\(\int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2(x^2)} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2(x^2)} (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+(-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)) \log (x^2))}{x^{300}}}{4 x-4 x^2+x^3+(4 x-2 x^2) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2(x^2)} (-8 x+8 x^2-2 x^3+(-8 x+4 x^2) \log (2)-2 x \log ^2(2))}{x^{300}}+\frac {e^{450+50 \log ^2(x^2)} (4 x-4 x^2+x^3+(4 x-2 x^2) \log (2)+x \log ^2(2))}{x^{600}}} \, dx\) [6767]

Optimal result

Integrand size = 280, antiderivative size = 38 \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=-e^{\frac {x}{2-x+\log (2)}}+\frac {1}{2 \left (-1+e^{25 \left (3-\log \left (x^2\right )\right )^2}\right )} \]

[Out]

1/(2*exp(5*(3-ln(x^2))*(15-5*ln(x^2)))-2)-exp(x/(ln(2)+2-x))

Rubi [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {\$Aborted} \]

[In]

Int[(E^(x/(2 - x + Log[2]))*(-2*x - x*Log[2]) + (E^(450 + x/(2 - x + Log[2]) + 50*Log[x^2]^2)*(-2*x - x*Log[2]
))/x^600 + (E^(225 + 25*Log[x^2]^2)*(600 - 600*x + 150*x^2 + (600 - 300*x)*Log[2] + 150*Log[2]^2 + E^(x/(2 - x
+ Log[2]))*(4*x + 2*x*Log[2]) + (-200 + 200*x - 50*x^2 + (-200 + 100*x)*Log[2] - 50*Log[2]^2)*Log[x^2]))/x^30
0)/(4*x - 4*x^2 + x^3 + (4*x - 2*x^2)*Log[2] + x*Log[2]^2 + (E^(225 + 25*Log[x^2]^2)*(-8*x + 8*x^2 - 2*x^3 + (
-8*x + 4*x^2)*Log[2] - 2*x*Log[2]^2))/x^300 + (E^(450 + 50*Log[x^2]^2)*(4*x - 4*x^2 + x^3 + (4*x - 2*x^2)*Log[
2] + x*Log[2]^2))/x^600),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {\$Aborted} \]

[In]

Integrate[(E^(x/(2 - x + Log[2]))*(-2*x - x*Log[2]) + (E^(450 + x/(2 - x + Log[2]) + 50*Log[x^2]^2)*(-2*x - x*
Log[2]))/x^600 + (E^(225 + 25*Log[x^2]^2)*(600 - 600*x + 150*x^2 + (600 - 300*x)*Log[2] + 150*Log[2]^2 + E^(x/
(2 - x + Log[2]))*(4*x + 2*x*Log[2]) + (-200 + 200*x - 50*x^2 + (-200 + 100*x)*Log[2] - 50*Log[2]^2)*Log[x^2])
)/x^300)/(4*x - 4*x^2 + x^3 + (4*x - 2*x^2)*Log[2] + x*Log[2]^2 + (E^(225 + 25*Log[x^2]^2)*(-8*x + 8*x^2 - 2*x
^3 + (-8*x + 4*x^2)*Log[2] - 2*x*Log[2]^2))/x^300 + (E^(450 + 50*Log[x^2]^2)*(4*x - 4*x^2 + x^3 + (4*x - 2*x^2
)*Log[2] + x*Log[2]^2))/x^600),x]

[Out]

$Aborted

Maple [A] (verified)

Time = 29.72 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.87

method	result	size
parallelrisch	\(\frac {1-2 \,{\mathrm e}^{25 \ln \left (x^{2}\right )^{2}-150 \ln \left (x^{2}\right )+225} {\mathrm e}^{\frac {x}{\ln \left (2\right )+2-x}}+2 \,{\mathrm e}^{\frac {x}{\ln \left (2\right )+2-x}}}{2 \,{\mathrm e}^{25 \ln \left (x^{2}\right )^{2}-150 \ln \left (x^{2}\right )+225}-2}\)	\(71\)
risch	\(-{\mathrm e}^{\frac {x}{\ln \left (2\right )+2-x}}+\frac {1}{\frac {2 x^{-100 i \pi \,\operatorname {csgn}\left (i x^{2}\right )} x^{100 i \pi \,\operatorname {csgn}\left (i x \right )} {\mathrm e}^{100 \ln \left (x \right )^{2}+225} {\mathrm e}^{-\frac {25 \operatorname {csgn}\left (i x^{2}\right )^{6} \pi ^{2}}{4}} {\mathrm e}^{25 \operatorname {csgn}\left (i x^{2}\right )^{5} \operatorname {csgn}\left (i x \right ) \pi ^{2}} {\mathrm e}^{-\frac {75 \operatorname {csgn}\left (i x^{2}\right )^{4} \operatorname {csgn}\left (i x \right )^{2} \pi ^{2}}{2}} {\mathrm e}^{25 \operatorname {csgn}\left (i x^{2}\right )^{3} \operatorname {csgn}\left (i x \right )^{3} \pi ^{2}} {\mathrm e}^{-\frac {25 \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )^{4} \pi ^{2}}{4}}}{x^{300}}-2}\)	\(162\)

[In]

int(((-x*ln(2)-2*x)*exp(x/(ln(2)+2-x))*exp(25*ln(x^2)^2-150*ln(x^2)+225)^2+((-50*ln(2)^2+(100*x-200)*ln(2)-50*
x^2+200*x-200)*ln(x^2)+(2*x*ln(2)+4*x)*exp(x/(ln(2)+2-x))+150*ln(2)^2+(-300*x+600)*ln(2)+150*x^2-600*x+600)*ex
p(25*ln(x^2)^2-150*ln(x^2)+225)+(-x*ln(2)-2*x)*exp(x/(ln(2)+2-x)))/((x*ln(2)^2+(-2*x^2+4*x)*ln(2)+x^3-4*x^2+4*
x)*exp(25*ln(x^2)^2-150*ln(x^2)+225)^2+(-2*x*ln(2)^2+(4*x^2-8*x)*ln(2)-2*x^3+8*x^2-8*x)*exp(25*ln(x^2)^2-150*l
n(x^2)+225)+x*ln(2)^2+(-2*x^2+4*x)*ln(2)+x^3-4*x^2+4*x),x,method=_RETURNVERBOSE)

[Out]

1/2*(1-2*exp(25*ln(x^2)^2-150*ln(x^2)+225)*exp(x/(ln(2)+2-x))+2*exp(x/(ln(2)+2-x)))/(exp(25*ln(x^2)^2-150*ln(x
^2)+225)-1)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (33) = 66\).

Time = 0.25 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.87 \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=-\frac {2 \, e^{\left (25 \, \log \left (x^{2}\right )^{2} - \frac {x}{x - \log \left (2\right ) - 2} - 150 \, \log \left (x^{2}\right ) + 225\right )} - 2 \, e^{\left (-\frac {x}{x - \log \left (2\right ) - 2}\right )} - 1}{2 \, {\left (e^{\left (25 \, \log \left (x^{2}\right )^{2} - 150 \, \log \left (x^{2}\right ) + 225\right )} - 1\right )}} \]

[In]

integrate(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+225)^2+((-50*log(2)^2+(100*x-200
)*log(2)-50*x^2+200*x-200)*log(x^2)+(2*x*log(2)+4*x)*exp(x/(log(2)+2-x))+150*log(2)^2+(-300*x+600)*log(2)+150*
x^2-600*x+600)*exp(25*log(x^2)^2-150*log(x^2)+225)+(-x*log(2)-2*x)*exp(x/(log(2)+2-x)))/((x*log(2)^2+(-2*x^2+4
*x)*log(2)+x^3-4*x^2+4*x)*exp(25*log(x^2)^2-150*log(x^2)+225)^2+(-2*x*log(2)^2+(4*x^2-8*x)*log(2)-2*x^3+8*x^2-
8*x)*exp(25*log(x^2)^2-150*log(x^2)+225)+x*log(2)^2+(-2*x^2+4*x)*log(2)+x^3-4*x^2+4*x),x, algorithm="fricas")

[Out]

-1/2*(2*e^(25*log(x^2)^2 - x/(x - log(2) - 2) - 150*log(x^2) + 225) - 2*e^(-x/(x - log(2) - 2)) - 1)/(e^(25*lo
g(x^2)^2 - 150*log(x^2) + 225) - 1)

Sympy [A] (verification not implemented)

Time = 0.56 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.82 \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\frac {x^{300}}{- 2 x^{300} + 2 e^{25 \log {\left (x^{2} \right )}^{2} + 225}} - e^{\frac {x}{- x + \log {\left (2 \right )} + 2}} \]

[In]

integrate(((-x*ln(2)-2*x)*exp(x/(ln(2)+2-x))*exp(25*ln(x**2)**2-150*ln(x**2)+225)**2+((-50*ln(2)**2+(100*x-200
)*ln(2)-50*x**2+200*x-200)*ln(x**2)+(2*x*ln(2)+4*x)*exp(x/(ln(2)+2-x))+150*ln(2)**2+(-300*x+600)*ln(2)+150*x**
2-600*x+600)*exp(25*ln(x**2)**2-150*ln(x**2)+225)+(-x*ln(2)-2*x)*exp(x/(ln(2)+2-x)))/((x*ln(2)**2+(-2*x**2+4*x
)*ln(2)+x**3-4*x**2+4*x)*exp(25*ln(x**2)**2-150*ln(x**2)+225)**2+(-2*x*ln(2)**2+(4*x**2-8*x)*ln(2)-2*x**3+8*x*
*2-8*x)*exp(25*ln(x**2)**2-150*ln(x**2)+225)+x*ln(2)**2+(-2*x**2+4*x)*ln(2)+x**3-4*x**2+4*x),x)

[Out]

x**300/(-2*x**300 + 2*exp(25*log(x**2)**2 + 225)) - exp(x/(-x + log(2) + 2))

Maxima [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {Timed out} \]

[In]

integrate(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+225)^2+((-50*log(2)^2+(100*x-200
)*log(2)-50*x^2+200*x-200)*log(x^2)+(2*x*log(2)+4*x)*exp(x/(log(2)+2-x))+150*log(2)^2+(-300*x+600)*log(2)+150*
x^2-600*x+600)*exp(25*log(x^2)^2-150*log(x^2)+225)+(-x*log(2)-2*x)*exp(x/(log(2)+2-x)))/((x*log(2)^2+(-2*x^2+4
*x)*log(2)+x^3-4*x^2+4*x)*exp(25*log(x^2)^2-150*log(x^2)+225)^2+(-2*x*log(2)^2+(4*x^2-8*x)*log(2)-2*x^3+8*x^2-
8*x)*exp(25*log(x^2)^2-150*log(x^2)+225)+x*log(2)^2+(-2*x^2+4*x)*log(2)+x^3-4*x^2+4*x),x, algorithm="maxima")

[Out]

Timed out

Giac [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+225)^2+((-50*log(2)^2+(100*x-200
)*log(2)-50*x^2+200*x-200)*log(x^2)+(2*x*log(2)+4*x)*exp(x/(log(2)+2-x))+150*log(2)^2+(-300*x+600)*log(2)+150*
x^2-600*x+600)*exp(25*log(x^2)^2-150*log(x^2)+225)+(-x*log(2)-2*x)*exp(x/(log(2)+2-x)))/((x*log(2)^2+(-2*x^2+4
*x)*log(2)+x^3-4*x^2+4*x)*exp(25*log(x^2)^2-150*log(x^2)+225)^2+(-2*x*log(2)^2+(4*x^2-8*x)*log(2)-2*x^3+8*x^2-
8*x)*exp(25*log(x^2)^2-150*log(x^2)+225)+x*log(2)^2+(-2*x^2+4*x)*log(2)+x^3-4*x^2+4*x),x, algorithm="giac")

[Out]

Exception raised: TypeError >> an error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Unable to divide, perhaps due to rounding error%%%{-24000000,[0,3,915,1,1]%%%}+%%%{-48000000,[0,3,915,0,1]%
%%}+%%%{264

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {Hanged} \]

[In]

int(-(exp(x/(log(2) - x + 2))*(2*x + x*log(2)) - exp(25*log(x^2)^2 - 150*log(x^2) + 225)*(exp(x/(log(2) - x +
2))*(4*x + 2*x*log(2)) - log(2)*(300*x - 600) - 600*x - log(x^2)*(50*log(2)^2 - log(2)*(100*x - 200) - 200*x +
50*x^2 + 200) + 150*log(2)^2 + 150*x^2 + 600) + exp(x/(log(2) - x + 2))*exp(50*log(x^2)^2 - 300*log(x^2) + 45
0)*(2*x + x*log(2)))/(4*x + log(2)*(4*x - 2*x^2) - exp(25*log(x^2)^2 - 150*log(x^2) + 225)*(8*x + log(2)*(8*x
- 4*x^2) + 2*x*log(2)^2 - 8*x^2 + 2*x^3) + x*log(2)^2 - 4*x^2 + x^3 + exp(50*log(x^2)^2 - 300*log(x^2) + 450)*
(4*x + log(2)*(4*x - 2*x^2) + x*log(2)^2 - 4*x^2 + x^3)),x)

[Out]

\text{Hanged}