\(\int \frac {(50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 (450 x^2-300 x^3+50 x^4)+e^x (-300 x+300 x^2-50 x^3+e^5 (-300 x+100 x^2))) \log (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 (-6 x^2+2 x^3)}{e^x-3 x+x^2})}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 (9 x^3-6 x^4+x^5)+e^x (-3 x^2+x^3+e^5 (-6 x^2+2 x^3))} \, dx\) [6558]

Optimal result

Integrand size = 196, antiderivative size = 32 \[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=e+25 \log ^2\left (2 x \left (e^5+\frac {x}{-\frac {e^x}{3-x}+x}\right )\right ) \]

[Out]

exp(1)+25*ln(2*(exp(5)+x/(x-exp(x)/(-x+3)))*x)^2

Rubi [F]

\[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=\int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx \]

[In]

Int[((50*E^(5 + 2*x) + 450*x^2 - 300*x^3 + 50*x^4 + E^5*(450*x^2 - 300*x^3 + 50*x^4) + E^x*(-300*x + 300*x^2 -
50*x^3 + E^5*(-300*x + 100*x^2)))*Log[(2*E^(5 + x)*x - 6*x^2 + 2*x^3 + E^5*(-6*x^2 + 2*x^3))/(E^x - 3*x + x^2
)])/(E^(5 + 2*x)*x + 9*x^3 - 6*x^4 + x^5 + E^5*(9*x^3 - 6*x^4 + x^5) + E^x*(-3*x^2 + x^3 + E^5*(-6*x^2 + 2*x^3
))),x]

[Out]

250*(1 + E^5)*Log[(2*x*(E^(5 + x) - (1 + E^5)*(3 - x)*x))/(E^x - (3 - x)*x)]*Defer[Int][x/(E^(5 + x) + (1 + E^
5)*(-3 + x)*x), x] + 150*Log[(2*x*(E^(5 + x) - (1 + E^5)*(3 - x)*x))/(E^x - (3 - x)*x)]*Defer[Int][(E^x - 3*x
+ x^2)^(-1), x] - 250*Log[(2*x*(E^(5 + x) - (1 + E^5)*(3 - x)*x))/(E^x - (3 - x)*x)]*Defer[Int][x/(E^x - 3*x +
x^2), x] + 50*Log[(2*x*(E^(5 + x) - (1 + E^5)*(3 - x)*x))/(E^x - (3 - x)*x)]*Defer[Int][x^2/(E^x - 3*x + x^2)
, x] + 150*(1 + E^5)*Log[(2*x*(E^(5 + x) - (1 + E^5)*(3 - x)*x))/(E^x - (3 - x)*x)]*Defer[Int][(-E^(5 + x) + 3
*(1 + E^5)*x - (1 + E^5)*x^2)^(-1), x] + 50*(1 + E^5)*Log[(2*x*(E^(5 + x) - (1 + E^5)*(3 - x)*x))/(E^x - (3 -
x)*x)]*Defer[Int][x^2/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] + 50*Defer[Int][Log[(2*x*(E^(5 + x) + (
1 + E^5)*(-3 + x)*x))/(E^x + (-3 + x)*x)]/x, x] - 150*Defer[Int][Defer[Int][(E^x + (-3 + x)*x)^(-1), x]/x, x]
- 750*(1 + E^5)*Defer[Int][(x*Defer[Int][(E^x + (-3 + x)*x)^(-1), x])/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x] -
450*Defer[Int][Defer[Int][(E^x + (-3 + x)*x)^(-1), x]/(E^x - 3*x + x^2), x] + 750*Defer[Int][(x*Defer[Int][(E
^x + (-3 + x)*x)^(-1), x])/(E^x - 3*x + x^2), x] - 150*Defer[Int][(x^2*Defer[Int][(E^x + (-3 + x)*x)^(-1), x])
/(E^x - 3*x + x^2), x] - 450*(1 + E^5)*Defer[Int][Defer[Int][(E^x + (-3 + x)*x)^(-1), x]/(-E^(5 + x) + 3*(1 +
E^5)*x - (1 + E^5)*x^2), x] - 150*(1 + E^5)*Defer[Int][(x^2*Defer[Int][(E^x + (-3 + x)*x)^(-1), x])/(-E^(5 + x
) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] + 250*Defer[Int][Defer[Int][x/(E^x + (-3 + x)*x), x]/x, x] - 750*(1 + E
^5)*Defer[Int][Defer[Int][x/(E^x + (-3 + x)*x), x]/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x] - 250*(1 + E^5)*Defe
r[Int][(x^2*Defer[Int][x/(E^x + (-3 + x)*x), x])/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x] + 750*Defer[Int][Defer
[Int][x/(E^x + (-3 + x)*x), x]/(E^x - 3*x + x^2), x] - 1250*Defer[Int][(x*Defer[Int][x/(E^x + (-3 + x)*x), x])
/(E^x - 3*x + x^2), x] + 250*Defer[Int][(x^2*Defer[Int][x/(E^x + (-3 + x)*x), x])/(E^x - 3*x + x^2), x] - 1250
*(1 + E^5)*Defer[Int][(x*Defer[Int][x/(E^x + (-3 + x)*x), x])/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x]
- 50*Defer[Int][Defer[Int][x^2/(E^x + (-3 + x)*x), x]/x, x] - 250*(1 + E^5)*Defer[Int][(x*Defer[Int][x^2/(E^x
+ (-3 + x)*x), x])/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x] - 150*Defer[Int][Defer[Int][x^2/(E^x + (-3 + x)*x),
x]/(E^x - 3*x + x^2), x] + 250*Defer[Int][(x*Defer[Int][x^2/(E^x + (-3 + x)*x), x])/(E^x - 3*x + x^2), x] - 5
0*Defer[Int][(x^2*Defer[Int][x^2/(E^x + (-3 + x)*x), x])/(E^x - 3*x + x^2), x] - 150*(1 + E^5)*Defer[Int][Defe
r[Int][x^2/(E^x + (-3 + x)*x), x]/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] - 50*(1 + E^5)*Defer[Int][(
x^2*Defer[Int][x^2/(E^x + (-3 + x)*x), x])/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] - 150*(1 + E^5)*De
fer[Int][Defer[Int][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x]/x, x] - 750*(1 + E^5)^2*Defer[Int][(x*Defer[I
nt][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x])/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x] - 450*(1 + E^5)*Defer
[Int][Defer[Int][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x]/(E^x - 3*x + x^2), x] + 750*(1 + E^5)*Defer[Int]
[(x*Defer[Int][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x])/(E^x - 3*x + x^2), x] - 150*(1 + E^5)*Defer[Int][
(x^2*Defer[Int][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x])/(E^x - 3*x + x^2), x] - 450*(1 + E^5)^2*Defer[In
t][Defer[Int][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x]/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] -
150*(1 + E^5)^2*Defer[Int][(x^2*Defer[Int][-(E^(5 + x) + (1 + E^5)*(-3 + x)*x)^(-1), x])/(-E^(5 + x) + 3*(1 +
E^5)*x - (1 + E^5)*x^2), x] - 250*(1 + E^5)*Defer[Int][Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x]/x,
x] - 1250*(1 + E^5)^2*Defer[Int][(x*Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x])/(E^(5 + x) + (1 + E^5
)*(-3 + x)*x), x] - 750*(1 + E^5)*Defer[Int][Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x]/(E^x - 3*x +
x^2), x] + 1250*(1 + E^5)*Defer[Int][(x*Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x])/(E^x - 3*x + x^2)
, x] - 250*(1 + E^5)*Defer[Int][(x^2*Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x])/(E^x - 3*x + x^2), x
] - 750*(1 + E^5)^2*Defer[Int][Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x]/(-E^(5 + x) + 3*(1 + E^5)*x
- (1 + E^5)*x^2), x] - 250*(1 + E^5)^2*Defer[Int][(x^2*Defer[Int][x/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x])/(
-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] - 50*(1 + E^5)*Defer[Int][Defer[Int][-(x^2/(E^(5 + x) + (1 + E
^5)*(-3 + x)*x)), x]/x, x] - 250*(1 + E^5)^2*Defer[Int][(x*Defer[Int][-(x^2/(E^(5 + x) + (1 + E^5)*(-3 + x)*x)
), x])/(E^(5 + x) + (1 + E^5)*(-3 + x)*x), x] - 150*(1 + E^5)*Defer[Int][Defer[Int][-(x^2/(E^(5 + x) + (1 + E^
5)*(-3 + x)*x)), x]/(E^x - 3*x + x^2), x] + 250*(1 + E^5)*Defer[Int][(x*Defer[Int][-(x^2/(E^(5 + x) + (1 + E^5
)*(-3 + x)*x)), x])/(E^x - 3*x + x^2), x] - 50*(1 + E^5)*Defer[Int][(x^2*Defer[Int][-(x^2/(E^(5 + x) + (1 + E^
5)*(-3 + x)*x)), x])/(E^x - 3*x + x^2), x] - 150*(1 + E^5)^2*Defer[Int][Defer[Int][-(x^2/(E^(5 + x) + (1 + E^5
)*(-3 + x)*x)), x]/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x] - 50*(1 + E^5)^2*Defer[Int][(x^2*Defer[Int
][-(x^2/(E^(5 + x) + (1 + E^5)*(-3 + x)*x)), x])/(-E^(5 + x) + 3*(1 + E^5)*x - (1 + E^5)*x^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {50 \left (e^{5+2 x}+2 e^{5+x} (-3+x) x+\left (1+e^5\right ) (-3+x)^2 x^2-e^x x \left (6-6 x+x^2\right )\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x \left (e^x+(-3+x) x\right ) \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )} \, dx \\ & = 50 \int \frac {\left (e^{5+2 x}+2 e^{5+x} (-3+x) x+\left (1+e^5\right ) (-3+x)^2 x^2-e^x x \left (6-6 x+x^2\right )\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x \left (e^x+(-3+x) x\right ) \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )} \, dx \\ & = 50 \int \left (\frac {\log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x}+\frac {\left (3-5 x+x^2\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{e^x-3 x+x^2}+\frac {\left (1+e^5\right ) \left (-3+5 x-x^2\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{e^{5+x}-3 \left (1+e^5\right ) x+\left (1+e^5\right ) x^2}\right ) \, dx \\ & = 50 \int \frac {\log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x} \, dx+50 \int \frac {\left (3-5 x+x^2\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{e^x-3 x+x^2} \, dx+\left (50 \left (1+e^5\right )\right ) \int \frac {\left (-3+5 x-x^2\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{e^{5+x}-3 \left (1+e^5\right ) x+\left (1+e^5\right ) x^2} \, dx \\ & = 50 \int \frac {\log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x} \, dx-50 \int \frac {\left (e^{5+2 x}+2 e^{5+x} (-3+x) x+\left (1+e^5\right ) (-3+x)^2 x^2-e^x x \left (6-6 x+x^2\right )\right ) \left (3 \int \frac {1}{e^x+(-3+x) x} \, dx-5 \int \frac {x}{e^x+(-3+x) x} \, dx+\int \frac {x^2}{e^x+(-3+x) x} \, dx\right )}{x \left (e^x+(-3+x) x\right ) \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )} \, dx-\left (50 \left (1+e^5\right )\right ) \int \frac {\left (e^{5+2 x}+2 e^{5+x} (-3+x) x+\left (1+e^5\right ) (-3+x)^2 x^2-e^x x \left (6-6 x+x^2\right )\right ) \left (3 \int -\frac {1}{e^{5+x}+(-3+x) x+e^5 (-3+x) x} \, dx+\int -\frac {x^2}{e^{5+x}+(-3+x) x+e^5 (-3+x) x} \, dx+5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx\right )}{x \left (e^x+(-3+x) x\right ) \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )} \, dx+\left (50 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x^2}{e^x-3 x+x^2} \, dx+\left (150 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {1}{e^x-3 x+x^2} \, dx-\left (250 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x}{e^x-3 x+x^2} \, dx+\left (50 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x^2}{-e^{5+x}+3 \left (1+e^5\right ) x-\left (1+e^5\right ) x^2} \, dx+\left (150 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {1}{-e^{5+x}+3 \left (1+e^5\right ) x-\left (1+e^5\right ) x^2} \, dx+\left (250 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx \\ & = 50 \int \frac {\log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x} \, dx-50 \int \left (\frac {\left (1+e^5\right ) \left (3-5 x+x^2\right ) \left (-3 \int \frac {1}{e^x+(-3+x) x} \, dx+5 \int \frac {x}{e^x+(-3+x) x} \, dx-\int \frac {x^2}{e^x+(-3+x) x} \, dx\right )}{e^{5+x}-3 \left (1+e^5\right ) x+\left (1+e^5\right ) x^2}+\frac {3 \int \frac {1}{e^x+(-3+x) x} \, dx-5 \int \frac {x}{e^x+(-3+x) x} \, dx+\int \frac {x^2}{e^x+(-3+x) x} \, dx}{x}+\frac {\left (3-5 x+x^2\right ) \left (3 \int \frac {1}{e^x+(-3+x) x} \, dx-5 \int \frac {x}{e^x+(-3+x) x} \, dx+\int \frac {x^2}{e^x+(-3+x) x} \, dx\right )}{e^x-3 x+x^2}\right ) \, dx-\left (50 \left (1+e^5\right )\right ) \int \left (\frac {-3 \int \frac {1}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx+5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx-\int \frac {x^2}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx}{x}-\frac {\left (3-5 x+x^2\right ) \left (3 \int \frac {1}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx-5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx+\int \frac {x^2}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx\right )}{e^x-3 x+x^2}+\frac {\left (1+e^5\right ) \left (3-5 x+x^2\right ) \left (3 \int \frac {1}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx-5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx+\int \frac {x^2}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx\right )}{e^{5+x}-3 \left (1+e^5\right ) x+\left (1+e^5\right ) x^2}\right ) \, dx+\left (50 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x^2}{e^x-3 x+x^2} \, dx+\left (150 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {1}{e^x-3 x+x^2} \, dx-\left (250 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x}{e^x-3 x+x^2} \, dx+\left (50 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x^2}{-e^{5+x}+3 \left (1+e^5\right ) x-\left (1+e^5\right ) x^2} \, dx+\left (150 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {1}{-e^{5+x}+3 \left (1+e^5\right ) x-\left (1+e^5\right ) x^2} \, dx+\left (250 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx \\ & = 50 \int \frac {\log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )}{x} \, dx-50 \int \frac {3 \int \frac {1}{e^x+(-3+x) x} \, dx-5 \int \frac {x}{e^x+(-3+x) x} \, dx+\int \frac {x^2}{e^x+(-3+x) x} \, dx}{x} \, dx-50 \int \frac {\left (3-5 x+x^2\right ) \left (3 \int \frac {1}{e^x+(-3+x) x} \, dx-5 \int \frac {x}{e^x+(-3+x) x} \, dx+\int \frac {x^2}{e^x+(-3+x) x} \, dx\right )}{e^x-3 x+x^2} \, dx-\left (50 \left (1+e^5\right )\right ) \int \frac {\left (3-5 x+x^2\right ) \left (-3 \int \frac {1}{e^x+(-3+x) x} \, dx+5 \int \frac {x}{e^x+(-3+x) x} \, dx-\int \frac {x^2}{e^x+(-3+x) x} \, dx\right )}{e^{5+x}-3 \left (1+e^5\right ) x+\left (1+e^5\right ) x^2} \, dx-\left (50 \left (1+e^5\right )\right ) \int \frac {-3 \int \frac {1}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx+5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx-\int \frac {x^2}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx}{x} \, dx+\left (50 \left (1+e^5\right )\right ) \int \frac {\left (3-5 x+x^2\right ) \left (3 \int \frac {1}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx-5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx+\int \frac {x^2}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx\right )}{e^x-3 x+x^2} \, dx-\left (50 \left (1+e^5\right )^2\right ) \int \frac {\left (3-5 x+x^2\right ) \left (3 \int \frac {1}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx-5 \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx+\int \frac {x^2}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx\right )}{e^{5+x}-3 \left (1+e^5\right ) x+\left (1+e^5\right ) x^2} \, dx+\left (50 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x^2}{e^x-3 x+x^2} \, dx+\left (150 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {1}{e^x-3 x+x^2} \, dx-\left (250 \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x}{e^x-3 x+x^2} \, dx+\left (50 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x^2}{-e^{5+x}+3 \left (1+e^5\right ) x-\left (1+e^5\right ) x^2} \, dx+\left (150 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {1}{-e^{5+x}+3 \left (1+e^5\right ) x-\left (1+e^5\right ) x^2} \, dx+\left (250 \left (1+e^5\right ) \log \left (\frac {2 x \left (e^{5+x}+\left (1+e^5\right ) (-3+x) x\right )}{e^x+(-3+x) x}\right )\right ) \int \frac {x}{e^{5+x}+\left (1+e^5\right ) (-3+x) x} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.12 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.19 \[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=25 \log ^2\left (\frac {2 x \left (e^{5+x}+(-3+x) x+e^5 (-3+x) x\right )}{e^x+(-3+x) x}\right ) \]

[In]

Integrate[((50*E^(5 + 2*x) + 450*x^2 - 300*x^3 + 50*x^4 + E^5*(450*x^2 - 300*x^3 + 50*x^4) + E^x*(-300*x + 300
*x^2 - 50*x^3 + E^5*(-300*x + 100*x^2)))*Log[(2*E^(5 + x)*x - 6*x^2 + 2*x^3 + E^5*(-6*x^2 + 2*x^3))/(E^x - 3*x
+ x^2)])/(E^(5 + 2*x)*x + 9*x^3 - 6*x^4 + x^5 + E^5*(9*x^3 - 6*x^4 + x^5) + E^x*(-3*x^2 + x^3 + E^5*(-6*x^2 +
2*x^3))),x]

[Out]

25*Log[(2*x*(E^(5 + x) + (-3 + x)*x + E^5*(-3 + x)*x))/(E^x + (-3 + x)*x)]^2

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 4.72 (sec) , antiderivative size = 1829, normalized size of antiderivative = 57.16

method	result	size
risch	\(\text {Expression too large to display}\)	\(1829\)

[In]

int((50*exp(5)*exp(x)^2+((100*x^2-300*x)*exp(5)-50*x^3+300*x^2-300*x)*exp(x)+(50*x^4-300*x^3+450*x^2)*exp(5)+5
0*x^4-300*x^3+450*x^2)*ln((2*x*exp(5)*exp(x)+(2*x^3-6*x^2)*exp(5)+2*x^3-6*x^2)/(exp(x)+x^2-3*x))/(x*exp(5)*exp
(x)^2+((2*x^3-6*x^2)*exp(5)+x^3-3*x^2)*exp(x)+(x^5-6*x^4+9*x^3)*exp(5)+x^5-6*x^4+9*x^3),x,method=_RETURNVERBOS
E)

[Out]

-25*I*Pi*ln(x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I/(exp(x)+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp
(5)+x^2-3*x)/(exp(x)+x^2-3*x))-25*I*Pi*ln(x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))*csgn(I
*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I*x)+25*I*Pi*ln(x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)
+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^2+25*I*Pi*ln(x)*csgn(I/(exp(x)+x^2-3*x))
*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^2+25*I*Pi*ln(x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^
2-3*x)/(exp(x)+x^2-3*x))*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^2+25*I*Pi*ln(x)*csgn(I*x
/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^2*csgn(I*x)-25*I*Pi*ln(exp(x)+x^2-3*x)*csgn(I*((exp(x)+x^
2-3*x)*exp(5)+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^2-25*I*Pi*ln(exp(x)+x^2-3*x
)*csgn(I/(exp(x)+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^2-25*I*Pi*ln(exp(x)+x^2-
3*x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*ex
p(5)+x^2-3*x))^2-25*I*Pi*ln(exp(x)+x^2-3*x)*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^2*csg
n(I*x)+50*ln(2)*ln(x)+25*ln(x)^2+(50*ln(x)-50*ln(exp(x)+x^2-3*x))*ln((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)-50*ln(2)
*ln(exp(x)+x^2-3*x)-50*ln(x)*ln(exp(x)+x^2-3*x)+25*I*Pi*ln(x^2-3*x+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I*((ex
p(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^2+25*I*Pi*ln(x^2-3*x
+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I/(exp(x)+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2
-3*x))^2+25*I*Pi*ln(x^2-3*x+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x
^2-3*x))*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^2+25*I*Pi*ln(x^2-3*x+x^2*exp(-5)-3*exp(-
5)*x+exp(x))*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^2*csgn(I*x)+25*I*Pi*ln(exp(x)+x^2-3*
x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I/(exp(x)+x^2-3*x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)
/(exp(x)+x^2-3*x))+25*I*Pi*ln(exp(x)+x^2-3*x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))*csgn(
I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I*x)+25*ln((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)^2+25*
ln(exp(x)+x^2-3*x)^2-25*I*Pi*ln(x^2-3*x+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*
x)/(exp(x)+x^2-3*x))*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I*x)-25*I*Pi*ln(x^2-3*x
+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^3-25*I*Pi*ln(x^2-3
*x+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^3-25*I*Pi*ln(x
^2-3*x+x^2*exp(-5)-3*exp(-5)*x+exp(x))*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))*csgn(I/(exp(x)+x^2-3*x))*csgn
(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))+50*ln(2)*ln(x^2-3*x+x^2*exp(-5)-3*exp(-5)*x+exp(x))-25*
I*Pi*ln(x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(exp(x)+x^2-3*x))^3-25*I*Pi*ln(x)*csgn(I*x/(exp(x)+x^2-3*x
)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^3+25*I*Pi*ln(exp(x)+x^2-3*x)*csgn(I*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x)/(ex
p(x)+x^2-3*x))^3+25*I*Pi*ln(exp(x)+x^2-3*x)*csgn(I*x/(exp(x)+x^2-3*x)*((exp(x)+x^2-3*x)*exp(5)+x^2-3*x))^3

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.72 \[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=25 \, \log \left (\frac {2 \, {\left ({\left (x^{3} - 3 \, x^{2}\right )} e^{10} + {\left (x^{3} - 3 \, x^{2}\right )} e^{5} + x e^{\left (x + 10\right )}\right )}}{{\left (x^{2} - 3 \, x\right )} e^{5} + e^{\left (x + 5\right )}}\right )^{2} \]

[In]

integrate((50*exp(5)*exp(x)^2+((100*x^2-300*x)*exp(5)-50*x^3+300*x^2-300*x)*exp(x)+(50*x^4-300*x^3+450*x^2)*ex
p(5)+50*x^4-300*x^3+450*x^2)*log((2*x*exp(5)*exp(x)+(2*x^3-6*x^2)*exp(5)+2*x^3-6*x^2)/(exp(x)+x^2-3*x))/(x*exp
(5)*exp(x)^2+((2*x^3-6*x^2)*exp(5)+x^3-3*x^2)*exp(x)+(x^5-6*x^4+9*x^3)*exp(5)+x^5-6*x^4+9*x^3),x, algorithm="f
ricas")

[Out]

25*log(2*((x^3 - 3*x^2)*e^10 + (x^3 - 3*x^2)*e^5 + x*e^(x + 10))/((x^2 - 3*x)*e^5 + e^(x + 5)))^2

Sympy [A] (verification not implemented)

Time = 0.50 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.50 \[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=25 \log {\left (\frac {2 x^{3} - 6 x^{2} + 2 x e^{5} e^{x} + \left (2 x^{3} - 6 x^{2}\right ) e^{5}}{x^{2} - 3 x + e^{x}} \right )}^{2} \]

[In]

integrate((50*exp(5)*exp(x)**2+((100*x**2-300*x)*exp(5)-50*x**3+300*x**2-300*x)*exp(x)+(50*x**4-300*x**3+450*x
**2)*exp(5)+50*x**4-300*x**3+450*x**2)*ln((2*x*exp(5)*exp(x)+(2*x**3-6*x**2)*exp(5)+2*x**3-6*x**2)/(exp(x)+x**
2-3*x))/(x*exp(5)*exp(x)**2+((2*x**3-6*x**2)*exp(5)+x**3-3*x**2)*exp(x)+(x**5-6*x**4+9*x**3)*exp(5)+x**5-6*x**
4+9*x**3),x)

[Out]

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

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 189 vs. \(2 (28) = 56\).

Time = 0.27 (sec) , antiderivative size = 189, normalized size of antiderivative = 5.91 \[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=50 \, {\left (\log \left (x^{2} - 3 \, x + e^{x}\right ) - \log \left (x\right ) + 5\right )} \log \left (x^{2} {\left (e^{5} + 1\right )} - 3 \, x {\left (e^{5} + 1\right )} + e^{\left (x + 5\right )}\right ) - 25 \, \log \left (x^{2} {\left (e^{5} + 1\right )} - 3 \, x {\left (e^{5} + 1\right )} + e^{\left (x + 5\right )}\right )^{2} + 50 \, {\left (\log \left (x\right ) - 5\right )} \log \left (x^{2} - 3 \, x + e^{x}\right ) - 25 \, \log \left (x^{2} - 3 \, x + e^{x}\right )^{2} - 25 \, \log \left (x\right )^{2} - 50 \, {\left (\log \left (x^{2} - 3 \, x + e^{x}\right ) - \log \left ({\left (x^{2} {\left (e^{5} + 1\right )} - 3 \, x {\left (e^{5} + 1\right )} + e^{\left (x + 5\right )}\right )} e^{\left (-5\right )}\right ) - \log \left (x\right )\right )} \log \left (\frac {2 \, {\left (x^{3} - 3 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{5} + x e^{\left (x + 5\right )}\right )}}{x^{2} - 3 \, x + e^{x}}\right ) + 250 \, \log \left (x\right ) \]

[In]

integrate((50*exp(5)*exp(x)^2+((100*x^2-300*x)*exp(5)-50*x^3+300*x^2-300*x)*exp(x)+(50*x^4-300*x^3+450*x^2)*ex
p(5)+50*x^4-300*x^3+450*x^2)*log((2*x*exp(5)*exp(x)+(2*x^3-6*x^2)*exp(5)+2*x^3-6*x^2)/(exp(x)+x^2-3*x))/(x*exp
(5)*exp(x)^2+((2*x^3-6*x^2)*exp(5)+x^3-3*x^2)*exp(x)+(x^5-6*x^4+9*x^3)*exp(5)+x^5-6*x^4+9*x^3),x, algorithm="m
axima")

[Out]

50*(log(x^2 - 3*x + e^x) - log(x) + 5)*log(x^2*(e^5 + 1) - 3*x*(e^5 + 1) + e^(x + 5)) - 25*log(x^2*(e^5 + 1) -
3*x*(e^5 + 1) + e^(x + 5))^2 + 50*(log(x) - 5)*log(x^2 - 3*x + e^x) - 25*log(x^2 - 3*x + e^x)^2 - 25*log(x)^2
- 50*(log(x^2 - 3*x + e^x) - log((x^2*(e^5 + 1) - 3*x*(e^5 + 1) + e^(x + 5))*e^(-5)) - log(x))*log(2*(x^3 - 3
*x^2 + (x^3 - 3*x^2)*e^5 + x*e^(x + 5))/(x^2 - 3*x + e^x)) + 250*log(x)

Giac [F]

\[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=\int { \frac {50 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2} + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{5} - {\left (x^{3} - 6 \, x^{2} - 2 \, {\left (x^{2} - 3 \, x\right )} e^{5} + 6 \, x\right )} e^{x} + e^{\left (2 \, x + 5\right )}\right )} \log \left (\frac {2 \, {\left (x^{3} - 3 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{5} + x e^{\left (x + 5\right )}\right )}}{x^{2} - 3 \, x + e^{x}}\right )}{x^{5} - 6 \, x^{4} + 9 \, x^{3} + {\left (x^{5} - 6 \, x^{4} + 9 \, x^{3}\right )} e^{5} + x e^{\left (2 \, x + 5\right )} + {\left (x^{3} - 3 \, x^{2} + 2 \, {\left (x^{3} - 3 \, x^{2}\right )} e^{5}\right )} e^{x}} \,d x } \]

[In]

integrate((50*exp(5)*exp(x)^2+((100*x^2-300*x)*exp(5)-50*x^3+300*x^2-300*x)*exp(x)+(50*x^4-300*x^3+450*x^2)*ex
p(5)+50*x^4-300*x^3+450*x^2)*log((2*x*exp(5)*exp(x)+(2*x^3-6*x^2)*exp(5)+2*x^3-6*x^2)/(exp(x)+x^2-3*x))/(x*exp
(5)*exp(x)^2+((2*x^3-6*x^2)*exp(5)+x^3-3*x^2)*exp(x)+(x^5-6*x^4+9*x^3)*exp(5)+x^5-6*x^4+9*x^3),x, algorithm="g
iac")

[Out]

integrate(50*(x^4 - 6*x^3 + 9*x^2 + (x^4 - 6*x^3 + 9*x^2)*e^5 - (x^3 - 6*x^2 - 2*(x^2 - 3*x)*e^5 + 6*x)*e^x +
e^(2*x + 5))*log(2*(x^3 - 3*x^2 + (x^3 - 3*x^2)*e^5 + x*e^(x + 5))/(x^2 - 3*x + e^x))/(x^5 - 6*x^4 + 9*x^3 + (
x^5 - 6*x^4 + 9*x^3)*e^5 + x*e^(2*x + 5) + (x^3 - 3*x^2 + 2*(x^3 - 3*x^2)*e^5)*e^x), x)

Mupad [B] (verification not implemented)

Time = 13.05 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.56 \[ \int \frac {\left (50 e^{5+2 x}+450 x^2-300 x^3+50 x^4+e^5 \left (450 x^2-300 x^3+50 x^4\right )+e^x \left (-300 x+300 x^2-50 x^3+e^5 \left (-300 x+100 x^2\right )\right )\right ) \log \left (\frac {2 e^{5+x} x-6 x^2+2 x^3+e^5 \left (-6 x^2+2 x^3\right )}{e^x-3 x+x^2}\right )}{e^{5+2 x} x+9 x^3-6 x^4+x^5+e^5 \left (9 x^3-6 x^4+x^5\right )+e^x \left (-3 x^2+x^3+e^5 \left (-6 x^2+2 x^3\right )\right )} \, dx=25\,{\ln \left (-\frac {{\mathrm {e}}^5\,\left (6\,x^2-2\,x^3\right )+6\,x^2-2\,x^3-2\,x\,{\mathrm {e}}^5\,{\mathrm {e}}^x}{{\mathrm {e}}^x-3\,x+x^2}\right )}^2 \]

[In]

int((log(-(exp(5)*(6*x^2 - 2*x^3) + 6*x^2 - 2*x^3 - 2*x*exp(5)*exp(x))/(exp(x) - 3*x + x^2))*(50*exp(2*x)*exp(
5) - exp(x)*(300*x + exp(5)*(300*x - 100*x^2) - 300*x^2 + 50*x^3) + exp(5)*(450*x^2 - 300*x^3 + 50*x^4) + 450*
x^2 - 300*x^3 + 50*x^4))/(exp(5)*(9*x^3 - 6*x^4 + x^5) - exp(x)*(exp(5)*(6*x^2 - 2*x^3) + 3*x^2 - x^3) + 9*x^3
- 6*x^4 + x^5 + x*exp(2*x)*exp(5)),x)

[Out]

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