3.14.14 \(\int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+(6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5) \log (2)+(1600-375 x+25 x^2) \log ^2(2)}{100-20 x^3+x^6+(100-10 x^3) \log (2)+25 \log ^2(2)}} (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+(-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7) \log (2)+(-8050+700 x+1125 x^3-150 x^4) \log ^2(2)+(-1875+250 x) \log ^3(2))}{1000-300 x^3+30 x^6-x^9+(1500-300 x^3+15 x^6) \log (2)+(750-75 x^3) \log ^2(2)+125 \log ^3(2)} \, dx\)
Optimal. Leaf size=31 \[ e^{x+\left (x-2 \left (4+\frac {4}{-x^2+\frac {5 (2+\log (2))}{x}}\right )\right )^2} \]
________________________________________________________________________________________
Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(E^((6400 - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 - 15*x^7 + x^8 + (6400 - 860*x + 20*x^2 -
640*x^3 + 150*x^4 - 10*x^5)*Log[2] + (1600 - 375*x + 25*x^2)*Log[2]^2)/(100 - 20*x^3 + x^6 + (100 - 10*x^3)*Lo
g[2] + 25*Log[2]^2))*(-2200 + 80*x + 5780*x^3 - 184*x^4 - 706*x^6 + 76*x^7 + 15*x^9 - 2*x^10 + (-9700 + 440*x
+ 5140*x^3 - 520*x^4 - 225*x^6 + 30*x^7)*Log[2] + (-8050 + 700*x + 1125*x^3 - 150*x^4)*Log[2]^2 + (-1875 + 250
*x)*Log[2]^3))/(1000 - 300*x^3 + 30*x^6 - x^9 + (1500 - 300*x^3 + 15*x^6)*Log[2] + (750 - 75*x^3)*Log[2]^2 + 1
25*Log[2]^3),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [F] time = 16.30, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[(E^((6400 - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 - 15*x^7 + x^8 + (6400 - 860*x + 20*
x^2 - 640*x^3 + 150*x^4 - 10*x^5)*Log[2] + (1600 - 375*x + 25*x^2)*Log[2]^2)/(100 - 20*x^3 + x^6 + (100 - 10*x
^3)*Log[2] + 25*Log[2]^2))*(-2200 + 80*x + 5780*x^3 - 184*x^4 - 706*x^6 + 76*x^7 + 15*x^9 - 2*x^10 + (-9700 +
440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 30*x^7)*Log[2] + (-8050 + 700*x + 1125*x^3 - 150*x^4)*Log[2]^2 + (-1875
+ 250*x)*Log[2]^3))/(1000 - 300*x^3 + 30*x^6 - x^9 + (1500 - 300*x^3 + 15*x^6)*Log[2] + (750 - 75*x^3)*Log[2]
^2 + 125*Log[2]^3),x]
[Out]
Integrate[(E^((6400 - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 - 15*x^7 + x^8 + (6400 - 860*x + 20*
x^2 - 640*x^3 + 150*x^4 - 10*x^5)*Log[2] + (1600 - 375*x + 25*x^2)*Log[2]^2)/(100 - 20*x^3 + x^6 + (100 - 10*x
^3)*Log[2] + 25*Log[2]^2))*(-2200 + 80*x + 5780*x^3 - 184*x^4 - 706*x^6 + 76*x^7 + 15*x^9 - 2*x^10 + (-9700 +
440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 30*x^7)*Log[2] + (-8050 + 700*x + 1125*x^3 - 150*x^4)*Log[2]^2 + (-1875
+ 250*x)*Log[2]^3))/(1000 - 300*x^3 + 30*x^6 - x^9 + (1500 - 300*x^3 + 15*x^6)*Log[2] + (750 - 75*x^3)*Log[2]
^2 + 125*Log[2]^3), x]
________________________________________________________________________________________
fricas [B] time = 1.24, size = 108, normalized size = 3.48 \begin {gather*} e^{\left (\frac {x^{8} - 15 \, x^{7} + 64 \, x^{6} - 4 \, x^{5} + 172 \, x^{4} - 1280 \, x^{3} + 25 \, {\left (x^{2} - 15 \, x + 64\right )} \log \relax (2)^{2} + 4 \, x^{2} - 10 \, {\left (x^{5} - 15 \, x^{4} + 64 \, x^{3} - 2 \, x^{2} + 86 \, x - 640\right )} \log \relax (2) - 220 \, x + 6400}{x^{6} - 20 \, x^{3} - 10 \, {\left (x^{3} - 10\right )} \log \relax (2) + 25 \, \log \relax (2)^{2} + 100}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+(30*x^7-225*x^6-520*x^4+5140*x^3+440*
x-9700)*log(2)-2*x^10+15*x^9+76*x^7-706*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10
*x^5+150*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-1280*x^3+4*x^2-220*x+6400)/(25*
log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3+100))/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(
2)-x^9+30*x^6-300*x^3+1000),x, algorithm="fricas")
[Out]
e^((x^8 - 15*x^7 + 64*x^6 - 4*x^5 + 172*x^4 - 1280*x^3 + 25*(x^2 - 15*x + 64)*log(2)^2 + 4*x^2 - 10*(x^5 - 15*
x^4 + 64*x^3 - 2*x^2 + 86*x - 640)*log(2) - 220*x + 6400)/(x^6 - 20*x^3 - 10*(x^3 - 10)*log(2) + 25*log(2)^2 +
100))
________________________________________________________________________________________
giac [B] time = 0.79, size = 622, normalized size = 20.06 \begin {gather*} e^{\left (\frac {x^{8}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {15 \, x^{7}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {64 \, x^{6}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {10 \, x^{5} \log \relax (2)}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {4 \, x^{5}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {150 \, x^{4} \log \relax (2)}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {172 \, x^{4}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {640 \, x^{3} \log \relax (2)}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {25 \, x^{2} \log \relax (2)^{2}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {1280 \, x^{3}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {20 \, x^{2} \log \relax (2)}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {375 \, x \log \relax (2)^{2}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {4 \, x^{2}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {860 \, x \log \relax (2)}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {1600 \, \log \relax (2)^{2}}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} - \frac {220 \, x}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {6400 \, \log \relax (2)}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {6400}{x^{6} - 10 \, x^{3} \log \relax (2) - 20 \, x^{3} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+(30*x^7-225*x^6-520*x^4+5140*x^3+440*
x-9700)*log(2)-2*x^10+15*x^9+76*x^7-706*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10
*x^5+150*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-1280*x^3+4*x^2-220*x+6400)/(25*
log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3+100))/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(
2)-x^9+30*x^6-300*x^3+1000),x, algorithm="giac")
[Out]
e^(x^8/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 15*x^7/(x^6 - 10*x^3*log(2) - 20*x^3
+ 25*log(2)^2 + 100*log(2) + 100) + 64*x^6/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 1
0*x^5*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 4*x^5/(x^6 - 10*x^3*log(2) - 20
*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 150*x^4*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(
2) + 100) + 172*x^4/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 640*x^3*log(2)/(x^6 - 10
*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 25*x^2*log(2)^2/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*lo
g(2)^2 + 100*log(2) + 100) - 1280*x^3/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 20*x^2
*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 375*x*log(2)^2/(x^6 - 10*x^3*log(2)
- 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 4*x^2/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) +
100) - 860*x*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 1600*log(2)^2/(x^6 - 10*
x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 220*x/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 10
0*log(2) + 100) + 6400*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 6400/(x^6 - 10
*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100))
________________________________________________________________________________________
maple [B] time = 0.02, size = 129, normalized size = 4.16 \[{\mathrm e}^{\frac {x^{8}-15 x^{7}-10 x^{5} \ln \relax (2)+64 x^{6}+150 x^{4} \ln \relax (2)-4 x^{5}+25 x^{2} \ln \relax (2)^{2}-640 x^{3} \ln \relax (2)+172 x^{4}-375 x \ln \relax (2)^{2}+20 x^{2} \ln \relax (2)-1280 x^{3}+1600 \ln \relax (2)^{2}-860 x \ln \relax (2)+4 x^{2}+6400 \ln \relax (2)-220 x +6400}{x^{6}-10 x^{3} \ln \relax (2)-20 x^{3}+25 \ln \relax (2)^{2}+100 \ln \relax (2)+100}}\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((250*x-1875)*ln(2)^3+(-150*x^4+1125*x^3+700*x-8050)*ln(2)^2+(30*x^7-225*x^6-520*x^4+5140*x^3+440*x-9700)*
ln(2)-2*x^10+15*x^9+76*x^7-706*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*ln(2)^2+(-10*x^5+150*x
^4-640*x^3+20*x^2-860*x+6400)*ln(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-1280*x^3+4*x^2-220*x+6400)/(25*ln(2)^2+(-1
0*x^3+100)*ln(2)+x^6-20*x^3+100))/(125*ln(2)^3+(-75*x^3+750)*ln(2)^2+(15*x^6-300*x^3+1500)*ln(2)-x^9+30*x^6-30
0*x^3+1000),x)
[Out]
exp((x^8-15*x^7-10*x^5*ln(2)+64*x^6+150*x^4*ln(2)-4*x^5+25*x^2*ln(2)^2-640*x^3*ln(2)+172*x^4-375*x*ln(2)^2+20*
x^2*ln(2)-1280*x^3+1600*ln(2)^2-860*x*ln(2)+4*x^2+6400*ln(2)-220*x+6400)/(x^6-10*x^3*ln(2)-20*x^3+25*ln(2)^2+1
00*ln(2)+100))
________________________________________________________________________________________
maxima [B] time = 1.93, size = 70, normalized size = 2.26 \begin {gather*} e^{\left (x^{2} - 15 \, x + \frac {64 \, x^{2}}{x^{6} - 10 \, x^{3} {\left (\log \relax (2) + 2\right )} + 25 \, \log \relax (2)^{2} + 100 \, \log \relax (2) + 100} + \frac {16 \, x^{2}}{x^{3} - 5 \, \log \relax (2) - 10} - \frac {128 \, x}{x^{3} - 5 \, \log \relax (2) - 10} + 64\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+(30*x^7-225*x^6-520*x^4+5140*x^3+440*
x-9700)*log(2)-2*x^10+15*x^9+76*x^7-706*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10
*x^5+150*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-1280*x^3+4*x^2-220*x+6400)/(25*
log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3+100))/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(
2)-x^9+30*x^6-300*x^3+1000),x, algorithm="maxima")
[Out]
e^(x^2 - 15*x + 64*x^2/(x^6 - 10*x^3*(log(2) + 2) + 25*log(2)^2 + 100*log(2) + 100) + 16*x^2/(x^3 - 5*log(2) -
10) - 128*x/(x^3 - 5*log(2) - 10) + 64)
________________________________________________________________________________________
mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp((log(2)^2*(25*x^2 - 375*x + 1600) - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 - 15*x^7 + x^
8 - log(2)*(860*x - 20*x^2 + 640*x^3 - 150*x^4 + 10*x^5 - 6400) + 6400)/(25*log(2)^2 - log(2)*(10*x^3 - 100) -
20*x^3 + x^6 + 100))*(80*x + log(2)^3*(250*x - 1875) + log(2)^2*(700*x + 1125*x^3 - 150*x^4 - 8050) + 5780*x^
3 - 184*x^4 - 706*x^6 + 76*x^7 + 15*x^9 - 2*x^10 + log(2)*(440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 30*x^7 - 970
0) - 2200))/(log(2)*(15*x^6 - 300*x^3 + 1500) - log(2)^2*(75*x^3 - 750) + 125*log(2)^3 - 300*x^3 + 30*x^6 - x^
9 + 1000),x)
[Out]
\text{Hanged}
________________________________________________________________________________________
sympy [B] time = 5.27, size = 110, normalized size = 3.55 \begin {gather*} e^{\frac {x^{8} - 15 x^{7} + 64 x^{6} - 4 x^{5} + 172 x^{4} - 1280 x^{3} + 4 x^{2} - 220 x + \left (25 x^{2} - 375 x + 1600\right ) \log {\relax (2 )}^{2} + \left (- 10 x^{5} + 150 x^{4} - 640 x^{3} + 20 x^{2} - 860 x + 6400\right ) \log {\relax (2 )} + 6400}{x^{6} - 20 x^{3} + \left (100 - 10 x^{3}\right ) \log {\relax (2 )} + 25 \log {\relax (2 )}^{2} + 100}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((250*x-1875)*ln(2)**3+(-150*x**4+1125*x**3+700*x-8050)*ln(2)**2+(30*x**7-225*x**6-520*x**4+5140*x**
3+440*x-9700)*ln(2)-2*x**10+15*x**9+76*x**7-706*x**6-184*x**4+5780*x**3+80*x-2200)*exp(((25*x**2-375*x+1600)*l
n(2)**2+(-10*x**5+150*x**4-640*x**3+20*x**2-860*x+6400)*ln(2)+x**8-15*x**7+64*x**6-4*x**5+172*x**4-1280*x**3+4
*x**2-220*x+6400)/(25*ln(2)**2+(-10*x**3+100)*ln(2)+x**6-20*x**3+100))/(125*ln(2)**3+(-75*x**3+750)*ln(2)**2+(
15*x**6-300*x**3+1500)*ln(2)-x**9+30*x**6-300*x**3+1000),x)
[Out]
exp((x**8 - 15*x**7 + 64*x**6 - 4*x**5 + 172*x**4 - 1280*x**3 + 4*x**2 - 220*x + (25*x**2 - 375*x + 1600)*log(
2)**2 + (-10*x**5 + 150*x**4 - 640*x**3 + 20*x**2 - 860*x + 6400)*log(2) + 6400)/(x**6 - 20*x**3 + (100 - 10*x
**3)*log(2) + 25*log(2)**2 + 100))
________________________________________________________________________________________