Integrand size = 280, antiderivative size = 38 \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=-e^{\frac {x}{2-x+\log (2)}}+\frac {1}{2 \left (-1+e^{25 \left (3-\log \left (x^2\right )\right )^2}\right )} \] Output:
1/(2*exp(5*(3-ln(x^2))*(15-5*ln(x^2)))-2)-exp(x/(ln(2)+2-x))
Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {\$Aborted} \] Input:
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]
Output:
$Aborted
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\frac {e^{50 \log ^2\left (x^2\right )+\frac {x}{-x+2+\log (2)}+450} (x (-\log (2))-2 x)}{x^{600}}+\frac {e^{25 \log ^2\left (x^2\right )+225} \left (150 x^2+\left (-50 x^2+200 x+(100 x-200) \log (2)-200-50 \log ^2(2)\right ) \log \left (x^2\right )-600 x+e^{\frac {x}{-x+2+\log (2)}} (4 x+2 x \log (2))+(600-300 x) \log (2)+600+150 \log ^2(2)\right )}{x^{300}}+e^{\frac {x}{-x+2+\log (2)}} (x (-\log (2))-2 x)}{x^3-4 x^2+\left (4 x-2 x^2\right ) \log (2)+\frac {e^{50 \log ^2\left (x^2\right )+450} \left (x^3-4 x^2+\left (4 x-2 x^2\right ) \log (2)+4 x+x \log ^2(2)\right )}{x^{600}}+\frac {e^{25 \log ^2\left (x^2\right )+225} \left (-2 x^3+8 x^2+\left (4 x^2-8 x\right ) \log (2)-8 x-2 x \log ^2(2)\right )}{x^{300}}+4 x+x \log ^2(2)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\frac {e^{50 \log ^2\left (x^2\right )+\frac {x}{-x+2+\log (2)}+450} (x (-\log (2))-2 x)}{x^{600}}+\frac {e^{25 \log ^2\left (x^2\right )+225} \left (150 x^2+\left (-50 x^2+200 x+(100 x-200) \log (2)-200-50 \log ^2(2)\right ) \log \left (x^2\right )-600 x+e^{\frac {x}{-x+2+\log (2)}} (4 x+2 x \log (2))+(600-300 x) \log (2)+600+150 \log ^2(2)\right )}{x^{300}}+e^{\frac {x}{-x+2+\log (2)}} (x (-\log (2))-2 x)}{x^3-4 x^2+\left (4 x-2 x^2\right ) \log (2)+\frac {e^{50 \log ^2\left (x^2\right )+450} \left (x^3-4 x^2+\left (4 x-2 x^2\right ) \log (2)+4 x+x \log ^2(2)\right )}{x^{600}}+\frac {e^{25 \log ^2\left (x^2\right )+225} \left (-2 x^3+8 x^2+\left (4 x^2-8 x\right ) \log (2)-8 x-2 x \log ^2(2)\right )}{x^{300}}+x \left (4+\log ^2(2)\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^{599} \left (-\frac {(2+\log (2)) e^{50 \log ^2\left (x^2\right )+\frac {x}{-x+2+\log (2)}+450}}{x^{599}}-\frac {2 e^{25 \left (\log ^2\left (x^2\right )+9\right )} \left (-75 x^2+25 (-x+2+\log (2))^2 \log \left (x^2\right )-x (2+\log (2)) \left (e^{\frac {x}{-x+2+\log (2)}}-150\right )-75 (2+\log (2))^2\right )}{x^{300}}+x (2+\log (2)) \left (-e^{\frac {x}{-x+2+\log (2)}}\right )\right )}{\left (e^{25 \left (\log ^2\left (x^2\right )+9\right )}-x^{300}\right )^2 (-x+2+\log (2))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {300 x^{300} (-2-\log (2)) e^{25 \left (\log ^2\left (x^2\right )+9\right )}}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2 (-x+2+\log (2))^2}+\frac {150 x^{301} e^{25 \left (\log ^2\left (x^2\right )+9\right )}}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2 (-x+2+\log (2))^2}-\frac {50 x^{299} e^{25 \left (\log ^2\left (x^2\right )+9\right )} \log \left (x^2\right )}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2}+\frac {150 x^{299} (2+\log (2))^2 e^{25 \left (\log ^2\left (x^2\right )+9\right )}}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2 (-x+2+\log (2))^2}-\frac {(2+\log (2)) e^{\frac {x}{-x+2+\log (2)}}}{(x-2-\log (2))^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {300 x^{300} (-2-\log (2)) e^{25 \left (\log ^2\left (x^2\right )+9\right )}}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2 (-x+2+\log (2))^2}+\frac {150 x^{301} e^{25 \left (\log ^2\left (x^2\right )+9\right )}}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2 (-x+2+\log (2))^2}-\frac {50 x^{299} e^{25 \left (\log ^2\left (x^2\right )+9\right )} \log \left (x^2\right )}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2}+\frac {150 x^{299} (2+\log (2))^2 e^{25 \left (\log ^2\left (x^2\right )+9\right )}}{\left (e^{25 \log ^2\left (x^2\right )+225}-x^{300}\right )^2 (-x+2+\log (2))^2}-\frac {(2+\log (2)) e^{\frac {x}{-x+2+\log (2)}}}{(x-2-\log (2))^2}\right )dx\) |
Input:
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)*(6 00 - 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)*Lo g[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]
Output:
$Aborted
Time = 48.54 (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 | \(-{\mathrm e}^{\frac {x}{\ln \left (2\right )+2-x}}+\frac {1}{\frac {2 x^{-100 i \pi \,\operatorname {csgn}\left (i x^{2}\right )} x^{100 i \pi \,\operatorname {csgn}\left (i x \right )} {\mathrm e}^{100 \ln \left (x \right )^{2}+225} {\mathrm e}^{-\frac {25 \pi ^{2} \operatorname {csgn}\left (i x^{2}\right )^{6}}{4}} {\mathrm e}^{25 \pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{5}} {\mathrm e}^{-\frac {75 \pi ^{2} \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )^{4}}{2}} {\mathrm e}^{25 \pi ^{2} \operatorname {csgn}\left (i x \right )^{3} \operatorname {csgn}\left (i x^{2}\right )^{3}} {\mathrm e}^{-\frac {25 \pi ^{2} \operatorname {csgn}\left (i x \right )^{4} \operatorname {csgn}\left (i x^{2}\right )^{2}}{4}}}{x^{300}}-2}\) | \(162\) |
Input:
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)*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,method=_RETURNVERBOS E)
Output:
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)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (33) = 66\).
Time = 0.09 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.87 \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=-\frac {2 \, e^{\left (25 \, \log \left (x^{2}\right )^{2} - \frac {x}{x - \log \left (2\right ) - 2} - 150 \, \log \left (x^{2}\right ) + 225\right )} - 2 \, e^{\left (-\frac {x}{x - \log \left (2\right ) - 2}\right )} - 1}{2 \, {\left (e^{\left (25 \, \log \left (x^{2}\right )^{2} - 150 \, \log \left (x^{2}\right ) + 225\right )} - 1\right )}} \] Input:
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/(lo g(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")
Output:
-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*log(x^2)^2 - 150*log(x^2) + 225) - 1)
Time = 0.55 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.82 \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\frac {x^{300}}{- 2 x^{300} + 2 e^{25 \log {\left (x^{2} \right )}^{2} + 225}} - e^{\frac {x}{- x + \log {\left (2 \right )} + 2}} \] Input:
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)
Output:
x**300/(-2*x**300 + 2*exp(25*log(x**2)**2 + 225)) - exp(x/(-x + log(2) + 2 ))
Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {Timed out} \] Input:
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/(lo g(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")
Output:
Timed out
Exception generated. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {Exception raised: TypeError} \] Input:
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/(lo g(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")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro unding error%%%{-24000000,[0,3,915,1,1]%%%}+%%%{-48000000,[0,3,915,0,1]%%% }+%%%{264
Timed out. \[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {Hanged} \] Input:
int(-(exp(x/(log(2) - x + 2))*(2*x + x*log(2)) - exp(25*log(x^2)^2 - 150*l og(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 + 5 0*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) + 450)*(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*l og(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)
Output:
\text{Hanged}
\[ \int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2\left (x^2\right )} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+\left (-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)\right ) \log \left (x^2\right )\right )}{x^{300}}}{4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2\left (x^2\right )} \left (-8 x+8 x^2-2 x^3+\left (-8 x+4 x^2\right ) \log (2)-2 x \log ^2(2)\right )}{x^{300}}+\frac {e^{450+50 \log ^2\left (x^2\right )} \left (4 x-4 x^2+x^3+\left (4 x-2 x^2\right ) \log (2)+x \log ^2(2)\right )}{x^{600}}} \, dx=\text {too large to display} \] Input:
int(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+22 5)^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)^2-15 0*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(2 5*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)
Output:
- int(e**((50*log(x**2)**2*log(2) - 50*log(x**2)**2*x + 100*log(x**2)**2 + x)/(log(2) - x + 2))/(e**(50*log(x**2)**2)*log(2)**2*e**450 - 2*e**(50*l og(x**2)**2)*log(2)*e**450*x + 4*e**(50*log(x**2)**2)*log(2)*e**450 + e**( 50*log(x**2)**2)*e**450*x**2 - 4*e**(50*log(x**2)**2)*e**450*x + 4*e**(50* log(x**2)**2)*e**450 - 2*e**(25*log(x**2)**2)*log(2)**2*e**225*x**300 + 4* e**(25*log(x**2)**2)*log(2)*e**225*x**301 - 8*e**(25*log(x**2)**2)*log(2)* e**225*x**300 - 2*e**(25*log(x**2)**2)*e**225*x**302 + 8*e**(25*log(x**2)* *2)*e**225*x**301 - 8*e**(25*log(x**2)**2)*e**225*x**300 + log(2)**2*x**60 0 - 2*log(2)*x**601 + 4*log(2)*x**600 + x**602 - 4*x**601 + 4*x**600),x)*l og(2)*e**450 - 2*int(e**((50*log(x**2)**2*log(2) - 50*log(x**2)**2*x + 100 *log(x**2)**2 + x)/(log(2) - x + 2))/(e**(50*log(x**2)**2)*log(2)**2*e**45 0 - 2*e**(50*log(x**2)**2)*log(2)*e**450*x + 4*e**(50*log(x**2)**2)*log(2) *e**450 + e**(50*log(x**2)**2)*e**450*x**2 - 4*e**(50*log(x**2)**2)*e**450 *x + 4*e**(50*log(x**2)**2)*e**450 - 2*e**(25*log(x**2)**2)*log(2)**2*e**2 25*x**300 + 4*e**(25*log(x**2)**2)*log(2)*e**225*x**301 - 8*e**(25*log(x** 2)**2)*log(2)*e**225*x**300 - 2*e**(25*log(x**2)**2)*e**225*x**302 + 8*e** (25*log(x**2)**2)*e**225*x**301 - 8*e**(25*log(x**2)**2)*e**225*x**300 + l og(2)**2*x**600 - 2*log(2)*x**601 + 4*log(2)*x**600 + x**602 - 4*x**601 + 4*x**600),x)*e**450 + 2*int((e**((25*log(x**2)**2*log(2) - 25*log(x**2)**2 *x + 50*log(x**2)**2 + x)/(log(2) - x + 2))*x**300)/(e**(50*log(x**2)**...