3.30.46 \(\int \frac {e^{-\frac {2 e^x}{x}} (-1250 x+e^x (-1250+1250 x)+(-1250 x+e^x (-2500+2500 x)) \log (x)+e^x (-1250+1250 x) \log ^2(x)+e^{\frac {2 e^x}{x}} (-200 x+2 x^2-200 x \log (x))+e^{\frac {e^x}{x}} (e^x (500-500 x)+1000 x+(e^x (1000-1000 x)+1000 x) \log (x)+e^x (500-500 x) \log ^2(x)))}{x^2} \, dx\)

Optimal. Leaf size=31 \[ 2+2 x-\left (-2+5 e^{-\frac {e^x}{x}}\right )^2 (5+5 \log (x))^2 \]

________________________________________________________________________________________

Rubi [F]  time = 14.27, 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*} \int \frac {e^{-\frac {2 e^x}{x}} \left (-1250 x+e^x (-1250+1250 x)+\left (-1250 x+e^x (-2500+2500 x)\right ) \log (x)+e^x (-1250+1250 x) \log ^2(x)+e^{\frac {2 e^x}{x}} \left (-200 x+2 x^2-200 x \log (x)\right )+e^{\frac {e^x}{x}} \left (e^x (500-500 x)+1000 x+\left (e^x (1000-1000 x)+1000 x\right ) \log (x)+e^x (500-500 x) \log ^2(x)\right )\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1250*x + E^x*(-1250 + 1250*x) + (-1250*x + E^x*(-2500 + 2500*x))*Log[x] + E^x*(-1250 + 1250*x)*Log[x]^2
+ E^((2*E^x)/x)*(-200*x + 2*x^2 - 200*x*Log[x]) + E^(E^x/x)*(E^x*(500 - 500*x) + 1000*x + (E^x*(1000 - 1000*x)
+ 1000*x)*Log[x] + E^x*(500 - 500*x)*Log[x]^2))/(E^((2*E^x)/x)*x^2),x]

[Out]

2*x - 200*Log[x] - 100*Log[x]^2 - 1250*Defer[Int][E^((-2*E^x)/x + x)/x^2, x] - 2500*Log[x]*Defer[Int][E^((-2*E
^x)/x + x)/x^2, x] + 500*Defer[Int][E^(-(E^x/x) + x)/x^2, x] + 1000*Log[x]*Defer[Int][E^(-(E^x/x) + x)/x^2, x]
- 1250*Defer[Int][1/(E^((2*E^x)/x)*x), x] - 1250*Log[x]*Defer[Int][1/(E^((2*E^x)/x)*x), x] + 1000*Defer[Int][
1/(E^(E^x/x)*x), x] + 1000*Log[x]*Defer[Int][1/(E^(E^x/x)*x), x] + 1250*Defer[Int][E^((-2*E^x)/x + x)/x, x] +
2500*Log[x]*Defer[Int][E^((-2*E^x)/x + x)/x, x] - 500*Defer[Int][E^(-(E^x/x) + x)/x, x] - 1000*Log[x]*Defer[In
t][E^(-(E^x/x) + x)/x, x] - 1250*Defer[Int][(E^((-2*E^x)/x + x)*Log[x]^2)/x^2, x] + 500*Defer[Int][(E^(-(E^x/x
) + x)*Log[x]^2)/x^2, x] + 1250*Defer[Int][(E^((-2*E^x)/x + x)*Log[x]^2)/x, x] - 500*Defer[Int][(E^(-(E^x/x) +
x)*Log[x]^2)/x, x] + 2500*Defer[Int][Defer[Int][E^((-2*E^x)/x + x)/x^2, x]/x, x] - 1000*Defer[Int][Defer[Int]
[E^(-(E^x/x) + x)/x^2, x]/x, x] + 1250*Defer[Int][Defer[Int][1/(E^((2*E^x)/x)*x), x]/x, x] - 1000*Defer[Int][D
efer[Int][1/(E^(E^x/x)*x), x]/x, x] - 2500*Defer[Int][Defer[Int][E^((-2*E^x)/x + x)/x, x]/x, x] + 1000*Defer[I
nt][Defer[Int][E^(-(E^x/x) + x)/x, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {250 e^{-\frac {2 e^x}{x}+x} \left (-5+2 e^{\frac {e^x}{x}}\right ) (-1+x) (1+\log (x))^2}{x^2}+\frac {2 e^{-\frac {2 e^x}{x}} \left (-625+500 e^{\frac {e^x}{x}}-100 e^{\frac {2 e^x}{x}}+e^{\frac {2 e^x}{x}} x-625 \log (x)+500 e^{\frac {e^x}{x}} \log (x)-100 e^{\frac {2 e^x}{x}} \log (x)\right )}{x}\right ) \, dx\\ &=2 \int \frac {e^{-\frac {2 e^x}{x}} \left (-625+500 e^{\frac {e^x}{x}}-100 e^{\frac {2 e^x}{x}}+e^{\frac {2 e^x}{x}} x-625 \log (x)+500 e^{\frac {e^x}{x}} \log (x)-100 e^{\frac {2 e^x}{x}} \log (x)\right )}{x} \, dx-250 \int \frac {e^{-\frac {2 e^x}{x}+x} \left (-5+2 e^{\frac {e^x}{x}}\right ) (-1+x) (1+\log (x))^2}{x^2} \, dx\\ &=2 \int \frac {e^{-\frac {2 e^x}{x}} \left (-625+500 e^{\frac {e^x}{x}}+e^{\frac {2 e^x}{x}} (-100+x)-25 \left (5-2 e^{\frac {e^x}{x}}\right )^2 \log (x)\right )}{x} \, dx-250 \int \left (-\frac {5 e^{-\frac {2 e^x}{x}+x} (-1+x) (1+\log (x))^2}{x^2}+\frac {2 e^{-\frac {e^x}{x}+x} (-1+x) (1+\log (x))^2}{x^2}\right ) \, dx\\ &=2 \int \left (\frac {-100+x-100 \log (x)}{x}-\frac {625 e^{-\frac {2 e^x}{x}} (1+\log (x))}{x}+\frac {500 e^{-\frac {e^x}{x}} (1+\log (x))}{x}\right ) \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x} (-1+x) (1+\log (x))^2}{x^2} \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x} (-1+x) (1+\log (x))^2}{x^2} \, dx\\ &=2 \int \frac {-100+x-100 \log (x)}{x} \, dx-500 \int \left (\frac {e^{-\frac {e^x}{x}+x} (-1+x)}{x^2}+\frac {2 e^{-\frac {e^x}{x}+x} (-1+x) \log (x)}{x^2}+\frac {e^{-\frac {e^x}{x}+x} (-1+x) \log ^2(x)}{x^2}\right ) \, dx+1000 \int \frac {e^{-\frac {e^x}{x}} (1+\log (x))}{x} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}} (1+\log (x))}{x} \, dx+1250 \int \left (\frac {e^{-\frac {2 e^x}{x}+x} (-1+x)}{x^2}+\frac {2 e^{-\frac {2 e^x}{x}+x} (-1+x) \log (x)}{x^2}+\frac {e^{-\frac {2 e^x}{x}+x} (-1+x) \log ^2(x)}{x^2}\right ) \, dx\\ &=2 \int \left (\frac {-100+x}{x}-\frac {100 \log (x)}{x}\right ) \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x} (-1+x)}{x^2} \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x} (-1+x) \log ^2(x)}{x^2} \, dx-1000 \int \frac {e^{-\frac {e^x}{x}+x} (-1+x) \log (x)}{x^2} \, dx+1000 \int \left (\frac {e^{-\frac {e^x}{x}}}{x}+\frac {e^{-\frac {e^x}{x}} \log (x)}{x}\right ) \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x} (-1+x)}{x^2} \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x} (-1+x) \log ^2(x)}{x^2} \, dx-1250 \int \left (\frac {e^{-\frac {2 e^x}{x}}}{x}+\frac {e^{-\frac {2 e^x}{x}} \log (x)}{x}\right ) \, dx+2500 \int \frac {e^{-\frac {2 e^x}{x}+x} (-1+x) \log (x)}{x^2} \, dx\\ &=2 \int \frac {-100+x}{x} \, dx-200 \int \frac {\log (x)}{x} \, dx-500 \int \left (-\frac {e^{-\frac {e^x}{x}+x}}{x^2}+\frac {e^{-\frac {e^x}{x}+x}}{x}\right ) \, dx-500 \int \left (-\frac {e^{-\frac {e^x}{x}+x} \log ^2(x)}{x^2}+\frac {e^{-\frac {e^x}{x}+x} \log ^2(x)}{x}\right ) \, dx+1000 \int \frac {e^{-\frac {e^x}{x}}}{x} \, dx+1000 \int \frac {e^{-\frac {e^x}{x}} \log (x)}{x} \, dx+1000 \int \frac {-\int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx+\int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx}{x} \, dx+1250 \int \left (-\frac {e^{-\frac {2 e^x}{x}+x}}{x^2}+\frac {e^{-\frac {2 e^x}{x}+x}}{x}\right ) \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}} \log (x)}{x} \, dx+1250 \int \left (-\frac {e^{-\frac {2 e^x}{x}+x} \log ^2(x)}{x^2}+\frac {e^{-\frac {2 e^x}{x}+x} \log ^2(x)}{x}\right ) \, dx-2500 \int \frac {-\int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx+\int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx}{x} \, dx+(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx-(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx-(2500 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx+(2500 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx\\ &=-100 \log ^2(x)+2 \int \left (1-\frac {100}{x}\right ) \, dx+500 \int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx+500 \int \frac {e^{-\frac {e^x}{x}+x} \log ^2(x)}{x^2} \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x} \log ^2(x)}{x} \, dx+1000 \int \frac {e^{-\frac {e^x}{x}}}{x} \, dx-1000 \int \frac {\int \frac {e^{-\frac {e^x}{x}}}{x} \, dx}{x} \, dx+1000 \int \left (-\frac {\int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx}{x}+\frac {\int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx}{x}\right ) \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}+x} \log ^2(x)}{x^2} \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x} \log ^2(x)}{x} \, dx+1250 \int \frac {\int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx}{x} \, dx-2500 \int \left (-\frac {\int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx}{x}+\frac {\int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx}{x}\right ) \, dx+(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx+(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}}}{x} \, dx-(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx-(1250 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx-(2500 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx+(2500 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx\\ &=2 x-200 \log (x)-100 \log ^2(x)+500 \int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx+500 \int \frac {e^{-\frac {e^x}{x}+x} \log ^2(x)}{x^2} \, dx-500 \int \frac {e^{-\frac {e^x}{x}+x} \log ^2(x)}{x} \, dx+1000 \int \frac {e^{-\frac {e^x}{x}}}{x} \, dx-1000 \int \frac {\int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx}{x} \, dx-1000 \int \frac {\int \frac {e^{-\frac {e^x}{x}}}{x} \, dx}{x} \, dx+1000 \int \frac {\int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx}{x} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx-1250 \int \frac {e^{-\frac {2 e^x}{x}+x} \log ^2(x)}{x^2} \, dx+1250 \int \frac {e^{-\frac {2 e^x}{x}+x} \log ^2(x)}{x} \, dx+1250 \int \frac {\int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx}{x} \, dx+2500 \int \frac {\int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx}{x} \, dx-2500 \int \frac {\int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx}{x} \, dx+(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}+x}}{x^2} \, dx+(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}}}{x} \, dx-(1000 \log (x)) \int \frac {e^{-\frac {e^x}{x}+x}}{x} \, dx-(1250 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}}}{x} \, dx-(2500 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}+x}}{x^2} \, dx+(2500 \log (x)) \int \frac {e^{-\frac {2 e^x}{x}+x}}{x} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.16, size = 52, normalized size = 1.68 \begin {gather*} 2 \left (x-100 \log (x)-50 \log ^2(x)-\frac {625}{2} e^{-\frac {2 e^x}{x}} (1+\log (x))^2+250 e^{-\frac {e^x}{x}} (1+\log (x))^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1250*x + E^x*(-1250 + 1250*x) + (-1250*x + E^x*(-2500 + 2500*x))*Log[x] + E^x*(-1250 + 1250*x)*Log
[x]^2 + E^((2*E^x)/x)*(-200*x + 2*x^2 - 200*x*Log[x]) + E^(E^x/x)*(E^x*(500 - 500*x) + 1000*x + (E^x*(1000 - 1
000*x) + 1000*x)*Log[x] + E^x*(500 - 500*x)*Log[x]^2))/(E^((2*E^x)/x)*x^2),x]

[Out]

2*(x - 100*Log[x] - 50*Log[x]^2 - (625*(1 + Log[x])^2)/(2*E^((2*E^x)/x)) + (250*(1 + Log[x])^2)/E^(E^x/x))

________________________________________________________________________________________

fricas [B]  time = 0.51, size = 65, normalized size = 2.10 \begin {gather*} -{\left (2 \, {\left (50 \, \log \relax (x)^{2} - x + 100 \, \log \relax (x)\right )} e^{\left (\frac {2 \, e^{x}}{x}\right )} - 500 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )} e^{\left (\frac {e^{x}}{x}\right )} + 625 \, \log \relax (x)^{2} + 1250 \, \log \relax (x) + 625\right )} e^{\left (-\frac {2 \, e^{x}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x*log(x)+2*x^2-200*x)*exp(exp(x)/x)^2+((-500*x+500)*exp(x)*log(x)^2+((-1000*x+1000)*exp(x)+10
00*x)*log(x)+(-500*x+500)*exp(x)+1000*x)*exp(exp(x)/x)+(1250*x-1250)*exp(x)*log(x)^2+((2500*x-2500)*exp(x)-125
0*x)*log(x)+(1250*x-1250)*exp(x)-1250*x)/x^2/exp(exp(x)/x)^2,x, algorithm="fricas")

[Out]

-(2*(50*log(x)^2 - x + 100*log(x))*e^(2*e^x/x) - 500*(log(x)^2 + 2*log(x) + 1)*e^(e^x/x) + 625*log(x)^2 + 1250
*log(x) + 625)*e^(-2*e^x/x)

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (625 \, {\left (x - 1\right )} e^{x} \log \relax (x)^{2} + 625 \, {\left (x - 1\right )} e^{x} + {\left (x^{2} - 100 \, x \log \relax (x) - 100 \, x\right )} e^{\left (\frac {2 \, e^{x}}{x}\right )} - 250 \, {\left ({\left (x - 1\right )} e^{x} \log \relax (x)^{2} + {\left (x - 1\right )} e^{x} + 2 \, {\left ({\left (x - 1\right )} e^{x} - x\right )} \log \relax (x) - 2 \, x\right )} e^{\left (\frac {e^{x}}{x}\right )} + 625 \, {\left (2 \, {\left (x - 1\right )} e^{x} - x\right )} \log \relax (x) - 625 \, x\right )} e^{\left (-\frac {2 \, e^{x}}{x}\right )}}{x^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x*log(x)+2*x^2-200*x)*exp(exp(x)/x)^2+((-500*x+500)*exp(x)*log(x)^2+((-1000*x+1000)*exp(x)+10
00*x)*log(x)+(-500*x+500)*exp(x)+1000*x)*exp(exp(x)/x)+(1250*x-1250)*exp(x)*log(x)^2+((2500*x-2500)*exp(x)-125
0*x)*log(x)+(1250*x-1250)*exp(x)-1250*x)/x^2/exp(exp(x)/x)^2,x, algorithm="giac")

[Out]

integrate(2*(625*(x - 1)*e^x*log(x)^2 + 625*(x - 1)*e^x + (x^2 - 100*x*log(x) - 100*x)*e^(2*e^x/x) - 250*((x -
1)*e^x*log(x)^2 + (x - 1)*e^x + 2*((x - 1)*e^x - x)*log(x) - 2*x)*e^(e^x/x) + 625*(2*(x - 1)*e^x - x)*log(x)
- 625*x)*e^(-2*e^x/x)/x^2, x)

________________________________________________________________________________________

maple [A]  time = 0.11, size = 57, normalized size = 1.84

method	result	size
risch	\(-100 \ln \relax (x )^{2}+2 x -200 \ln \relax (x )+\left (500 \ln \relax (x )^{2}+1000 \ln \relax (x )+500\right ) {\mathrm e}^{-\frac {{\mathrm e}^{x}}{x}}+\left (-625 \ln \relax (x )^{2}-1250 \ln \relax (x )-625\right ) {\mathrm e}^{-\frac {2 \,{\mathrm e}^{x}}{x}}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-200*x*ln(x)+2*x^2-200*x)*exp(exp(x)/x)^2+((-500*x+500)*exp(x)*ln(x)^2+((-1000*x+1000)*exp(x)+1000*x)*ln
(x)+(-500*x+500)*exp(x)+1000*x)*exp(exp(x)/x)+(1250*x-1250)*exp(x)*ln(x)^2+((2500*x-2500)*exp(x)-1250*x)*ln(x)
+(1250*x-1250)*exp(x)-1250*x)/x^2/exp(exp(x)/x)^2,x,method=_RETURNVERBOSE)

[Out]

-100*ln(x)^2+2*x-200*ln(x)+(500*ln(x)^2+1000*ln(x)+500)*exp(-exp(x)/x)+(-625*ln(x)^2-1250*ln(x)-625)*exp(-2*ex
p(x)/x)

________________________________________________________________________________________

maxima [A]  time = 0.70, size = 54, normalized size = 1.74 \begin {gather*} 500 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )} e^{\left (-\frac {e^{x}}{x}\right )} - 625 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )} e^{\left (-\frac {2 \, e^{x}}{x}\right )} - 100 \, \log \relax (x)^{2} + 2 \, x - 200 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x*log(x)+2*x^2-200*x)*exp(exp(x)/x)^2+((-500*x+500)*exp(x)*log(x)^2+((-1000*x+1000)*exp(x)+10
00*x)*log(x)+(-500*x+500)*exp(x)+1000*x)*exp(exp(x)/x)+(1250*x-1250)*exp(x)*log(x)^2+((2500*x-2500)*exp(x)-125
0*x)*log(x)+(1250*x-1250)*exp(x)-1250*x)/x^2/exp(exp(x)/x)^2,x, algorithm="maxima")

[Out]

500*(log(x)^2 + 2*log(x) + 1)*e^(-e^x/x) - 625*(log(x)^2 + 2*log(x) + 1)*e^(-2*e^x/x) - 100*log(x)^2 + 2*x - 2
00*log(x)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^x}{x}}\,\left (1250\,x+{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^x}{x}}\,\left (200\,x+200\,x\,\ln \relax (x)-2\,x^2\right )-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\left (-{\mathrm {e}}^x\,\left (500\,x-500\right )\,{\ln \relax (x)}^2+\left (1000\,x-{\mathrm {e}}^x\,\left (1000\,x-1000\right )\right )\,\ln \relax (x)+1000\,x-{\mathrm {e}}^x\,\left (500\,x-500\right )\right )-{\mathrm {e}}^x\,\left (1250\,x-1250\right )+\ln \relax (x)\,\left (1250\,x-{\mathrm {e}}^x\,\left (2500\,x-2500\right )\right )-{\mathrm {e}}^x\,{\ln \relax (x)}^2\,\left (1250\,x-1250\right )\right )}{x^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(2*exp(x))/x)*(1250*x + exp((2*exp(x))/x)*(200*x + 200*x*log(x) - 2*x^2) - exp(exp(x)/x)*(1000*x -
exp(x)*(500*x - 500) + log(x)*(1000*x - exp(x)*(1000*x - 1000)) - exp(x)*log(x)^2*(500*x - 500)) - exp(x)*(125
0*x - 1250) + log(x)*(1250*x - exp(x)*(2500*x - 2500)) - exp(x)*log(x)^2*(1250*x - 1250)))/x^2,x)

[Out]

int(-(exp(-(2*exp(x))/x)*(1250*x + exp((2*exp(x))/x)*(200*x + 200*x*log(x) - 2*x^2) - exp(exp(x)/x)*(1000*x -
exp(x)*(500*x - 500) + log(x)*(1000*x - exp(x)*(1000*x - 1000)) - exp(x)*log(x)^2*(500*x - 500)) - exp(x)*(125
0*x - 1250) + log(x)*(1250*x - exp(x)*(2500*x - 2500)) - exp(x)*log(x)^2*(1250*x - 1250)))/x^2, x)

________________________________________________________________________________________

sympy [B]  time = 24.30, size = 58, normalized size = 1.87 \begin {gather*} 2 x + \left (- 625 \log {\relax (x )}^{2} - 1250 \log {\relax (x )} - 625\right ) e^{- \frac {2 e^{x}}{x}} + \left (500 \log {\relax (x )}^{2} + 1000 \log {\relax (x )} + 500\right ) e^{- \frac {e^{x}}{x}} - 100 \log {\relax (x )}^{2} - 200 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x*ln(x)+2*x**2-200*x)*exp(exp(x)/x)**2+((-500*x+500)*exp(x)*ln(x)**2+((-1000*x+1000)*exp(x)+1
000*x)*ln(x)+(-500*x+500)*exp(x)+1000*x)*exp(exp(x)/x)+(1250*x-1250)*exp(x)*ln(x)**2+((2500*x-2500)*exp(x)-125
0*x)*ln(x)+(1250*x-1250)*exp(x)-1250*x)/x**2/exp(exp(x)/x)**2,x)

[Out]

2*x + (-625*log(x)**2 - 1250*log(x) - 625)*exp(-2*exp(x)/x) + (500*log(x)**2 + 1000*log(x) + 500)*exp(-exp(x)/
x) - 100*log(x)**2 - 200*log(x)

________________________________________________________________________________________