left (x - 1\right ) + 8\right )} + 81}{x^{8} + 100 \, x^{6} + 3750 \, x^{4} + 62500 \, x^{2} + 390625}\right )}}{x^{11} - x^{10} + 125 \, x^{9} - 125 \, x^{8} + 6250 \, x^{7} - 6250 \, x^{6} + 156250 \, x^{5} - 156250 \, x^{4} + 1953125 \, x^{3} - 1953125 \, x^{2} + 9765625 \, x - 9765625} \,d x } \]

[In]

integrate((((-8*x^3+8*x^2-200*x+200)*exp(x)^2-4*x^2+8*x+100)*exp(log(-1+x)-exp(x)^2+2)^4+((-72*x^3+72*x^2-1800
*x+1800)*exp(x)^2-60*x^2+96*x+900)*exp(log(-1+x)-exp(x)^2+2)^3+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-324*x^
2+432*x+2700)*exp(log(-1+x)-exp(x)^2+2)^2+((-216*x^3+216*x^2-5400*x+5400)*exp(x)^2-756*x^2+864*x+2700)*exp(log
(-1+x)-exp(x)^2+2)-648*x^2+648*x)*exp((exp(log(-1+x)-exp(x)^2+2)^4+12*exp(log(-1+x)-exp(x)^2+2)^3+54*exp(log(-
1+x)-exp(x)^2+2)^2+108*exp(log(-1+x)-exp(x)^2+2)+81)/(x^8+100*x^6+3750*x^4+62500*x^2+390625))/(x^11-x^10+125*x
^9-125*x^8+6250*x^7-6250*x^6+156250*x^5-156250*x^4+1953125*x^3-1953125*x^2+9765625*x-9765625),x, algorithm="gi
ac")

[Out]

integrate(-4*(162*x^2 + 27*(7*x^2 + 2*(x^3 - x^2 + 25*x - 25)*e^(2*x) - 8*x - 25)*e^(-e^(2*x) + log(x - 1) + 2
) + 27*(3*x^2 + 2*(x^3 - x^2 + 25*x - 25)*e^(2*x) - 4*x - 25)*e^(-2*e^(2*x) + 2*log(x - 1) + 4) + 3*(5*x^2 + 6
*(x^3 - x^2 + 25*x - 25)*e^(2*x) - 8*x - 75)*e^(-3*e^(2*x) + 3*log(x - 1) + 6) + (x^2 + 2*(x^3 - x^2 + 25*x -
25)*e^(2*x) - 2*x - 25)*e^(-4*e^(2*x) + 4*log(x - 1) + 8) - 162*x)*e^((108*e^(-e^(2*x) + log(x - 1) + 2) + 54*
e^(-2*e^(2*x) + 2*log(x - 1) + 4) + 12*e^(-3*e^(2*x) + 3*log(x - 1) + 6) + e^(-4*e^(2*x) + 4*log(x - 1) + 8) +
81)/(x^8 + 100*x^6 + 3750*x^4 + 62500*x^2 + 390625))/(x^11 - x^10 + 125*x^9 - 125*x^8 + 6250*x^7 - 6250*x^6 +
156250*x^5 - 156250*x^4 + 1953125*x^3 - 1953125*x^2 + 9765625*x - 9765625), x)

Mupad [B] (verification not implemented)

Time = 16.34 (sec) , antiderivative size = 522, normalized size of antiderivative = 18.00 \[ \int \frac {e^{\frac {81+108 e^{2-e^{2 x}} (-1+x)+54 e^{4-2 e^{2 x}} (-1+x)^2+12 e^{6-3 e^{2 x}} (-1+x)^3+e^{8-4 e^{2 x}} (-1+x)^4}{390625+62500 x^2+3750 x^4+100 x^6+x^8}} \left (648 x-648 x^2+e^{2-e^{2 x}} (-1+x) \left (2700+864 x-756 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{4-2 e^{2 x}} (-1+x)^2 \left (2700+432 x-324 x^2+e^{2 x} \left (5400-5400 x+216 x^2-216 x^3\right )\right )+e^{6-3 e^{2 x}} (-1+x)^3 \left (900+96 x-60 x^2+e^{2 x} \left (1800-1800 x+72 x^2-72 x^3\right )\right )+e^{8-4 e^{2 x}} (-1+x)^4 \left (100+8 x-4 x^2+e^{2 x} \left (200-200 x+8 x^2-8 x^3\right )\right )\right )}{-9765625+9765625 x-1953125 x^2+1953125 x^3-156250 x^4+156250 x^5-6250 x^6+6250 x^7-125 x^8+125 x^9-x^{10}+x^{11}} \, dx={\mathrm {e}}^{\frac {x^4\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^8}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{-\frac {4\,x^3\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^8}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {6\,x^2\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^8}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {12\,x^3\,{\mathrm {e}}^{-3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^6}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{-\frac {36\,x^2\,{\mathrm {e}}^{-3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^6}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {54\,x^2\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^4}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^8}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{-\frac {12\,{\mathrm {e}}^{-3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^6}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {54\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^4}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{-\frac {108\,{\mathrm {e}}^{-{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^2}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{-\frac {4\,x\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^8}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {36\,x\,{\mathrm {e}}^{-3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^6}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {108\,x\,{\mathrm {e}}^{-{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^2}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{-\frac {108\,x\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^4}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}}\,{\mathrm {e}}^{\frac {81}{x^8+100\,x^6+3750\,x^4+62500\,x^2+390625}} \]

[In]

int((exp((54*exp(2*log(x - 1) - 2*exp(2*x) + 4) + 12*exp(3*log(x - 1) - 3*exp(2*x) + 6) + exp(4*log(x - 1) - 4
*exp(2*x) + 8) + 108*exp(log(x - 1) - exp(2*x) + 2) + 81)/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*(64
8*x + exp(4*log(x - 1) - 4*exp(2*x) + 8)*(8*x - exp(2*x)*(200*x - 8*x^2 + 8*x^3 - 200) - 4*x^2 + 100) + exp(3*
log(x - 1) - 3*exp(2*x) + 6)*(96*x - exp(2*x)*(1800*x - 72*x^2 + 72*x^3 - 1800) - 60*x^2 + 900) + exp(2*log(x
- 1) - 2*exp(2*x) + 4)*(432*x - exp(2*x)*(5400*x - 216*x^2 + 216*x^3 - 5400) - 324*x^2 + 2700) + exp(log(x - 1
) - exp(2*x) + 2)*(864*x - exp(2*x)*(5400*x - 216*x^2 + 216*x^3 - 5400) - 756*x^2 + 2700) - 648*x^2))/(9765625
*x - 1953125*x^2 + 1953125*x^3 - 156250*x^4 + 156250*x^5 - 6250*x^6 + 6250*x^7 - 125*x^8 + 125*x^9 - x^10 + x^
11 - 9765625),x)

[Out]

exp((x^4*exp(-4*exp(2*x))*exp(8))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp(-(4*x^3*exp(-4*exp(2*x)
)*exp(8))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp((6*x^2*exp(-4*exp(2*x))*exp(8))/(62500*x^2 + 37
50*x^4 + 100*x^6 + x^8 + 390625))*exp((12*x^3*exp(-3*exp(2*x))*exp(6))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 +
390625))*exp(-(36*x^2*exp(-3*exp(2*x))*exp(6))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp((54*x^2*e
xp(-2*exp(2*x))*exp(4))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp((exp(-4*exp(2*x))*exp(8))/(62500*
x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp(-(12*exp(-3*exp(2*x))*exp(6))/(62500*x^2 + 3750*x^4 + 100*x^6 +
x^8 + 390625))*exp((54*exp(-2*exp(2*x))*exp(4))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp(-(108*exp
(-exp(2*x))*exp(2))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp(-(4*x*exp(-4*exp(2*x))*exp(8))/(62500
*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp((36*x*exp(-3*exp(2*x))*exp(6))/(62500*x^2 + 3750*x^4 + 100*x^6
+ x^8 + 390625))*exp((108*x*exp(-exp(2*x))*exp(2))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp(-(108*
x*exp(-2*exp(2*x))*exp(4))/(62500*x^2 + 3750*x^4 + 100*x^6 + x^8 + 390625))*exp(81/(62500*x^2 + 3750*x^4 + 100
*x^6 + x^8 + 390625))