\(\int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+(-2 x^3-2 x^2 \log (5)) \log (x)-x^2 \log ^2(x)}} (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+(12 x+36 x^2) \log (5)+12 x \log ^2(5)+(12 x+36 x^2+24 x \log (5)) \log (x)+12 x \log ^2(x))}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+(4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)) \log (x)+(6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)) \log ^2(x)+(4 x^5+4 x^4 \log (5)) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+(-4 x^3-4 x^2 \log (5)) \log (x)-2 x^2 \log ^2(x))} \, dx\) [7950]

Optimal result

Integrand size = 318, antiderivative size = 32 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=4-e^{\frac {6}{-e^{e^{5 x}}+x^2 (x+\log (5)+\log (x))^2}} \]

[Out]

4-exp(3/(x^2*(ln(5)+x+ln(x))^2-exp(exp(5*x))))^2

Rubi [F]

\[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=\int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}\right ) \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx \]

[In]

Int[(-30*E^(E^(5*x) + 5*x) + 12*x^2 + 24*x^3 + (12*x + 36*x^2)*Log[5] + 12*x*Log[5]^2 + (12*x + 36*x^2 + 24*x*
Log[5])*Log[x] + 12*x*Log[x]^2)/(E^(6/(E^E^(5*x) - x^4 - 2*x^3*Log[5] - x^2*Log[5]^2 + (-2*x^3 - 2*x^2*Log[5])
*Log[x] - x^2*Log[x]^2))*(E^(2*E^(5*x)) + x^8 + 4*x^7*Log[5] + 6*x^6*Log[5]^2 + 4*x^5*Log[5]^3 + x^4*Log[5]^4
+ (4*x^7 + 12*x^6*Log[5] + 12*x^5*Log[5]^2 + 4*x^4*Log[5]^3)*Log[x] + (6*x^6 + 12*x^5*Log[5] + 6*x^4*Log[5]^2)
*Log[x]^2 + (4*x^5 + 4*x^4*Log[5])*Log[x]^3 + x^4*Log[x]^4 + E^E^(5*x)*(-2*x^4 - 4*x^3*Log[5] - 2*x^2*Log[5]^2
+ (-4*x^3 - 4*x^2*Log[5])*Log[x] - 2*x^2*Log[x]^2))),x]

[Out]

-30*Defer[Int][E^(E^(5*x) + 5*x - 6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2
))/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2)^2, x] + 12*Log[5]*(1 + Log[5])*
Defer[Int][x/(E^(6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2))*(-E^E^(5*x) +
x^4 + 2*x^3*Log[5] + x^2*Log[5]^2 + 2*x^3*Log[x] + 2*x^2*Log[5]*Log[x] + x^2*Log[x]^2)^2), x] + 12*(1 + Log[12
5])*Defer[Int][x^2/(E^(6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2))*(-E^E^(5
*x) + x^4 + 2*x^3*Log[5] + x^2*Log[5]^2 + 2*x^3*Log[x] + 2*x^2*Log[5]*Log[x] + x^2*Log[x]^2)^2), x] + 24*Defer
[Int][x^3/(E^(6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2))*(-E^E^(5*x) + x^4
+ 2*x^3*Log[5] + x^2*Log[5]^2 + 2*x^3*Log[x] + 2*x^2*Log[5]*Log[x] + x^2*Log[x]^2)^2), x] + 12*(1 + Log[25])*
Defer[Int][(x*Log[x])/(E^(6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2))*(-E^E
^(5*x) + x^4 + 2*x^3*Log[5] + x^2*Log[5]^2 + 2*x^3*Log[x] + 2*x^2*Log[5]*Log[x] + x^2*Log[x]^2)^2), x] + 36*De
fer[Int][(x^2*Log[x])/(E^(6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2))*(-E^E
^(5*x) + x^4 + 2*x^3*Log[5] + x^2*Log[5]^2 + 2*x^3*Log[x] + 2*x^2*Log[5]*Log[x] + x^2*Log[x]^2)^2), x] + 12*De
fer[Int][(x*Log[x]^2)/(E^(6/(E^E^(5*x) - x^2*(x + Log[5])^2 - 2*x^2*(x + Log[5])*Log[x] - x^2*Log[x]^2))*(-E^E
^(5*x) + x^4 + 2*x^3*Log[5] + x^2*Log[5]^2 + 2*x^3*Log[x] + 2*x^2*Log[5]*Log[x] + x^2*Log[x]^2)^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {6 \exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) \left (-5 e^{e^{5 x}+5 x}+2 x \left (x+2 x^2+\log (5)+3 x \log (5)+\log ^2(5)\right )+2 x (1+3 x+\log (25)) \log (x)+2 x \log ^2(x)\right )}{\left (e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)\right )^2} \, dx \\ & = 6 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) \left (-5 e^{e^{5 x}+5 x}+2 x \left (x+2 x^2+\log (5)+3 x \log (5)+\log ^2(5)\right )+2 x (1+3 x+\log (25)) \log (x)+2 x \log ^2(x)\right )}{\left (e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)\right )^2} \, dx \\ & = 6 \int \left (-\frac {5 \exp \left (e^{5 x}+5 x-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right )}{\left (e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)-2 x^3 \log (x)-2 x^2 \log (5) \log (x)-x^2 \log ^2(x)\right )^2}+\frac {2 \exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x (x+\log (5)) (1+2 x+\log (5))}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}+\frac {2 \exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x (1+3 x+\log (25)) \log (x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}+\frac {2 \exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x \log ^2(x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}\right ) \, dx \\ & = 12 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x (x+\log (5)) (1+2 x+\log (5))}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+12 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x (1+3 x+\log (25)) \log (x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+12 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x \log ^2(x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx-30 \int \frac {\exp \left (e^{5 x}+5 x-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right )}{\left (e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)-2 x^3 \log (x)-2 x^2 \log (5) \log (x)-x^2 \log ^2(x)\right )^2} \, dx \\ & = 12 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x \log ^2(x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+12 \int \left (\frac {2 \exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x^3}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}+\frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x \log (5) (1+\log (5))}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}+\frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x^2 (1+\log (125))}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}\right ) \, dx+12 \int \left (\frac {3 \exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x^2 \log (x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}+\frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x (1+\log (25)) \log (x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2}\right ) \, dx-30 \int \frac {\exp \left (e^{5 x}+5 x-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right )}{\left (e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)\right )^2} \, dx \\ & = 12 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x \log ^2(x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+24 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x^3}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx-30 \int \frac {\exp \left (e^{5 x}+5 x-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right )}{\left (e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)\right )^2} \, dx+36 \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x^2 \log (x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+(12 \log (5) (1+\log (5))) \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+(12 (1+\log (25))) \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x \log (x)}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx+(12 (1+\log (125))) \int \frac {\exp \left (-\frac {6}{e^{e^{5 x}}-x^2 (x+\log (5))^2-2 x^2 (x+\log (5)) \log (x)-x^2 \log ^2(x)}\right ) x^2}{\left (-e^{e^{5 x}}+x^4+2 x^3 \log (5)+x^2 \log ^2(5)+2 x^3 \log (x)+2 x^2 \log (5) \log (x)+x^2 \log ^2(x)\right )^2} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=\int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx \]

[In]

Integrate[(-30*E^(E^(5*x) + 5*x) + 12*x^2 + 24*x^3 + (12*x + 36*x^2)*Log[5] + 12*x*Log[5]^2 + (12*x + 36*x^2 +
24*x*Log[5])*Log[x] + 12*x*Log[x]^2)/(E^(6/(E^E^(5*x) - x^4 - 2*x^3*Log[5] - x^2*Log[5]^2 + (-2*x^3 - 2*x^2*L
og[5])*Log[x] - x^2*Log[x]^2))*(E^(2*E^(5*x)) + x^8 + 4*x^7*Log[5] + 6*x^6*Log[5]^2 + 4*x^5*Log[5]^3 + x^4*Log
[5]^4 + (4*x^7 + 12*x^6*Log[5] + 12*x^5*Log[5]^2 + 4*x^4*Log[5]^3)*Log[x] + (6*x^6 + 12*x^5*Log[5] + 6*x^4*Log
[5]^2)*Log[x]^2 + (4*x^5 + 4*x^4*Log[5])*Log[x]^3 + x^4*Log[x]^4 + E^E^(5*x)*(-2*x^4 - 4*x^3*Log[5] - 2*x^2*Lo
g[5]^2 + (-4*x^3 - 4*x^2*Log[5])*Log[x] - 2*x^2*Log[x]^2))),x]

[Out]

Integrate[(-30*E^(E^(5*x) + 5*x) + 12*x^2 + 24*x^3 + (12*x + 36*x^2)*Log[5] + 12*x*Log[5]^2 + (12*x + 36*x^2 +
24*x*Log[5])*Log[x] + 12*x*Log[x]^2)/(E^(6/(E^E^(5*x) - x^4 - 2*x^3*Log[5] - x^2*Log[5]^2 + (-2*x^3 - 2*x^2*L
og[5])*Log[x] - x^2*Log[x]^2))*(E^(2*E^(5*x)) + x^8 + 4*x^7*Log[5] + 6*x^6*Log[5]^2 + 4*x^5*Log[5]^3 + x^4*Log
[5]^4 + (4*x^7 + 12*x^6*Log[5] + 12*x^5*Log[5]^2 + 4*x^4*Log[5]^3)*Log[x] + (6*x^6 + 12*x^5*Log[5] + 6*x^4*Log
[5]^2)*Log[x]^2 + (4*x^5 + 4*x^4*Log[5])*Log[x]^3 + x^4*Log[x]^4 + E^E^(5*x)*(-2*x^4 - 4*x^3*Log[5] - 2*x^2*Lo
g[5]^2 + (-4*x^3 - 4*x^2*Log[5])*Log[x] - 2*x^2*Log[x]^2))), x]

Maple [A] (verified)

Time = 0.24 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.81

\[-{\mathrm e}^{\frac {6}{x^{2} \ln \left (x \right )^{2}+2 x^{2} \ln \left (5\right ) \ln \left (x \right )+2 x^{3} \ln \left (x \right )+x^{2} \ln \left (5\right )^{2}+2 x^{3} \ln \left (5\right )+x^{4}-{\mathrm e}^{{\mathrm e}^{5 x}}}}\]

[In]

int((-30*exp(5*x)*exp(exp(5*x))+12*x*ln(x)^2+(24*x*ln(5)+36*x^2+12*x)*ln(x)+12*x*ln(5)^2+(36*x^2+12*x)*ln(5)+2
4*x^3+12*x^2)*exp(-3/(exp(exp(5*x))-x^2*ln(x)^2+(-2*x^2*ln(5)-2*x^3)*ln(x)-x^2*ln(5)^2-2*x^3*ln(5)-x^4))^2/(ex
p(exp(5*x))^2+(-2*x^2*ln(x)^2+(-4*x^2*ln(5)-4*x^3)*ln(x)-2*x^2*ln(5)^2-4*x^3*ln(5)-2*x^4)*exp(exp(5*x))+x^4*ln
(x)^4+(4*x^4*ln(5)+4*x^5)*ln(x)^3+(6*x^4*ln(5)^2+12*x^5*ln(5)+6*x^6)*ln(x)^2+(4*x^4*ln(5)^3+12*x^5*ln(5)^2+12*
x^6*ln(5)+4*x^7)*ln(x)+x^4*ln(5)^4+4*x^5*ln(5)^3+6*x^6*ln(5)^2+4*x^7*ln(5)+x^8),x)

[Out]

-exp(6/(x^2*ln(x)^2+2*x^2*ln(5)*ln(x)+2*x^3*ln(x)+x^2*ln(5)^2+2*x^3*ln(5)+x^4-exp(exp(5*x))))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (29) = 58\).

Time = 0.28 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.41 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-e^{\left (\frac {6 \, e^{\left (5 \, x\right )}}{x^{2} e^{\left (5 \, x\right )} \log \left (x\right )^{2} + 2 \, {\left (x^{3} + x^{2} \log \left (5\right )\right )} e^{\left (5 \, x\right )} \log \left (x\right ) + {\left (x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (5\right )^{2}\right )} e^{\left (5 \, x\right )} - e^{\left (5 \, x + e^{\left (5 \, x\right )}\right )}}\right )} \]

[In]

integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12*x)*log(x)+12*x*log(5)^2+(36*x^2+12*
x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(exp(5*x))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*lo
g(5)-x^4))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)-2*x^2*log(5)^2-4*x^3*log(5)-2*x^4)
*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5)+4*x^5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4
*log(5)^3+12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5)^3+6*x^6*log(5)^2+4*x^7*log(5)+
x^8),x, algorithm="fricas")

[Out]

-e^(6*e^(5*x)/(x^2*e^(5*x)*log(x)^2 + 2*(x^3 + x^2*log(5))*e^(5*x)*log(x) + (x^4 + 2*x^3*log(5) + x^2*log(5)^2
)*e^(5*x) - e^(5*x + e^(5*x))))

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=\text {Timed out} \]

[In]

integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*ln(x)**2+(24*x*ln(5)+36*x**2+12*x)*ln(x)+12*x*ln(5)**2+(36*x**2+12*
x)*ln(5)+24*x**3+12*x**2)*exp(-3/(exp(exp(5*x))-x**2*ln(x)**2+(-2*x**2*ln(5)-2*x**3)*ln(x)-x**2*ln(5)**2-2*x**
3*ln(5)-x**4))**2/(exp(exp(5*x))**2+(-2*x**2*ln(x)**2+(-4*x**2*ln(5)-4*x**3)*ln(x)-2*x**2*ln(5)**2-4*x**3*ln(5
)-2*x**4)*exp(exp(5*x))+x**4*ln(x)**4+(4*x**4*ln(5)+4*x**5)*ln(x)**3+(6*x**4*ln(5)**2+12*x**5*ln(5)+6*x**6)*ln
(x)**2+(4*x**4*ln(5)**3+12*x**5*ln(5)**2+12*x**6*ln(5)+4*x**7)*ln(x)+x**4*ln(5)**4+4*x**5*ln(5)**3+6*x**6*ln(5
)**2+4*x**7*ln(5)+x**8),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.46 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.72 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-e^{\left (\frac {6}{x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (5\right )^{2} + x^{2} \log \left (x\right )^{2} + 2 \, {\left (x^{3} + x^{2} \log \left (5\right )\right )} \log \left (x\right ) - e^{\left (e^{\left (5 \, x\right )}\right )}}\right )} \]

[In]

integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12*x)*log(x)+12*x*log(5)^2+(36*x^2+12*
x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(exp(5*x))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*lo
g(5)-x^4))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)-2*x^2*log(5)^2-4*x^3*log(5)-2*x^4)
*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5)+4*x^5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4
*log(5)^3+12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5)^3+6*x^6*log(5)^2+4*x^7*log(5)+
x^8),x, algorithm="maxima")

[Out]

-e^(6/(x^4 + 2*x^3*log(5) + x^2*log(5)^2 + x^2*log(x)^2 + 2*(x^3 + x^2*log(5))*log(x) - e^(e^(5*x))))

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.78 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-e^{\left (\frac {6}{x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (5\right )^{2} + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{2} \log \left (5\right ) \log \left (x\right ) + x^{2} \log \left (x\right )^{2} - e^{\left (e^{\left (5 \, x\right )}\right )}}\right )} \]

[In]

integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12*x)*log(x)+12*x*log(5)^2+(36*x^2+12*
x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(exp(5*x))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*lo
g(5)-x^4))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)-2*x^2*log(5)^2-4*x^3*log(5)-2*x^4)
*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5)+4*x^5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4
*log(5)^3+12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5)^3+6*x^6*log(5)^2+4*x^7*log(5)+
x^8),x, algorithm="giac")

[Out]

-e^(6/(x^4 + 2*x^3*log(5) + x^2*log(5)^2 + 2*x^3*log(x) + 2*x^2*log(5)*log(x) + x^2*log(x)^2 - e^(e^(5*x))))

Mupad [B] (verification not implemented)

Time = 50.20 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.78 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-{\mathrm {e}}^{\frac {6}{x^2\,{\ln \left (5\right )}^2-{\mathrm {e}}^{{\mathrm {e}}^{5\,x}}+2\,x^3\,\ln \left (x\right )+x^2\,{\ln \left (x\right )}^2+2\,x^3\,\ln \left (5\right )+x^4+2\,x^2\,\ln \left (5\right )\,\ln \left (x\right )}} \]

[In]

int((exp(6/(x^2*log(5)^2 - exp(exp(5*x)) + x^2*log(x)^2 + log(x)*(2*x^2*log(5) + 2*x^3) + 2*x^3*log(5) + x^4))
*(12*x*log(x)^2 + log(5)*(12*x + 36*x^2) - 30*exp(5*x)*exp(exp(5*x)) + 12*x*log(5)^2 + 12*x^2 + 24*x^3 + log(x
)*(12*x + 24*x*log(5) + 36*x^2)))/(exp(2*exp(5*x)) + x^4*log(5)^4 + 4*x^5*log(5)^3 + 6*x^6*log(5)^2 - exp(exp(
5*x))*(2*x^2*log(5)^2 + 2*x^2*log(x)^2 + log(x)*(4*x^2*log(5) + 4*x^3) + 4*x^3*log(5) + 2*x^4) + x^4*log(x)^4
+ log(x)*(4*x^4*log(5)^3 + 12*x^5*log(5)^2 + 12*x^6*log(5) + 4*x^7) + 4*x^7*log(5) + x^8 + log(x)^3*(4*x^4*log
(5) + 4*x^5) + log(x)^2*(6*x^4*log(5)^2 + 12*x^5*log(5) + 6*x^6)),x)

[Out]

-exp(6/(x^2*log(5)^2 - exp(exp(5*x)) + 2*x^3*log(x) + x^2*log(x)^2 + 2*x^3*log(5) + x^4 + 2*x^2*log(5)*log(x))
)