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3.60.49 \(\int \frac {4+4 x+e^{\frac {1}{16} (-625 e^{12+4 x}+16 x-2500 e^{9+3 x} x-3750 e^{6+2 x} x^2-2500 e^{3+x} x^3-625 x^4+(-500 e^{9+3 x}-1500 e^{6+2 x} x-1500 e^{3+x} x^2-500 x^3) \log (x)+(-150 e^{6+2 x}-300 e^{3+x} x-150 x^2) \log ^2(x)+(-20 e^{3+x}-20 x) \log ^3(x)-\log ^4(x))} (-4 x+625 e^{12+4 x} x+125 x^3+625 x^4+e^{9+3 x} (125+625 x+1875 x^2)+e^{6+2 x} (375 x+1875 x^2+1875 x^3)+e^{3+x} (375 x^2+1875 x^3+625 x^4)+(375 e^{9+3 x} x+75 x^2+375 x^3+e^{6+2 x} (75+375 x+750 x^2)+e^{3+x} (150 x+750 x^2+375 x^3)) \log (x)+(15 x+75 e^{6+2 x} x+75 x^2+e^{3+x} (15+75 x+75 x^2)) \log ^2(x)+(1+5 x+5 e^{3+x} x) \log ^3(x))}{4 x} \, dx\)

Optimal. Leaf size=28 \[ -e^{x-\frac {1}{16} \left (5 \left (e^{3+x}+x\right )+\log (x)\right )^4}+x+\log (x) \]

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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[(4 + 4*x + E^((-625*E^(12 + 4*x) + 16*x - 2500*E^(9 + 3*x)*x - 3750*E^(6 + 2*x)*x^2 - 2500*E^(3 + x)*x^3 -
 625*x^4 + (-500*E^(9 + 3*x) - 1500*E^(6 + 2*x)*x - 1500*E^(3 + x)*x^2 - 500*x^3)*Log[x] + (-150*E^(6 + 2*x) -
 300*E^(3 + x)*x - 150*x^2)*Log[x]^2 + (-20*E^(3 + x) - 20*x)*Log[x]^3 - Log[x]^4)/16)*(-4*x + 625*E^(12 + 4*x
)*x + 125*x^3 + 625*x^4 + E^(9 + 3*x)*(125 + 625*x + 1875*x^2) + E^(6 + 2*x)*(375*x + 1875*x^2 + 1875*x^3) + E
^(3 + x)*(375*x^2 + 1875*x^3 + 625*x^4) + (375*E^(9 + 3*x)*x + 75*x^2 + 375*x^3 + E^(6 + 2*x)*(75 + 375*x + 75
0*x^2) + E^(3 + x)*(150*x + 750*x^2 + 375*x^3))*Log[x] + (15*x + 75*E^(6 + 2*x)*x + 75*x^2 + E^(3 + x)*(15 + 7
5*x + 75*x^2))*Log[x]^2 + (1 + 5*x + 5*E^(3 + x)*x)*Log[x]^3))/(4*x),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 1.78, size = 111, normalized size = 3.96 \begin {gather*} x-e^{\frac {1}{16} \left (-625 e^{4 (3+x)}+16 x-2500 e^{9+3 x} x-3750 e^{6+2 x} x^2-2500 e^{3+x} x^3-625 x^4-150 \left (e^{3+x}+x\right )^2 \log ^2(x)-20 \left (e^{3+x}+x\right ) \log ^3(x)-\log ^4(x)\right )} x^{-\frac {125}{4} \left (e^{3+x}+x\right )^3}+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 + 4*x + E^((-625*E^(12 + 4*x) + 16*x - 2500*E^(9 + 3*x)*x - 3750*E^(6 + 2*x)*x^2 - 2500*E^(3 + x)
*x^3 - 625*x^4 + (-500*E^(9 + 3*x) - 1500*E^(6 + 2*x)*x - 1500*E^(3 + x)*x^2 - 500*x^3)*Log[x] + (-150*E^(6 +
2*x) - 300*E^(3 + x)*x - 150*x^2)*Log[x]^2 + (-20*E^(3 + x) - 20*x)*Log[x]^3 - Log[x]^4)/16)*(-4*x + 625*E^(12
 + 4*x)*x + 125*x^3 + 625*x^4 + E^(9 + 3*x)*(125 + 625*x + 1875*x^2) + E^(6 + 2*x)*(375*x + 1875*x^2 + 1875*x^
3) + E^(3 + x)*(375*x^2 + 1875*x^3 + 625*x^4) + (375*E^(9 + 3*x)*x + 75*x^2 + 375*x^3 + E^(6 + 2*x)*(75 + 375*
x + 750*x^2) + E^(3 + x)*(150*x + 750*x^2 + 375*x^3))*Log[x] + (15*x + 75*E^(6 + 2*x)*x + 75*x^2 + E^(3 + x)*(
15 + 75*x + 75*x^2))*Log[x]^2 + (1 + 5*x + 5*E^(3 + x)*x)*Log[x]^3))/(4*x),x]

[Out]

x - E^((-625*E^(4*(3 + x)) + 16*x - 2500*E^(9 + 3*x)*x - 3750*E^(6 + 2*x)*x^2 - 2500*E^(3 + x)*x^3 - 625*x^4 -
 150*(E^(3 + x) + x)^2*Log[x]^2 - 20*(E^(3 + x) + x)*Log[x]^3 - Log[x]^4)/16)/x^((125*(E^(3 + x) + x)^3)/4) +
Log[x]

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fricas [B]  time = 0.87, size = 124, normalized size = 4.43 \begin {gather*} x - e^{\left (-\frac {625}{16} \, x^{4} - \frac {625}{4} \, x^{3} e^{\left (x + 3\right )} - \frac {5}{4} \, {\left (x + e^{\left (x + 3\right )}\right )} \log \relax (x)^{3} - \frac {1}{16} \, \log \relax (x)^{4} - \frac {1875}{8} \, x^{2} e^{\left (2 \, x + 6\right )} - \frac {75}{8} \, {\left (x^{2} + 2 \, x e^{\left (x + 3\right )} + e^{\left (2 \, x + 6\right )}\right )} \log \relax (x)^{2} - \frac {625}{4} \, x e^{\left (3 \, x + 9\right )} - \frac {125}{4} \, {\left (x^{3} + 3 \, x^{2} e^{\left (x + 3\right )} + 3 \, x e^{\left (2 \, x + 6\right )} + e^{\left (3 \, x + 9\right )}\right )} \log \relax (x) + x - \frac {625}{16} \, e^{\left (4 \, x + 12\right )}\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(((5*exp(3+x)*x+1+5*x)*log(x)^3+(75*x*exp(3+x)^2+(75*x^2+75*x+15)*exp(3+x)+75*x^2+15*x)*log(x)^2
+(375*x*exp(3+x)^3+(750*x^2+375*x+75)*exp(3+x)^2+(375*x^3+750*x^2+150*x)*exp(3+x)+375*x^3+75*x^2)*log(x)+625*x
*exp(3+x)^4+(1875*x^2+625*x+125)*exp(3+x)^3+(1875*x^3+1875*x^2+375*x)*exp(3+x)^2+(625*x^4+1875*x^3+375*x^2)*ex
p(3+x)+625*x^4+125*x^3-4*x)*exp(-1/16*log(x)^4+1/16*(-20*exp(3+x)-20*x)*log(x)^3+1/16*(-150*exp(3+x)^2-300*exp
(3+x)*x-150*x^2)*log(x)^2+1/16*(-500*exp(3+x)^3-1500*x*exp(3+x)^2-1500*x^2*exp(3+x)-500*x^3)*log(x)-625/16*exp
(3+x)^4-625/4*x*exp(3+x)^3-1875/8*x^2*exp(3+x)^2-625/4*x^3*exp(3+x)-625/16*x^4+x)+4*x+4)/x,x, algorithm="frica
s")

[Out]

x - e^(-625/16*x^4 - 625/4*x^3*e^(x + 3) - 5/4*(x + e^(x + 3))*log(x)^3 - 1/16*log(x)^4 - 1875/8*x^2*e^(2*x +
6) - 75/8*(x^2 + 2*x*e^(x + 3) + e^(2*x + 6))*log(x)^2 - 625/4*x*e^(3*x + 9) - 125/4*(x^3 + 3*x^2*e^(x + 3) +
3*x*e^(2*x + 6) + e^(3*x + 9))*log(x) + x - 625/16*e^(4*x + 12)) + log(x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (625 \, x^{4} + {\left (5 \, x e^{\left (x + 3\right )} + 5 \, x + 1\right )} \log \relax (x)^{3} + 125 \, x^{3} + 15 \, {\left (5 \, x^{2} + 5 \, x e^{\left (2 \, x + 6\right )} + {\left (5 \, x^{2} + 5 \, x + 1\right )} e^{\left (x + 3\right )} + x\right )} \log \relax (x)^{2} + 625 \, x e^{\left (4 \, x + 12\right )} + 125 \, {\left (15 \, x^{2} + 5 \, x + 1\right )} e^{\left (3 \, x + 9\right )} + 375 \, {\left (5 \, x^{3} + 5 \, x^{2} + x\right )} e^{\left (2 \, x + 6\right )} + 125 \, {\left (5 \, x^{4} + 15 \, x^{3} + 3 \, x^{2}\right )} e^{\left (x + 3\right )} + 75 \, {\left (5 \, x^{3} + x^{2} + 5 \, x e^{\left (3 \, x + 9\right )} + {\left (10 \, x^{2} + 5 \, x + 1\right )} e^{\left (2 \, x + 6\right )} + {\left (5 \, x^{3} + 10 \, x^{2} + 2 \, x\right )} e^{\left (x + 3\right )}\right )} \log \relax (x) - 4 \, x\right )} e^{\left (-\frac {625}{16} \, x^{4} - \frac {625}{4} \, x^{3} e^{\left (x + 3\right )} - \frac {5}{4} \, {\left (x + e^{\left (x + 3\right )}\right )} \log \relax (x)^{3} - \frac {1}{16} \, \log \relax (x)^{4} - \frac {1875}{8} \, x^{2} e^{\left (2 \, x + 6\right )} - \frac {75}{8} \, {\left (x^{2} + 2 \, x e^{\left (x + 3\right )} + e^{\left (2 \, x + 6\right )}\right )} \log \relax (x)^{2} - \frac {625}{4} \, x e^{\left (3 \, x + 9\right )} - \frac {125}{4} \, {\left (x^{3} + 3 \, x^{2} e^{\left (x + 3\right )} + 3 \, x e^{\left (2 \, x + 6\right )} + e^{\left (3 \, x + 9\right )}\right )} \log \relax (x) + x - \frac {625}{16} \, e^{\left (4 \, x + 12\right )}\right )} + 4 \, x + 4}{4 \, x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(((5*exp(3+x)*x+1+5*x)*log(x)^3+(75*x*exp(3+x)^2+(75*x^2+75*x+15)*exp(3+x)+75*x^2+15*x)*log(x)^2
+(375*x*exp(3+x)^3+(750*x^2+375*x+75)*exp(3+x)^2+(375*x^3+750*x^2+150*x)*exp(3+x)+375*x^3+75*x^2)*log(x)+625*x
*exp(3+x)^4+(1875*x^2+625*x+125)*exp(3+x)^3+(1875*x^3+1875*x^2+375*x)*exp(3+x)^2+(625*x^4+1875*x^3+375*x^2)*ex
p(3+x)+625*x^4+125*x^3-4*x)*exp(-1/16*log(x)^4+1/16*(-20*exp(3+x)-20*x)*log(x)^3+1/16*(-150*exp(3+x)^2-300*exp
(3+x)*x-150*x^2)*log(x)^2+1/16*(-500*exp(3+x)^3-1500*x*exp(3+x)^2-1500*x^2*exp(3+x)-500*x^3)*log(x)-625/16*exp
(3+x)^4-625/4*x*exp(3+x)^3-1875/8*x^2*exp(3+x)^2-625/4*x^3*exp(3+x)-625/16*x^4+x)+4*x+4)/x,x, algorithm="giac"
)

[Out]

integrate(1/4*((625*x^4 + (5*x*e^(x + 3) + 5*x + 1)*log(x)^3 + 125*x^3 + 15*(5*x^2 + 5*x*e^(2*x + 6) + (5*x^2
+ 5*x + 1)*e^(x + 3) + x)*log(x)^2 + 625*x*e^(4*x + 12) + 125*(15*x^2 + 5*x + 1)*e^(3*x + 9) + 375*(5*x^3 + 5*
x^2 + x)*e^(2*x + 6) + 125*(5*x^4 + 15*x^3 + 3*x^2)*e^(x + 3) + 75*(5*x^3 + x^2 + 5*x*e^(3*x + 9) + (10*x^2 +
5*x + 1)*e^(2*x + 6) + (5*x^3 + 10*x^2 + 2*x)*e^(x + 3))*log(x) - 4*x)*e^(-625/16*x^4 - 625/4*x^3*e^(x + 3) -
5/4*(x + e^(x + 3))*log(x)^3 - 1/16*log(x)^4 - 1875/8*x^2*e^(2*x + 6) - 75/8*(x^2 + 2*x*e^(x + 3) + e^(2*x + 6
))*log(x)^2 - 625/4*x*e^(3*x + 9) - 125/4*(x^3 + 3*x^2*e^(x + 3) + 3*x*e^(2*x + 6) + e^(3*x + 9))*log(x) + x -
 625/16*e^(4*x + 12)) + 4*x + 4)/x, x)

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maple [B]  time = 0.18, size = 141, normalized size = 5.04

method result size
risch \(x +\ln \relax (x )-x^{-\frac {375 x^{2} {\mathrm e}^{3+x}}{4}-\frac {125 x^{3}}{4}-\frac {375 x \,{\mathrm e}^{2 x +6}}{4}-\frac {125 \,{\mathrm e}^{3 x +9}}{4}} {\mathrm e}^{-\frac {\ln \relax (x )^{4}}{16}-\frac {5 \ln \relax (x )^{3} {\mathrm e}^{3+x}}{4}-\frac {5 x \ln \relax (x )^{3}}{4}-\frac {75 \ln \relax (x )^{2} {\mathrm e}^{3+x} x}{4}-\frac {75 x^{2} \ln \relax (x )^{2}}{8}-\frac {75 \ln \relax (x )^{2} {\mathrm e}^{2 x +6}}{8}-\frac {625 \,{\mathrm e}^{4 x +12}}{16}-\frac {625 x \,{\mathrm e}^{3 x +9}}{4}-\frac {1875 x^{2} {\mathrm e}^{2 x +6}}{8}-\frac {625 x^{3} {\mathrm e}^{3+x}}{4}-\frac {625 x^{4}}{16}+x}\) \(141\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/4*(((5*exp(3+x)*x+1+5*x)*ln(x)^3+(75*x*exp(3+x)^2+(75*x^2+75*x+15)*exp(3+x)+75*x^2+15*x)*ln(x)^2+(375*x*
exp(3+x)^3+(750*x^2+375*x+75)*exp(3+x)^2+(375*x^3+750*x^2+150*x)*exp(3+x)+375*x^3+75*x^2)*ln(x)+625*x*exp(3+x)
^4+(1875*x^2+625*x+125)*exp(3+x)^3+(1875*x^3+1875*x^2+375*x)*exp(3+x)^2+(625*x^4+1875*x^3+375*x^2)*exp(3+x)+62
5*x^4+125*x^3-4*x)*exp(-1/16*ln(x)^4+1/16*(-20*exp(3+x)-20*x)*ln(x)^3+1/16*(-150*exp(3+x)^2-300*exp(3+x)*x-150
*x^2)*ln(x)^2+1/16*(-500*exp(3+x)^3-1500*x*exp(3+x)^2-1500*x^2*exp(3+x)-500*x^3)*ln(x)-625/16*exp(3+x)^4-625/4
*x*exp(3+x)^3-1875/8*x^2*exp(3+x)^2-625/4*x^3*exp(3+x)-625/16*x^4+x)+4*x+4)/x,x,method=_RETURNVERBOSE)

[Out]

x+ln(x)-x^(-375/4*x^2*exp(3+x)-125/4*x^3-375/4*x*exp(2*x+6)-125/4*exp(3*x+9))*exp(-1/16*ln(x)^4-5/4*ln(x)^3*ex
p(3+x)-5/4*x*ln(x)^3-75/4*ln(x)^2*exp(3+x)*x-75/8*x^2*ln(x)^2-75/8*ln(x)^2*exp(2*x+6)-625/16*exp(4*x+12)-625/4
*x*exp(3*x+9)-1875/8*x^2*exp(2*x+6)-625/4*x^3*exp(3+x)-625/16*x^4+x)

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maxima [B]  time = 1.22, size = 145, normalized size = 5.18 \begin {gather*} x - e^{\left (-\frac {625}{16} \, x^{4} - \frac {625}{4} \, x^{3} e^{\left (x + 3\right )} - \frac {125}{4} \, x^{3} \log \relax (x) - \frac {375}{4} \, x^{2} e^{\left (x + 3\right )} \log \relax (x) - \frac {75}{8} \, x^{2} \log \relax (x)^{2} - \frac {75}{4} \, x e^{\left (x + 3\right )} \log \relax (x)^{2} - \frac {5}{4} \, x \log \relax (x)^{3} - \frac {5}{4} \, e^{\left (x + 3\right )} \log \relax (x)^{3} - \frac {1}{16} \, \log \relax (x)^{4} - \frac {1875}{8} \, x^{2} e^{\left (2 \, x + 6\right )} - \frac {375}{4} \, x e^{\left (2 \, x + 6\right )} \log \relax (x) - \frac {75}{8} \, e^{\left (2 \, x + 6\right )} \log \relax (x)^{2} - \frac {625}{4} \, x e^{\left (3 \, x + 9\right )} - \frac {125}{4} \, e^{\left (3 \, x + 9\right )} \log \relax (x) + x - \frac {625}{16} \, e^{\left (4 \, x + 12\right )}\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(((5*exp(3+x)*x+1+5*x)*log(x)^3+(75*x*exp(3+x)^2+(75*x^2+75*x+15)*exp(3+x)+75*x^2+15*x)*log(x)^2
+(375*x*exp(3+x)^3+(750*x^2+375*x+75)*exp(3+x)^2+(375*x^3+750*x^2+150*x)*exp(3+x)+375*x^3+75*x^2)*log(x)+625*x
*exp(3+x)^4+(1875*x^2+625*x+125)*exp(3+x)^3+(1875*x^3+1875*x^2+375*x)*exp(3+x)^2+(625*x^4+1875*x^3+375*x^2)*ex
p(3+x)+625*x^4+125*x^3-4*x)*exp(-1/16*log(x)^4+1/16*(-20*exp(3+x)-20*x)*log(x)^3+1/16*(-150*exp(3+x)^2-300*exp
(3+x)*x-150*x^2)*log(x)^2+1/16*(-500*exp(3+x)^3-1500*x*exp(3+x)^2-1500*x^2*exp(3+x)-500*x^3)*log(x)-625/16*exp
(3+x)^4-625/4*x*exp(3+x)^3-1875/8*x^2*exp(3+x)^2-625/4*x^3*exp(3+x)-625/16*x^4+x)+4*x+4)/x,x, algorithm="maxim
a")

[Out]

x - e^(-625/16*x^4 - 625/4*x^3*e^(x + 3) - 125/4*x^3*log(x) - 375/4*x^2*e^(x + 3)*log(x) - 75/8*x^2*log(x)^2 -
 75/4*x*e^(x + 3)*log(x)^2 - 5/4*x*log(x)^3 - 5/4*e^(x + 3)*log(x)^3 - 1/16*log(x)^4 - 1875/8*x^2*e^(2*x + 6)
- 375/4*x*e^(2*x + 6)*log(x) - 75/8*e^(2*x + 6)*log(x)^2 - 625/4*x*e^(3*x + 9) - 125/4*e^(3*x + 9)*log(x) + x
- 625/16*e^(4*x + 12)) + log(x)

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mupad [B]  time = 4.99, size = 163, normalized size = 5.82 \begin {gather*} x+\ln \relax (x)-\frac {{\mathrm {e}}^{-\frac {{\ln \relax (x)}^4}{16}}\,{\mathrm {e}}^{-\frac {125\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^9\,\ln \relax (x)}{4}}\,{\mathrm {e}}^{-\frac {5\,{\mathrm {e}}^3\,{\mathrm {e}}^x\,{\ln \relax (x)}^3}{4}}\,{\mathrm {e}}^{-\frac {5\,x\,{\ln \relax (x)}^3}{4}}\,{\mathrm {e}}^{-\frac {125\,x^3\,\ln \relax (x)}{4}}\,{\mathrm {e}}^{-\frac {75\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6\,{\ln \relax (x)}^2}{8}}\,{\mathrm {e}}^{-\frac {375\,x\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6\,\ln \relax (x)}{4}}\,{\mathrm {e}}^{-\frac {75\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}{4}}\,{\mathrm {e}}^{-\frac {375\,x^2\,{\mathrm {e}}^3\,{\mathrm {e}}^x\,\ln \relax (x)}{4}}\,{\mathrm {e}}^x\,{\mathrm {e}}^{-\frac {75\,x^2\,{\ln \relax (x)}^2}{8}}}{{\left ({\mathrm {e}}^{x^4}\right )}^{625/16}\,{\left ({\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6}\right )}^{1875/8}\,{\left ({\mathrm {e}}^{{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{12}}\right )}^{625/16}\,{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^9}\right )}^{625/4}\,{\left ({\mathrm {e}}^{x^3\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\right )}^{625/4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + (exp(x - (625*exp(4*x + 12))/16 - log(x)^4/16 - (log(x)^2*(150*exp(2*x + 6) + 300*x*exp(x + 3) + 150*
x^2))/16 - (625*x*exp(3*x + 9))/4 - (625*x^3*exp(x + 3))/4 - (log(x)^3*(20*x + 20*exp(x + 3)))/16 - (log(x)*(5
00*exp(3*x + 9) + 1500*x*exp(2*x + 6) + 1500*x^2*exp(x + 3) + 500*x^3))/16 - (1875*x^2*exp(2*x + 6))/8 - (625*
x^4)/16)*(log(x)*(exp(x + 3)*(150*x + 750*x^2 + 375*x^3) + exp(2*x + 6)*(375*x + 750*x^2 + 75) + 375*x*exp(3*x
 + 9) + 75*x^2 + 375*x^3) - 4*x + exp(3*x + 9)*(625*x + 1875*x^2 + 125) + 625*x*exp(4*x + 12) + log(x)^2*(15*x
 + exp(x + 3)*(75*x + 75*x^2 + 15) + 75*x*exp(2*x + 6) + 75*x^2) + exp(2*x + 6)*(375*x + 1875*x^2 + 1875*x^3)
+ exp(x + 3)*(375*x^2 + 1875*x^3 + 625*x^4) + 125*x^3 + 625*x^4 + log(x)^3*(5*x + 5*x*exp(x + 3) + 1)))/4 + 1)
/x,x)

[Out]

x + log(x) - (exp(-log(x)^4/16)*exp(-(125*exp(3*x)*exp(9)*log(x))/4)*exp(-(5*exp(3)*exp(x)*log(x)^3)/4)*exp(-(
5*x*log(x)^3)/4)*exp(-(125*x^3*log(x))/4)*exp(-(75*exp(2*x)*exp(6)*log(x)^2)/8)*exp(-(375*x*exp(2*x)*exp(6)*lo
g(x))/4)*exp(-(75*x*exp(3)*exp(x)*log(x)^2)/4)*exp(-(375*x^2*exp(3)*exp(x)*log(x))/4)*exp(x)*exp(-(75*x^2*log(
x)^2)/8))/(exp(x^4)^(625/16)*exp(x^2*exp(2*x)*exp(6))^(1875/8)*exp(exp(4*x)*exp(12))^(625/16)*exp(x*exp(3*x)*e
xp(9))^(625/4)*exp(x^3*exp(3)*exp(x))^(625/4))

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sympy [B]  time = 2.15, size = 168, normalized size = 6.00 \begin {gather*} x - e^{- \frac {625 x^{4}}{16} - \frac {625 x^{3} e^{x + 3}}{4} - \frac {1875 x^{2} e^{2 x + 6}}{8} - \frac {625 x e^{3 x + 9}}{4} + x + \left (- \frac {5 x}{4} - \frac {5 e^{x + 3}}{4}\right ) \log {\relax (x )}^{3} + \left (- \frac {75 x^{2}}{8} - \frac {75 x e^{x + 3}}{4} - \frac {75 e^{2 x + 6}}{8}\right ) \log {\relax (x )}^{2} + \left (- \frac {125 x^{3}}{4} - \frac {375 x^{2} e^{x + 3}}{4} - \frac {375 x e^{2 x + 6}}{4} - \frac {125 e^{3 x + 9}}{4}\right ) \log {\relax (x )} - \frac {625 e^{4 x + 12}}{16} - \frac {\log {\relax (x )}^{4}}{16}} + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(((5*exp(3+x)*x+1+5*x)*ln(x)**3+(75*x*exp(3+x)**2+(75*x**2+75*x+15)*exp(3+x)+75*x**2+15*x)*ln(x)
**2+(375*x*exp(3+x)**3+(750*x**2+375*x+75)*exp(3+x)**2+(375*x**3+750*x**2+150*x)*exp(3+x)+375*x**3+75*x**2)*ln
(x)+625*x*exp(3+x)**4+(1875*x**2+625*x+125)*exp(3+x)**3+(1875*x**3+1875*x**2+375*x)*exp(3+x)**2+(625*x**4+1875
*x**3+375*x**2)*exp(3+x)+625*x**4+125*x**3-4*x)*exp(-1/16*ln(x)**4+1/16*(-20*exp(3+x)-20*x)*ln(x)**3+1/16*(-15
0*exp(3+x)**2-300*exp(3+x)*x-150*x**2)*ln(x)**2+1/16*(-500*exp(3+x)**3-1500*x*exp(3+x)**2-1500*x**2*exp(3+x)-5
00*x**3)*ln(x)-625/16*exp(3+x)**4-625/4*x*exp(3+x)**3-1875/8*x**2*exp(3+x)**2-625/4*x**3*exp(3+x)-625/16*x**4+
x)+4*x+4)/x,x)

[Out]

x - exp(-625*x**4/16 - 625*x**3*exp(x + 3)/4 - 1875*x**2*exp(2*x + 6)/8 - 625*x*exp(3*x + 9)/4 + x + (-5*x/4 -
 5*exp(x + 3)/4)*log(x)**3 + (-75*x**2/8 - 75*x*exp(x + 3)/4 - 75*exp(2*x + 6)/8)*log(x)**2 + (-125*x**3/4 - 3
75*x**2*exp(x + 3)/4 - 375*x*exp(2*x + 6)/4 - 125*exp(3*x + 9)/4)*log(x) - 625*exp(4*x + 12)/16 - log(x)**4/16
) + log(x)

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