∫ −1+eee4x (−20x+4exx+ee4x+4x (16x−4exx))+5x log(x)_______________________________________

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

________________________________________________________________________________________

Rubi [F] time = 44.36, 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 {-1+e^{e^{e^{4 x}}} \left (-20 x+4 e^x x+e^{e^{4 x}+4 x} \left (16 x-4 e^x x\right )\right )+5 x \log (x)}{e^{e^{e^{4 x}}} \left (-20 x+5 e^x x\right )+5 x \log (x)} \, dx \end {gather*}

Int[(-1 + E^E^E^(4*x)*(-20*x + 4*E^x*x + E^(E^(4*x) + 4*x)*(16*x - 4*E^x*x)) + 5*x*Log[x])/(E^E^E^(4*x)*(-20*x

-1/5*E^E^(4*x) + (4*x)/5 - (192*Defer[Int][E^(-2*E^E^(4*x) + E^(4*x))*Log[x]^2, x])/5 - (32*Defer[Int][E^(-2*E

^E^(4*x) + E^(4*x) + x)*Log[x]^2, x])/5 - (4*Defer[Int][E^(-2*E^E^(4*x) + E^(4*x) + 2*x)*Log[x]^2, x])/5 + (48

*Defer[Int][E^(-3*E^E^(4*x) + E^(4*x))*Log[x]^3, x])/5 + (4*Defer[Int][E^(-3*E^E^(4*x) + E^(4*x) + x)*Log[x]^3

, x])/5 - (4*Defer[Int][E^(-4*E^E^(4*x) + E^(4*x))*Log[x]^4, x])/5 - (4*Defer[Int][E^E^E^(4*x)/(E^E^E^(4*x)*(-

4 + E^x) + Log[x]), x])/5 - Defer[Int][1/(x*(E^E^E^(4*x)*(-4 + E^x) + Log[x])), x]/5 + Defer[Int][Log[x]/(E^E^

E^(4*x)*(-4 + E^x) + Log[x]), x]/5 + (1024*Defer[Int][(E^E^(4*x)*Log[x])/(E^E^E^(4*x)*(-4 + E^x) + Log[x]), x]

)/5 - (1024*Defer[Int][(E^(-E^E^(4*x) + E^(4*x))*Log[x]^2)/(E^E^E^(4*x)*(-4 + E^x) + Log[x]), x])/5 + (384*Def

er[Int][(E^(-2*E^E^(4*x) + E^(4*x))*Log[x]^3)/(E^E^E^(4*x)*(-4 + E^x) + Log[x]), x])/5 - (64*Defer[Int][(E^(-3

*E^E^(4*x) + E^(4*x))*Log[x]^4)/(E^E^E^(4*x)*(-4 + E^x) + Log[x]), x])/5 + (4*Defer[Int][(E^(-4*E^E^(4*x) + E^

(4*x))*Log[x]^5)/(E^E^E^(4*x)*(-4 + E^x) + Log[x]), x])/5 - (8*Defer[Int][Defer[Subst][Defer[Int][E^(-E^x^2 +

x^2), x], x, E^(2*x)]/x, x])/5 - (64*Defer[Int][Defer[Subst][Defer[Int][E^(-E^x^4 + x^4), x], x, E^x]/x, x])/5

- (64*Defer[Int][Defer[Subst][Defer[Int][E^(-E^x + x)/x, x], x, E^(4*x)]/x, x])/5 - (4*Defer[Int][Defer[Subst

][Defer[Int][E^(-E^x^4 + x^4)*x^2, x], x, E^x]/x, x])/5 + (8*Log[x]*Defer[Subst][Defer[Int][E^(-E^x^2 + x^2),

x], x, E^(2*x)])/5 + (64*Log[x]*Defer[Subst][Defer[Int][E^(-E^x^4 + x^4), x], x, E^x])/5 + (64*Log[x]*Defer[Su

bst][Defer[Int][E^(-E^x + x)/x, x], x, E^(4*x)])/5 + (4*Log[x]*Defer[Subst][Defer[Int][E^(-E^x^4 + x^4)*x^2, x

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1-e^{e^{e^{4 x}}} \left (-20 x+4 e^x x+e^{e^{4 x}+4 x} \left (16 x-4 e^x x\right )\right )-5 x \log (x)}{5 x \left (4 e^{e^{e^{4 x}}}-e^{e^{e^{4 x}}+x}-\log (x)\right )} \, dx\\ &=\frac {1}{5} \int \frac {1-e^{e^{e^{4 x}}} \left (-20 x+4 e^x x+e^{e^{4 x}+4 x} \left (16 x-4 e^x x\right )\right )-5 x \log (x)}{x \left (4 e^{e^{e^{4 x}}}-e^{e^{e^{4 x}}+x}-\log (x)\right )} \, dx\\ &=\frac {1}{5} \int \left (-4 e^{e^{4 x}+4 x}+4 e^{-e^{e^{4 x}}+e^{4 x}+3 x} \log (x)+4 e^{-2 e^{e^{4 x}}+e^{4 x}+2 x} \left (4 e^{e^{e^{4 x}}}-\log (x)\right ) \log (x)+4 e^{-3 e^{e^{4 x}}+e^{4 x}+x} \left (4 e^{e^{e^{4 x}}}-\log (x)\right )^2 \log (x)+4 e^{-4 e^{e^{4 x}}} \left (e^{4 e^{e^{4 x}}}+64 e^{3 e^{e^{4 x}}+e^{4 x}} \log (x)-48 e^{2 e^{e^{4 x}}+e^{4 x}} \log ^2(x)+12 e^{e^{e^{4 x}}+e^{4 x}} \log ^3(x)-e^{e^{4 x}} \log ^4(x)\right )-\frac {e^{-4 e^{e^{4 x}}} \left (e^{4 e^{e^{4 x}}}+4 e^{5 e^{e^{4 x}}} x-e^{4 e^{e^{4 x}}} x \log (x)-1024 e^{4 e^{e^{4 x}}+e^{4 x}} x \log (x)+1024 e^{3 e^{e^{4 x}}+e^{4 x}} x \log ^2(x)-384 e^{2 e^{e^{4 x}}+e^{4 x}} x \log ^3(x)+64 e^{e^{e^{4 x}}+e^{4 x}} x \log ^4(x)-4 e^{e^{4 x}} x \log ^5(x)\right )}{x \left (-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)\right )}\right ) \, dx\\ &=-\left (\frac {1}{5} \int \frac {e^{-4 e^{e^{4 x}}} \left (e^{4 e^{e^{4 x}}}+4 e^{5 e^{e^{4 x}}} x-e^{4 e^{e^{4 x}}} x \log (x)-1024 e^{4 e^{e^{4 x}}+e^{4 x}} x \log (x)+1024 e^{3 e^{e^{4 x}}+e^{4 x}} x \log ^2(x)-384 e^{2 e^{e^{4 x}}+e^{4 x}} x \log ^3(x)+64 e^{e^{e^{4 x}}+e^{4 x}} x \log ^4(x)-4 e^{e^{4 x}} x \log ^5(x)\right )}{x \left (-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)\right )} \, dx\right )-\frac {4}{5} \int e^{e^{4 x}+4 x} \, dx+\frac {4}{5} \int e^{-e^{e^{4 x}}+e^{4 x}+3 x} \log (x) \, dx+\frac {4}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+2 x} \left (4 e^{e^{e^{4 x}}}-\log (x)\right ) \log (x) \, dx+\frac {4}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}+x} \left (4 e^{e^{e^{4 x}}}-\log (x)\right )^2 \log (x) \, dx+\frac {4}{5} \int e^{-4 e^{e^{4 x}}} \left (e^{4 e^{e^{4 x}}}+64 e^{3 e^{e^{4 x}}+e^{4 x}} \log (x)-48 e^{2 e^{e^{4 x}}+e^{4 x}} \log ^2(x)+12 e^{e^{e^{4 x}}+e^{4 x}} \log ^3(x)-e^{e^{4 x}} \log ^4(x)\right ) \, dx\\ &=-\left (\frac {1}{5} \int \left (\frac {4 e^{e^{e^{4 x}}}}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}+\frac {1}{x \left (-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)\right )}-\frac {\log (x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}-\frac {1024 e^{e^{4 x}} \log (x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}+\frac {1024 e^{-e^{e^{4 x}}+e^{4 x}} \log ^2(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}-\frac {384 e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^3(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}+\frac {64 e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^4(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}-\frac {4 e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^5(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)}\right ) \, dx\right )-\frac {1}{5} \operatorname {Subst}\left (\int e^x \, dx,x,e^{4 x}\right )+\frac {4}{5} \int \left (4 e^{-e^{e^{4 x}}+e^{4 x}+2 x} \log (x)-e^{-2 e^{e^{4 x}}+e^{4 x}+2 x} \log ^2(x)\right ) \, dx+\frac {4}{5} \int \left (16 e^{-e^{e^{4 x}}+e^{4 x}+x} \log (x)-8 e^{-2 e^{e^{4 x}}+e^{4 x}+x} \log ^2(x)+e^{-3 e^{e^{4 x}}+e^{4 x}+x} \log ^3(x)\right ) \, dx+\frac {4}{5} \int \left (1+64 e^{-e^{e^{4 x}}+e^{4 x}} \log (x)-48 e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^2(x)+12 e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^3(x)-e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^4(x)\right ) \, dx-\frac {4}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )}{x} \, dx+\frac {1}{5} (4 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )\\ &=-\frac {1}{5} e^{e^{4 x}}+\frac {4 x}{5}-\frac {1}{5} \int \frac {1}{x \left (-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)\right )} \, dx+\frac {1}{5} \int \frac {\log (x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx-\frac {4}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+2 x} \log ^2(x) \, dx+\frac {4}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}+x} \log ^3(x) \, dx-\frac {4}{5} \int e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^4(x) \, dx-\frac {4}{5} \int \frac {e^{e^{e^{4 x}}}}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx+\frac {4}{5} \int \frac {e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^5(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx-\frac {4}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )}{x} \, dx+\frac {16}{5} \int e^{-e^{e^{4 x}}+e^{4 x}+2 x} \log (x) \, dx-\frac {32}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+x} \log ^2(x) \, dx+\frac {48}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^3(x) \, dx+\frac {64}{5} \int e^{-e^{e^{4 x}}+e^{4 x}+x} \log (x) \, dx-\frac {64}{5} \int \frac {e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^4(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx-\frac {192}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^2(x) \, dx+\frac {256}{5} \int e^{-e^{e^{4 x}}+e^{4 x}} \log (x) \, dx+\frac {384}{5} \int \frac {e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^3(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx+\frac {1024}{5} \int \frac {e^{e^{4 x}} \log (x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx-\frac {1024}{5} \int \frac {e^{-e^{e^{4 x}}+e^{4 x}} \log ^2(x)}{-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)} \, dx+\frac {1}{5} (4 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )\\ &=-\frac {1}{5} e^{e^{4 x}}+\frac {4 x}{5}-\frac {1}{5} \int \frac {1}{x \left (e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)\right )} \, dx+\frac {1}{5} \int \frac {\log (x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {4}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+2 x} \log ^2(x) \, dx+\frac {4}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}+x} \log ^3(x) \, dx-\frac {4}{5} \int e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^4(x) \, dx-\frac {4}{5} \int \frac {e^{e^{e^{4 x}}}}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx+\frac {4}{5} \int \frac {e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^5(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {4}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )}{x} \, dx-\frac {16}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^2}+x^2} \, dx,x,e^{2 x}\right )}{2 x} \, dx-\frac {32}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+x} \log ^2(x) \, dx+\frac {48}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^3(x) \, dx-\frac {64}{5} \int \frac {e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^4(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {64}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} \, dx,x,e^x\right )}{x} \, dx-\frac {192}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^2(x) \, dx-\frac {256}{5} \int \frac {\operatorname {Subst}\left (\int \frac {e^{-e^x+x}}{x} \, dx,x,e^{4 x}\right )}{4 x} \, dx+\frac {384}{5} \int \frac {e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^3(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx+\frac {1024}{5} \int \frac {e^{e^{4 x}} \log (x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {1024}{5} \int \frac {e^{-e^{e^{4 x}}+e^{4 x}} \log ^2(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx+\frac {1}{5} (4 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )+\frac {1}{5} (8 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^2}+x^2} \, dx,x,e^{2 x}\right )+\frac {1}{5} (64 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} \, dx,x,e^x\right )+\frac {1}{5} (64 \log (x)) \operatorname {Subst}\left (\int \frac {e^{-e^x+x}}{x} \, dx,x,e^{4 x}\right )\\ &=-\frac {1}{5} e^{e^{4 x}}+\frac {4 x}{5}-\frac {1}{5} \int \frac {1}{x \left (e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)\right )} \, dx+\frac {1}{5} \int \frac {\log (x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {4}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+2 x} \log ^2(x) \, dx+\frac {4}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}+x} \log ^3(x) \, dx-\frac {4}{5} \int e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^4(x) \, dx-\frac {4}{5} \int \frac {e^{e^{e^{4 x}}}}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx+\frac {4}{5} \int \frac {e^{-4 e^{e^{4 x}}+e^{4 x}} \log ^5(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {4}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )}{x} \, dx-\frac {8}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^2}+x^2} \, dx,x,e^{2 x}\right )}{x} \, dx-\frac {32}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}+x} \log ^2(x) \, dx+\frac {48}{5} \int e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^3(x) \, dx-\frac {64}{5} \int \frac {e^{-3 e^{e^{4 x}}+e^{4 x}} \log ^4(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {64}{5} \int \frac {\operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} \, dx,x,e^x\right )}{x} \, dx-\frac {64}{5} \int \frac {\operatorname {Subst}\left (\int \frac {e^{-e^x+x}}{x} \, dx,x,e^{4 x}\right )}{x} \, dx-\frac {192}{5} \int e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^2(x) \, dx+\frac {384}{5} \int \frac {e^{-2 e^{e^{4 x}}+e^{4 x}} \log ^3(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx+\frac {1024}{5} \int \frac {e^{e^{4 x}} \log (x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx-\frac {1024}{5} \int \frac {e^{-e^{e^{4 x}}+e^{4 x}} \log ^2(x)}{e^{e^{e^{4 x}}} \left (-4+e^x\right )+\log (x)} \, dx+\frac {1}{5} (4 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} x^2 \, dx,x,e^x\right )+\frac {1}{5} (8 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^2}+x^2} \, dx,x,e^{2 x}\right )+\frac {1}{5} (64 \log (x)) \operatorname {Subst}\left (\int e^{-e^{x^4}+x^4} \, dx,x,e^x\right )+\frac {1}{5} (64 \log (x)) \operatorname {Subst}\left (\int \frac {e^{-e^x+x}}{x} \, dx,x,e^{4 x}\right )\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A] time = 0.99, size = 36, normalized size = 1.29 \begin {gather*} \frac {1}{5} \left (5 x-\log \left (-4 e^{e^{e^{4 x}}}+e^{e^{e^{4 x}}+x}+\log (x)\right )\right ) \end {gather*}

Integrate[(-1 + E^E^E^(4*x)*(-20*x + 4*E^x*x + E^(E^(4*x) + 4*x)*(16*x - 4*E^x*x)) + 5*x*Log[x])/(E^E^E^(4*x)*

(5*x - Log[-4*E^E^E^(4*x) + E^(E^E^(4*x) + x) + Log[x]])/5

________________________________________________________________________________________

fricas [A] time = 0.88, size = 33, normalized size = 1.18 \begin {gather*} x - \frac {1}{5} \, \log \left (\frac {{\left (e^{x} - 4\right )} e^{\left (e^{\left (e^{\left (4 \, x\right )}\right )}\right )} + \log \relax (x)}{e^{x} - 4}\right ) - \frac {1}{5} \, \log \left (e^{x} - 4\right ) \end {gather*}

integrate((((-4*exp(x)*x+16*x)*exp(4*x)*exp(exp(4*x))+4*exp(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*log(x)-1)/((5*ex

p(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*log(x)),x, algorithm="fricas")

x - 1/5*log(((e^x - 4)*e^(e^(e^(4*x))) + log(x))/(e^x - 4)) - 1/5*log(e^x - 4)

________________________________________________________________________________________

giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {4 \, {\left ({\left (x e^{x} - 4 \, x\right )} e^{\left (4 \, x + e^{\left (4 \, x\right )}\right )} - x e^{x} + 5 \, x\right )} e^{\left (e^{\left (e^{\left (4 \, x\right )}\right )}\right )} - 5 \, x \log \relax (x) + 1}{5 \, {\left ({\left (x e^{x} - 4 \, x\right )} e^{\left (e^{\left (e^{\left (4 \, x\right )}\right )}\right )} + x \log \relax (x)\right )}}\,{d x} \end {gather*}

integrate((((-4*exp(x)*x+16*x)*exp(4*x)*exp(exp(4*x))+4*exp(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*log(x)-1)/((5*ex

p(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*log(x)),x, algorithm="giac")

integrate(-1/5*(4*((x*e^x - 4*x)*e^(4*x + e^(4*x)) - x*e^x + 5*x)*e^(e^(e^(4*x))) - 5*x*log(x) + 1)/((x*e^x -

________________________________________________________________________________________


method	result	size

risch	\(x -\frac {\ln \left ({\mathrm e}^{x}-4\right )}{5}-\frac {\ln \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{4 x}}}+\frac {\ln \relax (x )}{{\mathrm e}^{x}-4}\right )}{5}\)	\(29\)

int((((-4*exp(x)*x+16*x)*exp(4*x)*exp(exp(4*x))+4*exp(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*ln(x)-1)/((5*exp(x)*x-

20*x)*exp(exp(exp(4*x)))+5*x*ln(x)),x,method=_RETURNVERBOSE)

x-1/5*ln(exp(x)-4)-1/5*ln(exp(exp(exp(4*x)))+ln(x)/(exp(x)-4))

________________________________________________________________________________________

maxima [A] time = 0.63, size = 33, normalized size = 1.18 \begin {gather*} x - \frac {1}{5} \, \log \left (\frac {{\left (e^{x} - 4\right )} e^{\left (e^{\left (e^{\left (4 \, x\right )}\right )}\right )} + \log \relax (x)}{e^{x} - 4}\right ) - \frac {1}{5} \, \log \left (e^{x} - 4\right ) \end {gather*}

integrate((((-4*exp(x)*x+16*x)*exp(4*x)*exp(exp(4*x))+4*exp(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*log(x)-1)/((5*ex

p(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*log(x)),x, algorithm="maxima")

x - 1/5*log(((e^x - 4)*e^(e^(e^(4*x))) + log(x))/(e^x - 4)) - 1/5*log(e^x - 4)

________________________________________________________________________________________

mupad [B] time = 1.28, size = 39, normalized size = 1.39 \begin {gather*} x-\frac {\ln \left (\frac {\ln \relax (x)-4\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{4\,x}}}+{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{4\,x}}}\,{\mathrm {e}}^x}{{\mathrm {e}}^x-4}\right )}{5}-\frac {\ln \left ({\mathrm {e}}^x-4\right )}{5} \end {gather*}

int(-(exp(exp(exp(4*x)))*(4*x*exp(x) - 20*x + exp(4*x)*exp(exp(4*x))*(16*x - 4*x*exp(x))) + 5*x*log(x) - 1)/(e

xp(exp(exp(4*x)))*(20*x - 5*x*exp(x)) - 5*x*log(x)),x)

x - log((log(x) - 4*exp(exp(exp(4*x))) + exp(exp(exp(4*x)))*exp(x))/(exp(x) - 4))/5 - log(exp(x) - 4)/5

________________________________________________________________________________________

sympy [A] time = 1.14, size = 29, normalized size = 1.04 \begin {gather*} x - \frac {\log {\left (e^{x} - 4 \right )}}{5} - \frac {\log {\left (e^{e^{e^{4 x}}} + \frac {\log {\relax (x )}}{e^{x} - 4} \right )}}{5} \end {gather*}

integrate((((-4*exp(x)*x+16*x)*exp(4*x)*exp(exp(4*x))+4*exp(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*ln(x)-1)/((5*exp

(x)*x-20*x)*exp(exp(exp(4*x)))+5*x*ln(x)),x)

x - log(exp(x) - 4)/5 - log(exp(exp(exp(4*x))) + log(x)/(exp(x) - 4))/5

________________________________________________________________________________________

3.17.30 \(\int \frac {-1+e^{e^{e^{4 x}}} (-20 x+4 e^x x+e^{e^{4 x}+4 x} (16 x-4 e^x x))+5 x \log (x)}{e^{e^{e^{4 x}}} (-20 x+5 e^x x)+5 x \log (x)} \, dx\)