\(\int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 (-4 x^3+12 x^5)+(8 x^2+8 x^3-24 x^4-24 x^5+e^3 (-8 x^2+24 x^4)) \log (1-e^3+x)+(4 x+4 x^2-12 x^3-12 x^4+e^3 (-4 x+12 x^3)) \log ^2(1-e^3+x)+\log ^2(x) (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 (-2 x+6 x^3)+(1+x-9 x^4-9 x^5+e^3 (-1+9 x^4)) \log (1-e^3+x))+\log (x) (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 (x+2 x^3+9 x^5)+(-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 (1+6 x^2+21 x^4)) \log (1-e^3+x)+(-4 x-4 x^2-12 x^3-12 x^4+e^3 (4 x+12 x^3)) \log ^2(1-e^3+x))}{-2 x^6+2 e^3 x^6-2 x^7+(-6 x^5+6 e^3 x^5-6 x^6) \log (1-e^3+x)+(-6 x^4+6 e^3 x^4-6 x^5) \log ^2(1-e^3+x)+(-2 x^3+2 e^3 x^3-2 x^4) \log ^3(1-e^3+x)} \, dx\) [9319]

Optimal result

Integrand size = 458, antiderivative size = 35 \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\left (-2+\frac {\left (\frac {1}{2} \left (\frac {1}{x}-x\right )-x\right ) \log (x)}{x+\log \left (1-e^3+x\right )}\right )^2 \]

[Out]

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

Rubi [F]

\[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx \]

[In]

Int[(4*x^3 + 4*x^4 - 12*x^5 - 12*x^6 + E^3*(-4*x^3 + 12*x^5) + (8*x^2 + 8*x^3 - 24*x^4 - 24*x^5 + E^3*(-8*x^2
+ 24*x^4))*Log[1 - E^3 + x] + (4*x + 4*x^2 - 12*x^3 - 12*x^4 + E^3*(-4*x + 12*x^3))*Log[1 - E^3 + x]^2 + Log[x
]^2*(3*x + 2*x^2 - 12*x^3 - 6*x^4 + 9*x^5 + E^3*(-2*x + 6*x^3) + (1 + x - 9*x^4 - 9*x^5 + E^3*(-1 + 9*x^4))*Lo
g[1 - E^3 + x]) + Log[x]*(-x - x^2 - 6*x^3 - 2*x^4 + 3*x^5 - 9*x^6 + E^3*(x + 2*x^3 + 9*x^5) + (-1 - x - 10*x^
2 - 6*x^3 - 9*x^4 - 21*x^5 + E^3*(1 + 6*x^2 + 21*x^4))*Log[1 - E^3 + x] + (-4*x - 4*x^2 - 12*x^3 - 12*x^4 + E^
3*(4*x + 12*x^3))*Log[1 - E^3 + x]^2))/(-2*x^6 + 2*E^3*x^6 - 2*x^7 + (-6*x^5 + 6*E^3*x^5 - 6*x^6)*Log[1 - E^3
+ x] + (-6*x^4 + 6*E^3*x^4 - 6*x^5)*Log[1 - E^3 + x]^2 + (-2*x^3 + 2*E^3*x^3 - 2*x^4)*Log[1 - E^3 + x]^3),x]

[Out]

(3*(5 - 3*E^3)*Defer[Int][Log[x]^2/(x + Log[1 - E^3 + x])^3, x])/2 + ((2 - 6*E^3 + 3*E^6)^2*Defer[Int][Log[x]^
2/((-1 + E^3 - x)*(x + Log[1 - E^3 + x])^3), x])/(2*(1 - E^3)^2) - ((2 - E^3)*Defer[Int][Log[x]^2/(x^2*(x + Lo
g[1 - E^3 + x])^3), x])/(2*(1 - E^3)) + Defer[Int][Log[x]^2/(x*(x + Log[1 - E^3 + x])^3), x]/(2*(1 - E^3)^2) -
(9*Defer[Int][(x*Log[x]^2)/(x + Log[1 - E^3 + x])^3, x])/2 - (9*Defer[Int][(x^2*Log[x]^2)/(x + Log[1 - E^3 +
x])^3, x])/2 + Defer[Int][Log[x]/(x + Log[1 - E^3 + x])^2, x]/(2*(1 - E^3)) - ((5 - E^3)*Defer[Int][Log[x]/(x
+ Log[1 - E^3 + x])^2, x])/(2*(1 - E^3)^2) + ((2 - 6*E^3 + 3*E^6)*Defer[Int][Log[x]/(x + Log[1 - E^3 + x])^2,
x])/(2*(1 - E^3)) - ((5 - E^3)*(2 - 6*E^3 + 3*E^6)*Defer[Int][Log[x]/(x + Log[1 - E^3 + x])^2, x])/(2*(1 - E^3
)^2) + ((2 - 6*E^3 + 3*E^6)*Defer[Int][Log[x]/((-1 + E^3 - x)*(x + Log[1 - E^3 + x])^2), x])/2 - ((5 - E^3)*(2
- 6*E^3 + 3*E^6)*Defer[Int][Log[x]/((-1 + E^3 - x)*(x + Log[1 - E^3 + x])^2), x])/(2*(1 - E^3)) + Defer[Int][
Log[x]/(x^3*(x + Log[1 - E^3 + x])^2), x]/2 - Defer[Int][Log[x]/(x*(x + Log[1 - E^3 + x])^2), x]/(2*(1 - E^3)^
2) + ((5 - E^3)*Defer[Int][Log[x]/(x*(x + Log[1 - E^3 + x])^2), x])/(2*(1 - E^3)) - ((2 - 6*E^3 + 3*E^6)*Defer
[Int][Log[x]/(x*(x + Log[1 - E^3 + x])^2), x])/(2*(1 - E^3)^2) - Defer[Int][(x*Log[x])/(x + Log[1 - E^3 + x])^
2, x]/(2*(1 - E^3)^2) - ((2 - 6*E^3 + 3*E^6)*Defer[Int][(x*Log[x])/(x + Log[1 - E^3 + x])^2, x])/(2*(1 - E^3)^
2) - Defer[Int][Log[x]^2/(x^3*(x + Log[1 - E^3 + x])^2), x]/2 - (3*Defer[Int][Log[x]^2/(x*(x + Log[1 - E^3 + x
])^2), x])/2 + Defer[Int][Log[x]^2/(x*(x + Log[1 - E^3 + x])^2), x]/(2*(1 - E^3)^2) + ((2 - 6*E^3 + 3*E^6)*Def
er[Int][Log[x]^2/(x*(x + Log[1 - E^3 + x])^2), x])/(2*(1 - E^3)^2) + (3*Defer[Int][(x*Log[x]^2)/(x + Log[1 - E
^3 + x])^2, x])/(2*(1 - E^3)^2) + (3*(2 - 6*E^3 + 3*E^6)*Defer[Int][(x*Log[x]^2)/(x + Log[1 - E^3 + x])^2, x])
/(2*(1 - E^3)^2) + 6*Defer[Int][(x + Log[1 - E^3 + x])^(-1), x] - 2*Defer[Int][1/(x^2*(x + Log[1 - E^3 + x])),
x] + 6*Defer[Int][Log[x]/(x + Log[1 - E^3 + x]), x] + 2*Defer[Int][Log[x]/(x^2*(x + Log[1 - E^3 + x])), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{\left (-2+2 e^3\right ) x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx \\ & = \int \frac {\left (\left (-1+3 x^2\right ) \log (x)+4 x \left (x+\log \left (1-e^3+x\right )\right )\right ) \left (\left (1-e^3+x\right ) \left (-1+3 x^2\right ) \left (x+\log \left (1-e^3+x\right )\right )+\log (x) \left (x \left (3-2 e^3+2 x-3 x^2\right )-\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log \left (1-e^3+x\right )\right )\right )}{2 x^3 \left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx \\ & = \frac {1}{2} \int \frac {\left (\left (-1+3 x^2\right ) \log (x)+4 x \left (x+\log \left (1-e^3+x\right )\right )\right ) \left (\left (1-e^3+x\right ) \left (-1+3 x^2\right ) \left (x+\log \left (1-e^3+x\right )\right )+\log (x) \left (x \left (3-2 e^3+2 x-3 x^2\right )-\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log \left (1-e^3+x\right )\right )\right )}{x^3 \left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx \\ & = \frac {1}{2} \int \left (-\frac {\left (-2+e^3-x\right ) \left (-1+3 x^2\right )^2 \log ^2(x)}{\left (-1+e^3-x\right ) x^2 \left (x+\log \left (1-e^3+x\right )\right )^3}+\frac {\left (1-3 x^2\right ) \log (x) \left (1-e^3+x+5 \left (1-\frac {e^3}{5}\right ) x^2+x^3-\left (1-e^3\right ) \log (x)-x \log (x)-3 \left (1-e^3\right ) x^2 \log (x)-3 x^3 \log (x)\right )}{x^3 \left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^2}+\frac {4 \left (-1+3 x^2+\log (x)+3 x^2 \log (x)\right )}{x^2 \left (x+\log \left (1-e^3+x\right )\right )}\right ) \, dx \\ & = -\left (\frac {1}{2} \int \frac {\left (-2+e^3-x\right ) \left (-1+3 x^2\right )^2 \log ^2(x)}{\left (-1+e^3-x\right ) x^2 \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx\right )+\frac {1}{2} \int \frac {\left (1-3 x^2\right ) \log (x) \left (1-e^3+x+5 \left (1-\frac {e^3}{5}\right ) x^2+x^3-\left (1-e^3\right ) \log (x)-x \log (x)-3 \left (1-e^3\right ) x^2 \log (x)-3 x^3 \log (x)\right )}{x^3 \left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx+2 \int \frac {-1+3 x^2+\log (x)+3 x^2 \log (x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx \\ & = \frac {1}{2} \int \frac {\left (1-3 x^2\right ) \log (x) \left (1+x+5 x^2+x^3-e^3 \left (1+x^2\right )+\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log (x)\right )}{x^3 \left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx-\frac {1}{2} \int \left (\frac {3 \left (-5+3 e^3\right ) \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3}-\frac {\left (2-6 e^3+3 e^6\right )^2 \log ^2(x)}{\left (-1+e^3\right )^2 \left (-1+e^3-x\right ) \left (x+\log \left (1-e^3+x\right )\right )^3}+\frac {\left (-2+e^3\right ) \log ^2(x)}{\left (-1+e^3\right ) x^2 \left (x+\log \left (1-e^3+x\right )\right )^3}-\frac {\log ^2(x)}{\left (-1+e^3\right )^2 x \left (x+\log \left (1-e^3+x\right )\right )^3}+\frac {9 x \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3}+\frac {9 x^2 \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3}\right ) \, dx+2 \int \left (\frac {3}{x+\log \left (1-e^3+x\right )}-\frac {1}{x^2 \left (x+\log \left (1-e^3+x\right )\right )}+\frac {3 \log (x)}{x+\log \left (1-e^3+x\right )}+\frac {\log (x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )}\right ) \, dx \\ & = \frac {1}{2} \int \left (\frac {\log (x) \left (1-e^3+x+5 \left (1-\frac {e^3}{5}\right ) x^2+x^3-\left (1-e^3\right ) \log (x)-x \log (x)-3 \left (1-e^3\right ) x^2 \log (x)-3 x^3 \log (x)\right )}{\left (1-e^3\right ) x^3 \left (x+\log \left (1-e^3+x\right )\right )^2}+\frac {\left (2-6 e^3+3 e^6\right ) \log (x) \left (1-e^3+x+5 \left (1-\frac {e^3}{5}\right ) x^2+x^3-\left (1-e^3\right ) \log (x)-x \log (x)-3 \left (1-e^3\right ) x^2 \log (x)-3 x^3 \log (x)\right )}{\left (1-e^3\right )^3 \left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^2}+\frac {\log (x) \left (-1+e^3-x-5 \left (1-\frac {e^3}{5}\right ) x^2-x^3+\left (1-e^3\right ) \log (x)+x \log (x)+3 \left (1-e^3\right ) x^2 \log (x)+3 x^3 \log (x)\right )}{\left (1-e^3\right )^2 x^2 \left (x+\log \left (1-e^3+x\right )\right )^2}+\frac {\left (2-6 e^3+3 e^6\right ) \log (x) \left (-1+e^3-x-5 \left (1-\frac {e^3}{5}\right ) x^2-x^3+\left (1-e^3\right ) \log (x)+x \log (x)+3 \left (1-e^3\right ) x^2 \log (x)+3 x^3 \log (x)\right )}{\left (1-e^3\right )^3 x \left (x+\log \left (1-e^3+x\right )\right )^2}\right ) \, dx-2 \int \frac {1}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx+2 \int \frac {\log (x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx-\frac {9}{2} \int \frac {x \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx-\frac {9}{2} \int \frac {x^2 \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx+6 \int \frac {1}{x+\log \left (1-e^3+x\right )} \, dx+6 \int \frac {\log (x)}{x+\log \left (1-e^3+x\right )} \, dx+\frac {1}{2} \left (3 \left (5-3 e^3\right )\right ) \int \frac {\log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx+\frac {\int \frac {\log ^2(x)}{x \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )^2}-\frac {\left (2-e^3\right ) \int \frac {\log ^2(x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )}+\frac {\left (2-6 e^3+3 e^6\right )^2 \int \frac {\log ^2(x)}{\left (-1+e^3-x\right ) \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )^2} \\ & = -\left (2 \int \frac {1}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx\right )+2 \int \frac {\log (x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx-\frac {9}{2} \int \frac {x \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx-\frac {9}{2} \int \frac {x^2 \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx+6 \int \frac {1}{x+\log \left (1-e^3+x\right )} \, dx+6 \int \frac {\log (x)}{x+\log \left (1-e^3+x\right )} \, dx+\frac {1}{2} \left (3 \left (5-3 e^3\right )\right ) \int \frac {\log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx+\frac {\int \frac {\log ^2(x)}{x \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )^2}+\frac {\int \frac {\log (x) \left (-1+e^3-x-5 \left (1-\frac {e^3}{5}\right ) x^2-x^3+\left (1-e^3\right ) \log (x)+x \log (x)+3 \left (1-e^3\right ) x^2 \log (x)+3 x^3 \log (x)\right )}{x^2 \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )^2}+\frac {\int \frac {\log (x) \left (1-e^3+x+5 \left (1-\frac {e^3}{5}\right ) x^2+x^3-\left (1-e^3\right ) \log (x)-x \log (x)-3 \left (1-e^3\right ) x^2 \log (x)-3 x^3 \log (x)\right )}{x^3 \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )}-\frac {\left (2-e^3\right ) \int \frac {\log ^2(x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )}+\frac {\left (2-6 e^3+3 e^6\right ) \int \frac {\log (x) \left (1-e^3+x+5 \left (1-\frac {e^3}{5}\right ) x^2+x^3-\left (1-e^3\right ) \log (x)-x \log (x)-3 \left (1-e^3\right ) x^2 \log (x)-3 x^3 \log (x)\right )}{\left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )^3}+\frac {\left (2-6 e^3+3 e^6\right ) \int \frac {\log (x) \left (-1+e^3-x-5 \left (1-\frac {e^3}{5}\right ) x^2-x^3+\left (1-e^3\right ) \log (x)+x \log (x)+3 \left (1-e^3\right ) x^2 \log (x)+3 x^3 \log (x)\right )}{x \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )^3}+\frac {\left (2-6 e^3+3 e^6\right )^2 \int \frac {\log ^2(x)}{\left (-1+e^3-x\right ) \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )^2} \\ & = -\left (2 \int \frac {1}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx\right )+2 \int \frac {\log (x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )} \, dx-\frac {9}{2} \int \frac {x \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx-\frac {9}{2} \int \frac {x^2 \log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx+6 \int \frac {1}{x+\log \left (1-e^3+x\right )} \, dx+6 \int \frac {\log (x)}{x+\log \left (1-e^3+x\right )} \, dx+\frac {1}{2} \left (3 \left (5-3 e^3\right )\right ) \int \frac {\log ^2(x)}{\left (x+\log \left (1-e^3+x\right )\right )^3} \, dx+\frac {\int \frac {\log ^2(x)}{x \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )^2}+\frac {\int \frac {\log (x) \left (-1-x-5 x^2-x^3+e^3 \left (1+x^2\right )-\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log (x)\right )}{x^2 \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )^2}+\frac {\int \frac {\log (x) \left (1+x+5 x^2+x^3-e^3 \left (1+x^2\right )+\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log (x)\right )}{x^3 \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )}-\frac {\left (2-e^3\right ) \int \frac {\log ^2(x)}{x^2 \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )}+\frac {\left (2-6 e^3+3 e^6\right ) \int \frac {\log (x) \left (-1-x-5 x^2-x^3+e^3 \left (1+x^2\right )-\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log (x)\right )}{x \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )^3}+\frac {\left (2-6 e^3+3 e^6\right ) \int \frac {\log (x) \left (1+x+5 x^2+x^3-e^3 \left (1+x^2\right )+\left (-1+e^3-x\right ) \left (1+3 x^2\right ) \log (x)\right )}{\left (1-e^3+x\right ) \left (x+\log \left (1-e^3+x\right )\right )^2} \, dx}{2 \left (1-e^3\right )^3}+\frac {\left (2-6 e^3+3 e^6\right )^2 \int \frac {\log ^2(x)}{\left (-1+e^3-x\right ) \left (x+\log \left (1-e^3+x\right )\right )^3} \, dx}{2 \left (1-e^3\right )^2} \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.54 \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\frac {\left (-1+3 x^2\right ) \log (x) \left (\left (-1+3 x^2\right ) \log (x)+8 x \left (x+\log \left (1-e^3+x\right )\right )\right )}{4 x^2 \left (x+\log \left (1-e^3+x\right )\right )^2} \]

[In]

Integrate[(4*x^3 + 4*x^4 - 12*x^5 - 12*x^6 + E^3*(-4*x^3 + 12*x^5) + (8*x^2 + 8*x^3 - 24*x^4 - 24*x^5 + E^3*(-
8*x^2 + 24*x^4))*Log[1 - E^3 + x] + (4*x + 4*x^2 - 12*x^3 - 12*x^4 + E^3*(-4*x + 12*x^3))*Log[1 - E^3 + x]^2 +
Log[x]^2*(3*x + 2*x^2 - 12*x^3 - 6*x^4 + 9*x^5 + E^3*(-2*x + 6*x^3) + (1 + x - 9*x^4 - 9*x^5 + E^3*(-1 + 9*x^
4))*Log[1 - E^3 + x]) + Log[x]*(-x - x^2 - 6*x^3 - 2*x^4 + 3*x^5 - 9*x^6 + E^3*(x + 2*x^3 + 9*x^5) + (-1 - x -
10*x^2 - 6*x^3 - 9*x^4 - 21*x^5 + E^3*(1 + 6*x^2 + 21*x^4))*Log[1 - E^3 + x] + (-4*x - 4*x^2 - 12*x^3 - 12*x^
4 + E^3*(4*x + 12*x^3))*Log[1 - E^3 + x]^2))/(-2*x^6 + 2*E^3*x^6 - 2*x^7 + (-6*x^5 + 6*E^3*x^5 - 6*x^6)*Log[1
- E^3 + x] + (-6*x^4 + 6*E^3*x^4 - 6*x^5)*Log[1 - E^3 + x]^2 + (-2*x^3 + 2*E^3*x^3 - 2*x^4)*Log[1 - E^3 + x]^3
),x]

[Out]

((-1 + 3*x^2)*Log[x]*((-1 + 3*x^2)*Log[x] + 8*x*(x + Log[1 - E^3 + x])))/(4*x^2*(x + Log[1 - E^3 + x])^2)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs. \(2(28)=56\).

Time = 8.87 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.03

method	result	size
risch	\(\frac {\left (9 x^{4} \ln \left (x \right )+24 x^{4}+24 x^{3} \ln \left (-{\mathrm e}^{3}+x +1\right )-6 x^{2} \ln \left (x \right )-8 x^{2}-8 x \ln \left (-{\mathrm e}^{3}+x +1\right )+\ln \left (x \right )\right ) \ln \left (x \right )}{4 x^{2} {\left (\ln \left (-{\mathrm e}^{3}+x +1\right )+x \right )}^{2}}\)	\(71\)
parallelrisch	\(-\frac {-9 x^{4} \ln \left (x \right )^{2}-24 x^{4} \ln \left (x \right )+6 x^{2} \ln \left (x \right )^{2}-\ln \left (x \right )^{2}+8 x^{2} \ln \left (x \right )-24 \ln \left (x \right ) \ln \left (-{\mathrm e}^{3}+x +1\right ) x^{3}+8 \ln \left (x \right ) \ln \left (-{\mathrm e}^{3}+x +1\right ) x}{4 x^{2} \left (x^{2}+2 x \ln \left (-{\mathrm e}^{3}+x +1\right )+\ln \left (-{\mathrm e}^{3}+x +1\right )^{2}\right )}\)	\(100\)

[In]

int(((((9*x^4-1)*exp(3)-9*x^5-9*x^4+x+1)*ln(-exp(3)+x+1)+(6*x^3-2*x)*exp(3)+9*x^5-6*x^4-12*x^3+2*x^2+3*x)*ln(x
)^2+(((12*x^3+4*x)*exp(3)-12*x^4-12*x^3-4*x^2-4*x)*ln(-exp(3)+x+1)^2+((21*x^4+6*x^2+1)*exp(3)-21*x^5-9*x^4-6*x
^3-10*x^2-x-1)*ln(-exp(3)+x+1)+(9*x^5+2*x^3+x)*exp(3)-9*x^6+3*x^5-2*x^4-6*x^3-x^2-x)*ln(x)+((12*x^3-4*x)*exp(3
)-12*x^4-12*x^3+4*x^2+4*x)*ln(-exp(3)+x+1)^2+((24*x^4-8*x^2)*exp(3)-24*x^5-24*x^4+8*x^3+8*x^2)*ln(-exp(3)+x+1)
+(12*x^5-4*x^3)*exp(3)-12*x^6-12*x^5+4*x^4+4*x^3)/((2*x^3*exp(3)-2*x^4-2*x^3)*ln(-exp(3)+x+1)^3+(6*x^4*exp(3)-
6*x^5-6*x^4)*ln(-exp(3)+x+1)^2+(6*x^5*exp(3)-6*x^6-6*x^5)*ln(-exp(3)+x+1)+2*x^6*exp(3)-2*x^7-2*x^6),x,method=_
RETURNVERBOSE)

[Out]

1/4*(9*x^4*ln(x)+24*x^4+24*x^3*ln(-exp(3)+x+1)-6*x^2*ln(x)-8*x^2-8*x*ln(-exp(3)+x+1)+ln(x))/x^2*ln(x)/(ln(-exp
(3)+x+1)+x)^2

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (30) = 60\).

Time = 0.32 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.46 \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\frac {{\left (9 \, x^{4} - 6 \, x^{2} + 1\right )} \log \left (x\right )^{2} + 8 \, {\left (3 \, x^{4} - x^{2} + {\left (3 \, x^{3} - x\right )} \log \left (x - e^{3} + 1\right )\right )} \log \left (x\right )}{4 \, {\left (x^{4} + 2 \, x^{3} \log \left (x - e^{3} + 1\right ) + x^{2} \log \left (x - e^{3} + 1\right )^{2}\right )}} \]

[In]

integrate(((((9*x^4-1)*exp(3)-9*x^5-9*x^4+x+1)*log(-exp(3)+x+1)+(6*x^3-2*x)*exp(3)+9*x^5-6*x^4-12*x^3+2*x^2+3*
x)*log(x)^2+(((12*x^3+4*x)*exp(3)-12*x^4-12*x^3-4*x^2-4*x)*log(-exp(3)+x+1)^2+((21*x^4+6*x^2+1)*exp(3)-21*x^5-
9*x^4-6*x^3-10*x^2-x-1)*log(-exp(3)+x+1)+(9*x^5+2*x^3+x)*exp(3)-9*x^6+3*x^5-2*x^4-6*x^3-x^2-x)*log(x)+((12*x^3
-4*x)*exp(3)-12*x^4-12*x^3+4*x^2+4*x)*log(-exp(3)+x+1)^2+((24*x^4-8*x^2)*exp(3)-24*x^5-24*x^4+8*x^3+8*x^2)*log
(-exp(3)+x+1)+(12*x^5-4*x^3)*exp(3)-12*x^6-12*x^5+4*x^4+4*x^3)/((2*x^3*exp(3)-2*x^4-2*x^3)*log(-exp(3)+x+1)^3+
(6*x^4*exp(3)-6*x^5-6*x^4)*log(-exp(3)+x+1)^2+(6*x^5*exp(3)-6*x^6-6*x^5)*log(-exp(3)+x+1)+2*x^6*exp(3)-2*x^7-2
*x^6),x, algorithm="fricas")

[Out]

1/4*((9*x^4 - 6*x^2 + 1)*log(x)^2 + 8*(3*x^4 - x^2 + (3*x^3 - x)*log(x - e^3 + 1))*log(x))/(x^4 + 2*x^3*log(x
- e^3 + 1) + x^2*log(x - e^3 + 1)^2)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (26) = 52\).

Time = 0.22 (sec) , antiderivative size = 99, normalized size of antiderivative = 2.83 \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\frac {9 x^{4} \log {\left (x \right )}^{2} + 24 x^{4} \log {\left (x \right )} - 6 x^{2} \log {\left (x \right )}^{2} - 8 x^{2} \log {\left (x \right )} + \left (24 x^{3} \log {\left (x \right )} - 8 x \log {\left (x \right )}\right ) \log {\left (x - e^{3} + 1 \right )} + \log {\left (x \right )}^{2}}{4 x^{4} + 8 x^{3} \log {\left (x - e^{3} + 1 \right )} + 4 x^{2} \log {\left (x - e^{3} + 1 \right )}^{2}} \]

[In]

integrate(((((9*x**4-1)*exp(3)-9*x**5-9*x**4+x+1)*ln(-exp(3)+x+1)+(6*x**3-2*x)*exp(3)+9*x**5-6*x**4-12*x**3+2*
x**2+3*x)*ln(x)**2+(((12*x**3+4*x)*exp(3)-12*x**4-12*x**3-4*x**2-4*x)*ln(-exp(3)+x+1)**2+((21*x**4+6*x**2+1)*e
xp(3)-21*x**5-9*x**4-6*x**3-10*x**2-x-1)*ln(-exp(3)+x+1)+(9*x**5+2*x**3+x)*exp(3)-9*x**6+3*x**5-2*x**4-6*x**3-
x**2-x)*ln(x)+((12*x**3-4*x)*exp(3)-12*x**4-12*x**3+4*x**2+4*x)*ln(-exp(3)+x+1)**2+((24*x**4-8*x**2)*exp(3)-24
*x**5-24*x**4+8*x**3+8*x**2)*ln(-exp(3)+x+1)+(12*x**5-4*x**3)*exp(3)-12*x**6-12*x**5+4*x**4+4*x**3)/((2*x**3*e
xp(3)-2*x**4-2*x**3)*ln(-exp(3)+x+1)**3+(6*x**4*exp(3)-6*x**5-6*x**4)*ln(-exp(3)+x+1)**2+(6*x**5*exp(3)-6*x**6
-6*x**5)*ln(-exp(3)+x+1)+2*x**6*exp(3)-2*x**7-2*x**6),x)

[Out]

(9*x**4*log(x)**2 + 24*x**4*log(x) - 6*x**2*log(x)**2 - 8*x**2*log(x) + (24*x**3*log(x) - 8*x*log(x))*log(x -
exp(3) + 1) + log(x)**2)/(4*x**4 + 8*x**3*log(x - exp(3) + 1) + 4*x**2*log(x - exp(3) + 1)**2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (30) = 60\).

Time = 0.28 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.54 \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\frac {8 \, {\left (3 \, x^{3} - x\right )} \log \left (x - e^{3} + 1\right ) \log \left (x\right ) + {\left (9 \, x^{4} - 6 \, x^{2} + 1\right )} \log \left (x\right )^{2} + 8 \, {\left (3 \, x^{4} - x^{2}\right )} \log \left (x\right )}{4 \, {\left (x^{4} + 2 \, x^{3} \log \left (x - e^{3} + 1\right ) + x^{2} \log \left (x - e^{3} + 1\right )^{2}\right )}} \]

[In]

integrate(((((9*x^4-1)*exp(3)-9*x^5-9*x^4+x+1)*log(-exp(3)+x+1)+(6*x^3-2*x)*exp(3)+9*x^5-6*x^4-12*x^3+2*x^2+3*
x)*log(x)^2+(((12*x^3+4*x)*exp(3)-12*x^4-12*x^3-4*x^2-4*x)*log(-exp(3)+x+1)^2+((21*x^4+6*x^2+1)*exp(3)-21*x^5-
9*x^4-6*x^3-10*x^2-x-1)*log(-exp(3)+x+1)+(9*x^5+2*x^3+x)*exp(3)-9*x^6+3*x^5-2*x^4-6*x^3-x^2-x)*log(x)+((12*x^3
-4*x)*exp(3)-12*x^4-12*x^3+4*x^2+4*x)*log(-exp(3)+x+1)^2+((24*x^4-8*x^2)*exp(3)-24*x^5-24*x^4+8*x^3+8*x^2)*log
(-exp(3)+x+1)+(12*x^5-4*x^3)*exp(3)-12*x^6-12*x^5+4*x^4+4*x^3)/((2*x^3*exp(3)-2*x^4-2*x^3)*log(-exp(3)+x+1)^3+
(6*x^4*exp(3)-6*x^5-6*x^4)*log(-exp(3)+x+1)^2+(6*x^5*exp(3)-6*x^6-6*x^5)*log(-exp(3)+x+1)+2*x^6*exp(3)-2*x^7-2
*x^6),x, algorithm="maxima")

[Out]

1/4*(8*(3*x^3 - x)*log(x - e^3 + 1)*log(x) + (9*x^4 - 6*x^2 + 1)*log(x)^2 + 8*(3*x^4 - x^2)*log(x))/(x^4 + 2*x
^3*log(x - e^3 + 1) + x^2*log(x - e^3 + 1)^2)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (30) = 60\).

Time = 0.43 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.86 \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\frac {9 \, x^{4} \log \left (x\right )^{2} + 24 \, x^{4} \log \left (x\right ) + 24 \, x^{3} \log \left (x - e^{3} + 1\right ) \log \left (x\right ) - 6 \, x^{2} \log \left (x\right )^{2} - 8 \, x^{2} \log \left (x\right ) - 8 \, x \log \left (x - e^{3} + 1\right ) \log \left (x\right ) + \log \left (x\right )^{2}}{4 \, {\left (x^{4} + 2 \, x^{3} \log \left (x - e^{3} + 1\right ) + x^{2} \log \left (x - e^{3} + 1\right )^{2}\right )}} \]

[In]

integrate(((((9*x^4-1)*exp(3)-9*x^5-9*x^4+x+1)*log(-exp(3)+x+1)+(6*x^3-2*x)*exp(3)+9*x^5-6*x^4-12*x^3+2*x^2+3*
x)*log(x)^2+(((12*x^3+4*x)*exp(3)-12*x^4-12*x^3-4*x^2-4*x)*log(-exp(3)+x+1)^2+((21*x^4+6*x^2+1)*exp(3)-21*x^5-
9*x^4-6*x^3-10*x^2-x-1)*log(-exp(3)+x+1)+(9*x^5+2*x^3+x)*exp(3)-9*x^6+3*x^5-2*x^4-6*x^3-x^2-x)*log(x)+((12*x^3
-4*x)*exp(3)-12*x^4-12*x^3+4*x^2+4*x)*log(-exp(3)+x+1)^2+((24*x^4-8*x^2)*exp(3)-24*x^5-24*x^4+8*x^3+8*x^2)*log
(-exp(3)+x+1)+(12*x^5-4*x^3)*exp(3)-12*x^6-12*x^5+4*x^4+4*x^3)/((2*x^3*exp(3)-2*x^4-2*x^3)*log(-exp(3)+x+1)^3+
(6*x^4*exp(3)-6*x^5-6*x^4)*log(-exp(3)+x+1)^2+(6*x^5*exp(3)-6*x^6-6*x^5)*log(-exp(3)+x+1)+2*x^6*exp(3)-2*x^7-2
*x^6),x, algorithm="giac")

[Out]

1/4*(9*x^4*log(x)^2 + 24*x^4*log(x) + 24*x^3*log(x - e^3 + 1)*log(x) - 6*x^2*log(x)^2 - 8*x^2*log(x) - 8*x*log
(x - e^3 + 1)*log(x) + log(x)^2)/(x^4 + 2*x^3*log(x - e^3 + 1) + x^2*log(x - e^3 + 1)^2)

Mupad [F(-1)]

Timed out. \[ \int \frac {4 x^3+4 x^4-12 x^5-12 x^6+e^3 \left (-4 x^3+12 x^5\right )+\left (8 x^2+8 x^3-24 x^4-24 x^5+e^3 \left (-8 x^2+24 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (4 x+4 x^2-12 x^3-12 x^4+e^3 \left (-4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )+\log ^2(x) \left (3 x+2 x^2-12 x^3-6 x^4+9 x^5+e^3 \left (-2 x+6 x^3\right )+\left (1+x-9 x^4-9 x^5+e^3 \left (-1+9 x^4\right )\right ) \log \left (1-e^3+x\right )\right )+\log (x) \left (-x-x^2-6 x^3-2 x^4+3 x^5-9 x^6+e^3 \left (x+2 x^3+9 x^5\right )+\left (-1-x-10 x^2-6 x^3-9 x^4-21 x^5+e^3 \left (1+6 x^2+21 x^4\right )\right ) \log \left (1-e^3+x\right )+\left (-4 x-4 x^2-12 x^3-12 x^4+e^3 \left (4 x+12 x^3\right )\right ) \log ^2\left (1-e^3+x\right )\right )}{-2 x^6+2 e^3 x^6-2 x^7+\left (-6 x^5+6 e^3 x^5-6 x^6\right ) \log \left (1-e^3+x\right )+\left (-6 x^4+6 e^3 x^4-6 x^5\right ) \log ^2\left (1-e^3+x\right )+\left (-2 x^3+2 e^3 x^3-2 x^4\right ) \log ^3\left (1-e^3+x\right )} \, dx=\int \frac {\ln \left (x-{\mathrm {e}}^3+1\right )\,\left ({\mathrm {e}}^3\,\left (8\,x^2-24\,x^4\right )-8\,x^2-8\,x^3+24\,x^4+24\,x^5\right )+\ln \left (x\right )\,\left (x-{\mathrm {e}}^3\,\left (9\,x^5+2\,x^3+x\right )+\ln \left (x-{\mathrm {e}}^3+1\right )\,\left (x-{\mathrm {e}}^3\,\left (21\,x^4+6\,x^2+1\right )+10\,x^2+6\,x^3+9\,x^4+21\,x^5+1\right )+{\ln \left (x-{\mathrm {e}}^3+1\right )}^2\,\left (4\,x-{\mathrm {e}}^3\,\left (12\,x^3+4\,x\right )+4\,x^2+12\,x^3+12\,x^4\right )+x^2+6\,x^3+2\,x^4-3\,x^5+9\,x^6\right )+{\mathrm {e}}^3\,\left (4\,x^3-12\,x^5\right )+{\ln \left (x-{\mathrm {e}}^3+1\right )}^2\,\left ({\mathrm {e}}^3\,\left (4\,x-12\,x^3\right )-4\,x-4\,x^2+12\,x^3+12\,x^4\right )-4\,x^3-4\,x^4+12\,x^5+12\,x^6-{\ln \left (x\right )}^2\,\left (3\,x+\ln \left (x-{\mathrm {e}}^3+1\right )\,\left (x+{\mathrm {e}}^3\,\left (9\,x^4-1\right )-9\,x^4-9\,x^5+1\right )-{\mathrm {e}}^3\,\left (2\,x-6\,x^3\right )+2\,x^2-12\,x^3-6\,x^4+9\,x^5\right )}{{\ln \left (x-{\mathrm {e}}^3+1\right )}^3\,\left (2\,x^3-2\,x^3\,{\mathrm {e}}^3+2\,x^4\right )+{\ln \left (x-{\mathrm {e}}^3+1\right )}^2\,\left (6\,x^4-6\,x^4\,{\mathrm {e}}^3+6\,x^5\right )-2\,x^6\,{\mathrm {e}}^3+\ln \left (x-{\mathrm {e}}^3+1\right )\,\left (6\,x^5-6\,x^5\,{\mathrm {e}}^3+6\,x^6\right )+2\,x^6+2\,x^7} \,d x \]

[In]

int((log(x - exp(3) + 1)*(exp(3)*(8*x^2 - 24*x^4) - 8*x^2 - 8*x^3 + 24*x^4 + 24*x^5) + log(x)*(x - exp(3)*(x +
2*x^3 + 9*x^5) + log(x - exp(3) + 1)*(x - exp(3)*(6*x^2 + 21*x^4 + 1) + 10*x^2 + 6*x^3 + 9*x^4 + 21*x^5 + 1)
+ log(x - exp(3) + 1)^2*(4*x - exp(3)*(4*x + 12*x^3) + 4*x^2 + 12*x^3 + 12*x^4) + x^2 + 6*x^3 + 2*x^4 - 3*x^5
+ 9*x^6) + exp(3)*(4*x^3 - 12*x^5) + log(x - exp(3) + 1)^2*(exp(3)*(4*x - 12*x^3) - 4*x - 4*x^2 + 12*x^3 + 12*
x^4) - 4*x^3 - 4*x^4 + 12*x^5 + 12*x^6 - log(x)^2*(3*x + log(x - exp(3) + 1)*(x + exp(3)*(9*x^4 - 1) - 9*x^4 -
9*x^5 + 1) - exp(3)*(2*x - 6*x^3) + 2*x^2 - 12*x^3 - 6*x^4 + 9*x^5))/(log(x - exp(3) + 1)^3*(2*x^3 - 2*x^3*ex
p(3) + 2*x^4) + log(x - exp(3) + 1)^2*(6*x^4 - 6*x^4*exp(3) + 6*x^5) - 2*x^6*exp(3) + log(x - exp(3) + 1)*(6*x
^5 - 6*x^5*exp(3) + 6*x^6) + 2*x^6 + 2*x^7),x)

[Out]

int((log(x - exp(3) + 1)*(exp(3)*(8*x^2 - 24*x^4) - 8*x^2 - 8*x^3 + 24*x^4 + 24*x^5) + log(x)*(x - exp(3)*(x +
2*x^3 + 9*x^5) + log(x - exp(3) + 1)*(x - exp(3)*(6*x^2 + 21*x^4 + 1) + 10*x^2 + 6*x^3 + 9*x^4 + 21*x^5 + 1)
+ log(x - exp(3) + 1)^2*(4*x - exp(3)*(4*x + 12*x^3) + 4*x^2 + 12*x^3 + 12*x^4) + x^2 + 6*x^3 + 2*x^4 - 3*x^5
+ 9*x^6) + exp(3)*(4*x^3 - 12*x^5) + log(x - exp(3) + 1)^2*(exp(3)*(4*x - 12*x^3) - 4*x - 4*x^2 + 12*x^3 + 12*
x^4) - 4*x^3 - 4*x^4 + 12*x^5 + 12*x^6 - log(x)^2*(3*x + log(x - exp(3) + 1)*(x + exp(3)*(9*x^4 - 1) - 9*x^4 -
9*x^5 + 1) - exp(3)*(2*x - 6*x^3) + 2*x^2 - 12*x^3 - 6*x^4 + 9*x^5))/(log(x - exp(3) + 1)^3*(2*x^3 - 2*x^3*ex
p(3) + 2*x^4) + log(x - exp(3) + 1)^2*(6*x^4 - 6*x^4*exp(3) + 6*x^5) - 2*x^6*exp(3) + log(x - exp(3) + 1)*(6*x
^5 - 6*x^5*exp(3) + 6*x^6) + 2*x^6 + 2*x^7), x)