\(\int \frac {-4 x-2 e^3 x-6 x^2+(10+4 e^3) \log (3)+(-6 x-2 e^3 x+6 x^2+(6+2 e^3-6 x) \log (3)) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+(-6 x-2 e^3 x+6 x^2+(6+2 e^3-6 x) \log (3)+(-x+\log (3)) \log (2 x)) \log (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+(12+4 e^3-12 x) \log (2 x)+\log ^2(2 x)}{4 x^2})}{(-6 x-2 e^3 x+6 x^2+(6+2 e^3-6 x) \log (3)) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+((-12 x-4 e^3 x+12 x^2+(12+4 e^3-12 x) \log (3)) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))) \log (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+(12+4 e^3-12 x) \log (2 x)+\log ^2(2 x)}{4 x^2})+(-6 x-2 e^3 x+6 x^2+(6+2 e^3-6 x) \log (3)+(-x+\log (3)) \log (2 x)) \log ^2(\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+(12+4 e^3-12 x) \log (2 x)+\log ^2(2 x)}{4 x^2})} \, dx\) [6633]

Optimal result

Integrand size = 449, antiderivative size = 34 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log (x-\log (3))+\log \left (\left (-3+\frac {3+e^3+\frac {1}{2} \log (2 x)}{x}\right )^2\right )} \]

[Out]

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

Rubi [F]

\[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx \]

[In]

Int[(-4*x - 2*E^3*x - 6*x^2 + (10 + 4*E^3)*Log[3] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x
- Log[3]] + Log[2*x]*(-x + 2*Log[3] + (-x + Log[3])*Log[x - Log[3]]) + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 -
6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*
Log[2*x] + Log[2*x]^2)/(4*x^2)])/((-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]]^2 + (-x
+ Log[3])*Log[2*x]*Log[x - Log[3]]^2 + ((-12*x - 4*E^3*x + 12*x^2 + (12 + 4*E^3 - 12*x)*Log[3])*Log[x - Log[3]
] + (-2*x + 2*Log[3])*Log[2*x]*Log[x - Log[3]])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^
3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3] + (-x + Log[3])
*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x
^2)]^2),x]

[Out]

(4 + 2*E^3 + Log[2])*Defer[Int][1/((6*(1 + E^3/3) - 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x +
Log[2*x])^2/(4*x^2)])^2), x] + (Log[3]*Log[42391158275216203514294433201]*Defer[Int][1/((6*(1 + E^3/3) - 6*x +
Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x + Log[2*x])^2/(4*x^2)])^2), x])/Log[59049] + (Log[423911582
75216203514294433201]*Defer[Int][x/((6*(1 + E^3/3) - 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x +
Log[2*x])^2/(4*x^2)])^2), x])/Log[59049] + (4 + 2*E^3 + Log[2])*Log[3]*Defer[Int][1/((x - Log[3])*(6*(1 + E^3
/3) - 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x + Log[2*x])^2/(4*x^2)])^2), x] - (5 + 2*E^3 + Lo
g[2])*Log[9]*Defer[Int][1/((x - Log[3])*(6*(1 + E^3/3) - 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6
*x + Log[2*x])^2/(4*x^2)])^2), x] + (Log[3]^2*Log[42391158275216203514294433201]*Defer[Int][1/((x - Log[3])*(6
*(1 + E^3/3) - 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x + Log[2*x])^2/(4*x^2)])^2), x])/Log[590
49] + Defer[Int][Log[x]/((6*(1 + E^3/3) - 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x + Log[2*x])^
2/(4*x^2)])^2), x] + Log[3]*Defer[Int][Log[x]/((x - Log[3])*(6*(1 + E^3/3) - 6*x + Log[2*x])*(Log[x - Log[3]]
+ Log[(6 + 2*E^3 - 6*x + Log[2*x])^2/(4*x^2)])^2), x] + Log[9]*Defer[Int][Log[x]/((-x + Log[3])*(6*(1 + E^3/3)
- 6*x + Log[2*x])*(Log[x - Log[3]] + Log[(6 + 2*E^3 - 6*x + Log[2*x])^2/(4*x^2)])^2), x] + Defer[Int][(Log[x
- Log[3]] + Log[(6 + 2*E^3 - 6*x + Log[2*x])^2/(4*x^2)])^(-1), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (-4-2 e^3\right ) x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx \\ & = \int \frac {4 \left (1+\frac {e^3}{2}\right ) x+6 x^2-10 \log (3) \left (1+\frac {e^3 \log (81)}{\log (59049)}\right )-\left (6 x^2+e^3 \log (9)-2 x \left (3+e^3+\log (27)\right )+\log (729)\right ) \log (x-\log (3))-6 x^2 \log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )-6 \left (1+\frac {e^3}{3}\right ) \log (3) \log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )+6 x \left (1+\frac {e^3}{3}+\log (3)\right ) \log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )-\log (2 x) \left (-x+\log (9)+(-x+\log (3)) \log (x-\log (3))+(-x+\log (3)) \log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx \\ & = \int \left (\frac {-\log (2) \log (9) \log (59049) \left (1+\frac {e^3 \log (81)+\log (59049)}{\log (2) \log (9)}\right )+x \log (2) \log (59049) \left (1+\frac {e^3 \log (3486784401)+\log (12157665459056928801)}{\log (2) \log (59049)}\right )+x^2 \log (42391158275216203514294433201)+x \log (59049) \log (x)-\log (9) \log (59049) \log (x)}{(x-\log (3)) \log (59049) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )}\right ) \, dx \\ & = \frac {\int \frac {-\log (2) \log (9) \log (59049) \left (1+\frac {e^3 \log (81)+\log (59049)}{\log (2) \log (9)}\right )+x \log (2) \log (59049) \left (1+\frac {e^3 \log (3486784401)+\log (12157665459056928801)}{\log (2) \log (59049)}\right )+x^2 \log (42391158275216203514294433201)+x \log (59049) \log (x)-\log (9) \log (59049) \log (x)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx}{\log (59049)}+\int \frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )} \, dx \\ & = \frac {\int \frac {-\log (59049) \left (\log (2) \log (9)+e^3 \log (81)+\log (59049)\right )+x \left (\log (2) \log (59049)+e^3 \log (3486784401)+\log (12157665459056928801)\right )+x^2 \log (42391158275216203514294433201)-(-x+\log (9)) \log (59049) \log (x)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx}{\log (59049)}+\int \frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )} \, dx \\ & = \frac {\int \left (\frac {\left (-\log (2) \log (9)-e^3 \log (81)-\log (59049)\right ) \log (59049)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {x \left (\log (2) \log (59049)+e^3 \log (3486784401)+\log (12157665459056928801)\right )}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {x^2 \log (42391158275216203514294433201)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {x \log (59049) \log (x)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {\log (9) \log (59049) \log (x)}{(-x+\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}\right ) \, dx}{\log (59049)}+\int \frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )} \, dx \\ & = \left (4+2 e^3+\log (2)\right ) \int \frac {x}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\log (9) \int \frac {\log (x)}{(-x+\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx-\left (\left (5+2 e^3+\log (2)\right ) \log (9)\right ) \int \frac {1}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\frac {\log (42391158275216203514294433201) \int \frac {x^2}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx}{\log (59049)}+\int \frac {x \log (x)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\int \frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )} \, dx \\ & = \left (4+2 e^3+\log (2)\right ) \int \left (\frac {1}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {\log (3)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}\right ) \, dx+\log (9) \int \frac {\log (x)}{(-x+\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx-\left (\left (5+2 e^3+\log (2)\right ) \log (9)\right ) \int \frac {1}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\frac {\log (42391158275216203514294433201) \int \left (\frac {x}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {\log (3)}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {\log ^2(3)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}\right ) \, dx}{\log (59049)}+\int \frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )} \, dx+\int \left (\frac {\log (x)}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}+\frac {\log (3) \log (x)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2}\right ) \, dx \\ & = \left (4+2 e^3+\log (2)\right ) \int \frac {1}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\log (3) \int \frac {\log (x)}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\left (\left (4+2 e^3+\log (2)\right ) \log (3)\right ) \int \frac {1}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\log (9) \int \frac {\log (x)}{(-x+\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx-\left (\left (5+2 e^3+\log (2)\right ) \log (9)\right ) \int \frac {1}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\frac {\log (42391158275216203514294433201) \int \frac {x}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx}{\log (59049)}+\frac {(\log (3) \log (42391158275216203514294433201)) \int \frac {1}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx}{\log (59049)}+\frac {\left (\log ^2(3) \log (42391158275216203514294433201)\right ) \int \frac {1}{(x-\log (3)) \left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx}{\log (59049)}+\int \frac {\log (x)}{\left (6 \left (1+\frac {e^3}{3}\right )-6 x+\log (2 x)\right ) \left (\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )\right )^2} \, dx+\int \frac {1}{\log (x-\log (3))+\log \left (\frac {\left (6+2 e^3-6 x+\log (2 x)\right )^2}{4 x^2}\right )} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx \]

[In]

Integrate[(-4*x - 2*E^3*x - 6*x^2 + (10 + 4*E^3)*Log[3] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*
Log[x - Log[3]] + Log[2*x]*(-x + 2*Log[3] + (-x + Log[3])*Log[x - Log[3]]) + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*
E^3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 -
12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)])/((-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]]^2
+ (-x + Log[3])*Log[2*x]*Log[x - Log[3]]^2 + ((-12*x - 4*E^3*x + 12*x^2 + (12 + 4*E^3 - 12*x)*Log[3])*Log[x -
Log[3]] + (-2*x + 2*Log[3])*Log[2*x]*Log[x - Log[3]])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12
+ 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3] + (-x + L
og[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2
)/(4*x^2)]^2),x]

[Out]

Integrate[(-4*x - 2*E^3*x - 6*x^2 + (10 + 4*E^3)*Log[3] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*
Log[x - Log[3]] + Log[2*x]*(-x + 2*Log[3] + (-x + Log[3])*Log[x - Log[3]]) + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*
E^3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 -
12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)])/((-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]]^2
+ (-x + Log[3])*Log[2*x]*Log[x - Log[3]]^2 + ((-12*x - 4*E^3*x + 12*x^2 + (12 + 4*E^3 - 12*x)*Log[3])*Log[x -
Log[3]] + (-2*x + 2*Log[3])*Log[2*x]*Log[x - Log[3]])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12
+ 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3] + (-x + L
og[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2
)/(4*x^2)]^2), x]

Maple [A] (verified)

Time = 31.29 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.85

method	result	size
parallelrisch	\(\frac {x}{\ln \left (-\ln \left (3\right )+x \right )+\ln \left (\frac {\ln \left (2 x \right )^{2}+\left (4 \,{\mathrm e}^{3}-12 x +12\right ) \ln \left (2 x \right )+4 \,{\mathrm e}^{6}+\left (-24 x +24\right ) {\mathrm e}^{3}+36 x^{2}-72 x +36}{4 x^{2}}\right )}\)	\(63\)
default	\(\frac {2 i x}{\pi {\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )\right )}^{2} \operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )\right ) {\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right )}^{2}+\pi {\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right )}^{3}+\pi \,\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right ) \operatorname {csgn}\left (\frac {i}{x^{2}}\right ) \operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )-\pi \,\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right ) {\operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )}^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{x^{2}}\right ) {\operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )}^{2}-\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-\pi \operatorname {csgn}\left (i x^{2}\right )^{3}+\pi {\operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )}^{3}-4 i \ln \left (2\right )+2 i \ln \left (-\ln \left (3\right )+x \right )+4 i \ln \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )-4 i \ln \left (x \right )}\)	\(351\)

[In]

int((((ln(3)-x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x^2-6*x)*ln(1/4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2
*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+((ln(3)-x)*ln(-ln(3)+x)+2*ln(3)-x)*ln(2*x)+((2*exp(3)+6-
6*x)*ln(3)-2*x*exp(3)+6*x^2-6*x)*ln(-ln(3)+x)+(4*exp(3)+10)*ln(3)-2*x*exp(3)-6*x^2-4*x)/(((ln(3)-x)*ln(2*x)+(2
*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x^2-6*x)*ln(1/4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(-24*x+24)*
exp(3)+36*x^2-72*x+36)/x^2)^2+((2*ln(3)-2*x)*ln(-ln(3)+x)*ln(2*x)+((4*exp(3)-12*x+12)*ln(3)-4*x*exp(3)+12*x^2-
12*x)*ln(-ln(3)+x))*ln(1/4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/
x^2)+(ln(3)-x)*ln(-ln(3)+x)^2*ln(2*x)+((2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x^2-6*x)*ln(-ln(3)+x)^2),x,method=_
RETURNVERBOSE)

[Out]

x/(ln(-ln(3)+x)+ln(1/4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)
)

Fricas [A] (verification not implemented)

none

Time = 0.37 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.76 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log \left (x - \log \left (3\right )\right ) + \log \left (\frac {36 \, x^{2} - 24 \, {\left (x - 1\right )} e^{3} - 4 \, {\left (3 \, x - e^{3} - 3\right )} \log \left (2 \, x\right ) + \log \left (2 \, x\right )^{2} - 72 \, x + 4 \, e^{6} + 36}{4 \, x^{2}}\right )} \]

[In]

integrate((((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12
*x+12)*log(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+((log(3)-x)*log(-log(3)+x)+2*log(3)-x)*log(2
*x)+((2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)+(4*exp(3)+10)*log(3)-2*x*exp(3)-6*x^2-4*x)/(
((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(
2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)^2+((2*log(3)-2*x)*log(-log(3)+x)*log(2*x)+((4*exp(3)-12
*x+12)*log(3)-4*x*exp(3)+12*x^2-12*x)*log(-log(3)+x))*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)
^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+(log(3)-x)*log(-log(3)+x)^2*log(2*x)+((2*exp(3)+6-6*x)*log(3)-2*x*ex
p(3)+6*x^2-6*x)*log(-log(3)+x)^2),x, algorithm="fricas")

[Out]

x/(log(x - log(3)) + log(1/4*(36*x^2 - 24*(x - 1)*e^3 - 4*(3*x - e^3 - 3)*log(2*x) + log(2*x)^2 - 72*x + 4*e^6
+ 36)/x^2))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (26) = 52\).

Time = 0.87 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.79 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log {\left (\frac {9 x^{2} - 18 x + \frac {\left (24 - 24 x\right ) e^{3}}{4} + \frac {\left (- 12 x + 12 + 4 e^{3}\right ) \log {\left (2 x \right )}}{4} + \frac {\log {\left (2 x \right )}^{2}}{4} + 9 + e^{6}}{x^{2}} \right )} + \log {\left (x - \log {\left (3 \right )} \right )}} \]

[In]

integrate((((ln(3)-x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x**2-6*x)*ln(1/4*(ln(2*x)**2+(4*exp(3)-12*x+
12)*ln(2*x)+4*exp(3)**2+(-24*x+24)*exp(3)+36*x**2-72*x+36)/x**2)+((ln(3)-x)*ln(-ln(3)+x)+2*ln(3)-x)*ln(2*x)+((
2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x**2-6*x)*ln(-ln(3)+x)+(4*exp(3)+10)*ln(3)-2*x*exp(3)-6*x**2-4*x)/(((ln(3)-
x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x**2-6*x)*ln(1/4*(ln(2*x)**2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3
)**2+(-24*x+24)*exp(3)+36*x**2-72*x+36)/x**2)**2+((2*ln(3)-2*x)*ln(-ln(3)+x)*ln(2*x)+((4*exp(3)-12*x+12)*ln(3)
-4*x*exp(3)+12*x**2-12*x)*ln(-ln(3)+x))*ln(1/4*(ln(2*x)**2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)**2+(-24*x+24)*e
xp(3)+36*x**2-72*x+36)/x**2)+(ln(3)-x)*ln(-ln(3)+x)**2*ln(2*x)+((2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x**2-6*x)*
ln(-ln(3)+x)**2),x)

[Out]

x/(log((9*x**2 - 18*x + (24 - 24*x)*exp(3)/4 + (-12*x + 12 + 4*exp(3))*log(2*x)/4 + log(2*x)**2/4 + 9 + exp(6)
)/x**2) + log(x - log(3)))

Maxima [A] (verification not implemented)

none

Time = 0.46 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.26 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=-\frac {x}{2 \, \log \left (2\right ) - 2 \, \log \left (6 \, x - 2 \, e^{3} - \log \left (2\right ) - \log \left (x\right ) - 6\right ) - \log \left (x - \log \left (3\right )\right ) + 2 \, \log \left (x\right )} \]

[In]

integrate((((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12
*x+12)*log(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+((log(3)-x)*log(-log(3)+x)+2*log(3)-x)*log(2
*x)+((2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)+(4*exp(3)+10)*log(3)-2*x*exp(3)-6*x^2-4*x)/(
((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(
2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)^2+((2*log(3)-2*x)*log(-log(3)+x)*log(2*x)+((4*exp(3)-12
*x+12)*log(3)-4*x*exp(3)+12*x^2-12*x)*log(-log(3)+x))*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)
^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+(log(3)-x)*log(-log(3)+x)^2*log(2*x)+((2*exp(3)+6-6*x)*log(3)-2*x*ex
p(3)+6*x^2-6*x)*log(-log(3)+x)^2),x, algorithm="maxima")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (33) = 66\).

Time = 16.09 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.35 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log \left (36 \, {\left (x - \log \left (3\right )\right )}^{2} - 24 \, {\left (x - \log \left (3\right )\right )} e^{3} + 72 \, {\left (x - \log \left (3\right )\right )} \log \left (3\right ) - 24 \, e^{3} \log \left (3\right ) + 36 \, \log \left (3\right )^{2} - 12 \, {\left (x - \log \left (3\right )\right )} \log \left (2 \, x\right ) + 4 \, e^{3} \log \left (2 \, x\right ) - 12 \, \log \left (3\right ) \log \left (2 \, x\right ) + \log \left (2 \, x\right )^{2} - 72 \, x + 4 \, e^{6} + 24 \, e^{3} + 12 \, \log \left (2 \, x\right ) + 36\right ) - 2 \, \log \left (2 \, x\right ) + \log \left (x - \log \left (3\right )\right )} \]

[In]

integrate((((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12
*x+12)*log(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+((log(3)-x)*log(-log(3)+x)+2*log(3)-x)*log(2
*x)+((2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)+(4*exp(3)+10)*log(3)-2*x*exp(3)-6*x^2-4*x)/(
((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(
2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)^2+((2*log(3)-2*x)*log(-log(3)+x)*log(2*x)+((4*exp(3)-12
*x+12)*log(3)-4*x*exp(3)+12*x^2-12*x)*log(-log(3)+x))*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)
^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+(log(3)-x)*log(-log(3)+x)^2*log(2*x)+((2*exp(3)+6-6*x)*log(3)-2*x*ex
p(3)+6*x^2-6*x)*log(-log(3)+x)^2),x, algorithm="giac")

[Out]

x/(log(36*(x - log(3))^2 - 24*(x - log(3))*e^3 + 72*(x - log(3))*log(3) - 24*e^3*log(3) + 36*log(3)^2 - 12*(x
- log(3))*log(2*x) + 4*e^3*log(2*x) - 12*log(3)*log(2*x) + log(2*x)^2 - 72*x + 4*e^6 + 24*e^3 + 12*log(2*x) +
36) - 2*log(2*x) + log(x - log(3)))

Mupad [F(-1)]

Timed out. \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\int \frac {4\,x+\ln \left (\frac {{\mathrm {e}}^6-18\,x+\frac {\ln \left (2\,x\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )}{4}+\frac {{\ln \left (2\,x\right )}^2}{4}+9\,x^2-\frac {{\mathrm {e}}^3\,\left (24\,x-24\right )}{4}+9}{x^2}\right )\,\left (6\,x+2\,x\,{\mathrm {e}}^3+\ln \left (2\,x\right )\,\left (x-\ln \left (3\right )\right )-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )+2\,x\,{\mathrm {e}}^3+\ln \left (2\,x\right )\,\left (x-2\,\ln \left (3\right )+\ln \left (x-\ln \left (3\right )\right )\,\left (x-\ln \left (3\right )\right )\right )+6\,x^2+\ln \left (x-\ln \left (3\right )\right )\,\left (6\,x+2\,x\,{\mathrm {e}}^3-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )-\ln \left (3\right )\,\left (4\,{\mathrm {e}}^3+10\right )}{{\ln \left (x-\ln \left (3\right )\right )}^2\,\left (6\,x+2\,x\,{\mathrm {e}}^3-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )+\ln \left (\frac {{\mathrm {e}}^6-18\,x+\frac {\ln \left (2\,x\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )}{4}+\frac {{\ln \left (2\,x\right )}^2}{4}+9\,x^2-\frac {{\mathrm {e}}^3\,\left (24\,x-24\right )}{4}+9}{x^2}\right )\,\left (\ln \left (x-\ln \left (3\right )\right )\,\left (12\,x+4\,x\,{\mathrm {e}}^3-\ln \left (3\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )-12\,x^2\right )+\ln \left (x-\ln \left (3\right )\right )\,\ln \left (2\,x\right )\,\left (2\,x-2\,\ln \left (3\right )\right )\right )+{\ln \left (\frac {{\mathrm {e}}^6-18\,x+\frac {\ln \left (2\,x\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )}{4}+\frac {{\ln \left (2\,x\right )}^2}{4}+9\,x^2-\frac {{\mathrm {e}}^3\,\left (24\,x-24\right )}{4}+9}{x^2}\right )}^2\,\left (6\,x+2\,x\,{\mathrm {e}}^3+\ln \left (2\,x\right )\,\left (x-\ln \left (3\right )\right )-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )+{\ln \left (x-\ln \left (3\right )\right )}^2\,\ln \left (2\,x\right )\,\left (x-\ln \left (3\right )\right )} \,d x \]

[In]

int((4*x + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log(2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 2
4))/4 + 9)/x^2)*(6*x + 2*x*exp(3) + log(2*x)*(x - log(3)) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + 2*x*exp(3)
+ log(2*x)*(x - 2*log(3) + log(x - log(3))*(x - log(3))) + 6*x^2 + log(x - log(3))*(6*x + 2*x*exp(3) - log(3)*
(2*exp(3) - 6*x + 6) - 6*x^2) - log(3)*(4*exp(3) + 10))/(log(x - log(3))^2*(6*x + 2*x*exp(3) - log(3)*(2*exp(3
) - 6*x + 6) - 6*x^2) + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log(2*x)^2/4 + 9*x^2 - (exp
(3)*(24*x - 24))/4 + 9)/x^2)*(log(x - log(3))*(12*x + 4*x*exp(3) - log(3)*(4*exp(3) - 12*x + 12) - 12*x^2) + l
og(x - log(3))*log(2*x)*(2*x - 2*log(3))) + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log(2*x
)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/x^2)^2*(6*x + 2*x*exp(3) + log(2*x)*(x - log(3)) - log(3)*(2*exp(3
) - 6*x + 6) - 6*x^2) + log(x - log(3))^2*log(2*x)*(x - log(3))),x)

[Out]

int((4*x + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log(2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 2
4))/4 + 9)/x^2)*(6*x + 2*x*exp(3) + log(2*x)*(x - log(3)) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + 2*x*exp(3)
+ log(2*x)*(x - 2*log(3) + log(x - log(3))*(x - log(3))) + 6*x^2 + log(x - log(3))*(6*x + 2*x*exp(3) - log(3)*
(2*exp(3) - 6*x + 6) - 6*x^2) - log(3)*(4*exp(3) + 10))/(log(x - log(3))^2*(6*x + 2*x*exp(3) - log(3)*(2*exp(3
) - 6*x + 6) - 6*x^2) + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log(2*x)^2/4 + 9*x^2 - (exp
(3)*(24*x - 24))/4 + 9)/x^2)*(log(x - log(3))*(12*x + 4*x*exp(3) - log(3)*(4*exp(3) - 12*x + 12) - 12*x^2) + l
og(x - log(3))*log(2*x)*(2*x - 2*log(3))) + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log(2*x
)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/x^2)^2*(6*x + 2*x*exp(3) + log(2*x)*(x - log(3)) - log(3)*(2*exp(3
) - 6*x + 6) - 6*x^2) + log(x - log(3))^2*log(2*x)*(x - log(3))), x)