\(\int \frac {(960-960 x+300 x^2-30 x^3+e^x (-960+960 x-300 x^2+30 x^3)) \log (-2+x)+(120-60 x+e^x (-120+60 x)) \log ^2(-2+x)+(-480 x+240 x^2-30 x^3+e^x (480 x-240 x^2+30 x^3)+(480 x-360 x^2+60 x^3+e^x (-1440 x+1320 x^2-360 x^3+30 x^4)) \log (-2+x)+e^x (-120 x+60 x^2) \log ^2(-2+x)) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+(-128 x+128 x^2-40 x^3+4 x^4) \log (-2+x)+(-8 x+4 x^2) \log ^2(-2+x)} \, dx\) [3184]

Optimal result

Integrand size = 227, antiderivative size = 25 \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\frac {30 \left (-1+e^x\right ) \log (x)}{2+\frac {(-4+x)^2}{\log (-2+x)}} \]

[Out]

30*ln(x)/(2+(x-4)^2/ln(-2+x))*(-1+exp(x))

Rubi [F]

\[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx \]

[In]

Int[((960 - 960*x + 300*x^2 - 30*x^3 + E^x*(-960 + 960*x - 300*x^2 + 30*x^3))*Log[-2 + x] + (120 - 60*x + E^x*
(-120 + 60*x))*Log[-2 + x]^2 + (-480*x + 240*x^2 - 30*x^3 + E^x*(480*x - 240*x^2 + 30*x^3) + (480*x - 360*x^2
+ 60*x^3 + E^x*(-1440*x + 1320*x^2 - 360*x^3 + 30*x^4))*Log[-2 + x] + E^x*(-120*x + 60*x^2)*Log[-2 + x]^2)*Log
[x])/(-512*x + 768*x^2 - 448*x^3 + 128*x^4 - 18*x^5 + x^6 + (-128*x + 128*x^2 - 40*x^3 + 4*x^4)*Log[-2 + x] +
(-8*x + 4*x^2)*Log[-2 + x]^2),x]

[Out]

15*ExpIntegralEi[x] - 15*Log[x] - 120*Defer[Int][(16 - 8*x + x^2 + 2*Log[-2 + x])^(-1), x] + 120*Defer[Int][E^
x/(16 - 8*x + x^2 + 2*Log[-2 + x]), x] + 240*Defer[Int][1/(x*(16 - 8*x + x^2 + 2*Log[-2 + x])), x] - 240*Defer
[Int][E^x/(x*(16 - 8*x + x^2 + 2*Log[-2 + x])), x] + 15*Defer[Int][x/(16 - 8*x + x^2 + 2*Log[-2 + x]), x] - 15
*Defer[Int][(E^x*x)/(16 - 8*x + x^2 + 2*Log[-2 + x]), x] + 180*Defer[Int][Log[x]/(16 - 8*x + x^2 + 2*Log[-2 +
x])^2, x] - 180*Defer[Int][(E^x*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x] - 120*Defer[Int][Log[x]/((-2 +
x)*(16 - 8*x + x^2 + 2*Log[-2 + x])^2), x] + 120*Defer[Int][(E^x*Log[x])/((-2 + x)*(16 - 8*x + x^2 + 2*Log[-2
+ x])^2), x] - 30*Defer[Int][(x*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x] + 30*Defer[Int][(E^x*x*Log[x])/
(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x] - 240*Defer[Int][(Log[-2 + x]*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^
2, x] + 720*Defer[Int][(E^x*Log[-2 + x]*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x] + 60*Defer[Int][(x*Log[
-2 + x]*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x] - 300*Defer[Int][(E^x*x*Log[-2 + x]*Log[x])/(16 - 8*x +
x^2 + 2*Log[-2 + x])^2, x] + 30*Defer[Int][(E^x*x^2*Log[-2 + x]*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x
] + 60*Defer[Int][(E^x*Log[-2 + x]^2*Log[x])/(16 - 8*x + x^2 + 2*Log[-2 + x])^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {30 \left (-\left (\left (-1+e^x\right ) (-4+x)^2 x \log (x)\right )-2 (-2+x) \log ^2(-2+x) \left (-1+e^x+e^x x \log (x)\right )-\left (8-6 x+x^2\right ) \log (-2+x) \left (\left (-1+e^x\right ) (-4+x)+\left (2+e^x (-6+x)\right ) x \log (x)\right )\right )}{(2-x) x \left ((-4+x)^2+2 \log (-2+x)\right )^2} \, dx \\ & = 30 \int \frac {-\left (\left (-1+e^x\right ) (-4+x)^2 x \log (x)\right )-2 (-2+x) \log ^2(-2+x) \left (-1+e^x+e^x x \log (x)\right )-\left (8-6 x+x^2\right ) \log (-2+x) \left (\left (-1+e^x\right ) (-4+x)+\left (2+e^x (-6+x)\right ) x \log (x)\right )}{(2-x) x \left ((-4+x)^2+2 \log (-2+x)\right )^2} \, dx \\ & = 30 \int \left (-\frac {(-4+x) \log (-2+x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {4 (-4+x) \log (-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {2 \log ^2(-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {(-4+x)^2 \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {2 (-4+x) \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {e^x \left (-32 \log (-2+x)+32 x \log (-2+x)-10 x^2 \log (-2+x)+x^3 \log (-2+x)-4 \log ^2(-2+x)+2 x \log ^2(-2+x)+16 x \log (x)-8 x^2 \log (x)+x^3 \log (x)-48 x \log (-2+x) \log (x)+44 x^2 \log (-2+x) \log (x)-12 x^3 \log (-2+x) \log (x)+x^4 \log (-2+x) \log (x)-4 x \log ^2(-2+x) \log (x)+2 x^2 \log ^2(-2+x) \log (x)\right )}{(-2+x) x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx \\ & = -\left (30 \int \frac {(-4+x) \log (-2+x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx\right )-30 \int \frac {(-4+x)^2 \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \frac {e^x \left (-32 \log (-2+x)+32 x \log (-2+x)-10 x^2 \log (-2+x)+x^3 \log (-2+x)-4 \log ^2(-2+x)+2 x \log ^2(-2+x)+16 x \log (x)-8 x^2 \log (x)+x^3 \log (x)-48 x \log (-2+x) \log (x)+44 x^2 \log (-2+x) \log (x)-12 x^3 \log (-2+x) \log (x)+x^4 \log (-2+x) \log (x)-4 x \log ^2(-2+x) \log (x)+2 x^2 \log ^2(-2+x) \log (x)\right )}{(-2+x) x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-60 \int \frac {\log ^2(-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+60 \int \frac {(-4+x) \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+120 \int \frac {(-4+x) \log (-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx \\ & = -\left (30 \int \left (-\frac {(-4+x)^3}{2 \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {-4+x}{2 \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx\right )-30 \int \left (-\frac {6 \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {4 \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {x \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx+30 \int \frac {e^x \left (-(-4+x)^2 x \log (x)-2 (-2+x) \log ^2(-2+x) (1+x \log (x))-\left (8-6 x+x^2\right ) \log (-2+x) (-4+x+(-6+x) x \log (x))\right )}{(2-x) x \left ((-4+x)^2+2 \log (-2+x)\right )^2} \, dx-60 \int \left (\frac {1}{4 x}+\frac {(-4+x)^4}{4 x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {(-4+x)^2}{2 x \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx+60 \int \left (-\frac {4 \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {x \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx+120 \int \left (-\frac {(-4+x)^3}{2 x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {-4+x}{2 x \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx \\ & = -15 \log (x)+15 \int \frac {(-4+x)^3}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-15 \int \frac {(-4+x)^4}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-15 \int \frac {-4+x}{16-8 x+x^2+2 \log (-2+x)} \, dx+30 \int \frac {(-4+x)^2}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx-30 \int \frac {x \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \left (\frac {e^x (-4+x) \log (-2+x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {4 e^x (-4+x) \log (-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {2 e^x \log ^2(-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {e^x \left (16-8 x+x^2-48 \log (-2+x)+44 x \log (-2+x)-12 x^2 \log (-2+x)+x^3 \log (-2+x)-4 \log ^2(-2+x)+2 x \log ^2(-2+x)\right ) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx-60 \int \frac {(-4+x)^3}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+60 \int \frac {-4+x}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx+60 \int \frac {x \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-120 \int \frac {\log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+180 \int \frac {\log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-240 \int \frac {\log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx \\ & = -15 \log (x)-15 \int \left (-\frac {256}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {256}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {96 x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {16 x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {x^3}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx+15 \int \left (-\frac {64}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {48 x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {12 x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {x^3}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx-15 \int \left (-\frac {4}{16-8 x+x^2+2 \log (-2+x)}+\frac {x}{16-8 x+x^2+2 \log (-2+x)}\right ) \, dx+30 \int \frac {e^x (-4+x) \log (-2+x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \left (-\frac {8}{16-8 x+x^2+2 \log (-2+x)}+\frac {16}{x \left (16-8 x+x^2+2 \log (-2+x)\right )}+\frac {x}{16-8 x+x^2+2 \log (-2+x)}\right ) \, dx-30 \int \frac {x \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \frac {e^x \left (16-8 x+x^2-48 \log (-2+x)+44 x \log (-2+x)-12 x^2 \log (-2+x)+x^3 \log (-2+x)-4 \log ^2(-2+x)+2 x \log ^2(-2+x)\right ) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+60 \int \frac {e^x \log ^2(-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-60 \int \left (\frac {48}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {64}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {12 x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx+60 \int \left (\frac {1}{16-8 x+x^2+2 \log (-2+x)}-\frac {4}{x \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx+60 \int \frac {x \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-120 \int \frac {e^x (-4+x) \log (-2+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-120 \int \frac {\log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+180 \int \frac {\log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-240 \int \frac {\log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx \\ & = -15 \log (x)-15 \int \frac {x}{16-8 x+x^2+2 \log (-2+x)} \, dx+30 \int \frac {x}{16-8 x+x^2+2 \log (-2+x)} \, dx+30 \int \left (-\frac {e^x (-4+x)^3}{2 \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {e^x (-4+x)}{2 \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx-30 \int \frac {x \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \left (\frac {16 e^x \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {8 e^x x \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {e^x x^2 \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {48 e^x \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {44 e^x x \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {12 e^x x^2 \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {e^x x^3 \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {4 e^x \log ^2(-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {2 e^x x \log ^2(-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2}\right ) \, dx-60 \int \frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+2 \left (60 \int \frac {1}{16-8 x+x^2+2 \log (-2+x)} \, dx\right )+60 \int \left (\frac {e^x}{4 x}+\frac {e^x (-4+x)^4}{4 x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}-\frac {e^x (-4+x)^2}{2 x \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx+60 \int \frac {x \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-120 \int \left (-\frac {e^x (-4+x)^3}{2 x \left (16-8 x+x^2+2 \log (-2+x)\right )^2}+\frac {e^x (-4+x)}{2 x \left (16-8 x+x^2+2 \log (-2+x)\right )}\right ) \, dx-120 \int \frac {\log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-180 \int \frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+180 \int \frac {\log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+240 \int \frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-240 \int \frac {1}{16-8 x+x^2+2 \log (-2+x)} \, dx-240 \int \frac {1}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx-240 \int \frac {\log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+480 \int \frac {1}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx+2 \left (720 \int \frac {x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx\right )-960 \int \frac {1}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-1440 \int \frac {x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-2880 \int \frac {1}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+3840 \int \frac {1}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx \\ & = -15 \log (x)+15 \int \frac {e^x}{x} \, dx-15 \int \frac {e^x (-4+x)^3}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+15 \int \frac {e^x (-4+x)^4}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+15 \int \frac {e^x (-4+x)}{16-8 x+x^2+2 \log (-2+x)} \, dx-15 \int \frac {x}{16-8 x+x^2+2 \log (-2+x)} \, dx-30 \int \frac {e^x (-4+x)^2}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx+30 \int \frac {x}{16-8 x+x^2+2 \log (-2+x)} \, dx-30 \int \frac {x \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \frac {e^x x^2 \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+30 \int \frac {e^x x^3 \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+60 \int \frac {e^x (-4+x)^3}{x \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-60 \int \frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+2 \left (60 \int \frac {1}{16-8 x+x^2+2 \log (-2+x)} \, dx\right )-60 \int \frac {e^x (-4+x)}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx+60 \int \frac {x \log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+60 \int \frac {e^x x \log ^2(-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-120 \int \frac {\log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-120 \int \frac {e^x \log ^2(-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-180 \int \frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+180 \int \frac {\log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+240 \int \frac {x^2}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-240 \int \frac {1}{16-8 x+x^2+2 \log (-2+x)} \, dx-240 \int \frac {1}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx-240 \int \frac {e^x x \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-240 \int \frac {\log (-2+x) \log (x)}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-360 \int \frac {e^x x^2 \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+480 \int \frac {1}{x \left (16-8 x+x^2+2 \log (-2+x)\right )} \, dx+480 \int \frac {e^x \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+2 \left (720 \int \frac {x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx\right )-960 \int \frac {1}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+1320 \int \frac {e^x x \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-1440 \int \frac {x}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-1440 \int \frac {e^x \log (-2+x) \log (x)}{(-2+x) \left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx-2880 \int \frac {1}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx+3840 \int \frac {1}{\left (16-8 x+x^2+2 \log (-2+x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\frac {30 \left (-1+e^x\right ) \log (-2+x) \log (x)}{(-4+x)^2+2 \log (-2+x)} \]

[In]

Integrate[((960 - 960*x + 300*x^2 - 30*x^3 + E^x*(-960 + 960*x - 300*x^2 + 30*x^3))*Log[-2 + x] + (120 - 60*x
+ E^x*(-120 + 60*x))*Log[-2 + x]^2 + (-480*x + 240*x^2 - 30*x^3 + E^x*(480*x - 240*x^2 + 30*x^3) + (480*x - 36
0*x^2 + 60*x^3 + E^x*(-1440*x + 1320*x^2 - 360*x^3 + 30*x^4))*Log[-2 + x] + E^x*(-120*x + 60*x^2)*Log[-2 + x]^
2)*Log[x])/(-512*x + 768*x^2 - 448*x^3 + 128*x^4 - 18*x^5 + x^6 + (-128*x + 128*x^2 - 40*x^3 + 4*x^4)*Log[-2 +
x] + (-8*x + 4*x^2)*Log[-2 + x]^2),x]

[Out]

(30*(-1 + E^x)*Log[-2 + x]*Log[x])/((-4 + x)^2 + 2*Log[-2 + x])

Maple [A] (verified)

Time = 23.53 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52

method	result	size
parallelrisch	\(\frac {240 \ln \left (-2+x \right ) \ln \left (x \right ) {\mathrm e}^{x}-240 \ln \left (x \right ) \ln \left (-2+x \right )}{8 x^{2}+16 \ln \left (-2+x \right )-64 x +128}\)	\(38\)
risch	\(15 \,{\mathrm e}^{x} \ln \left (x \right )-15 \ln \left (x \right )-\frac {15 \left ({\mathrm e}^{x} x^{2}-x^{2}-8 \,{\mathrm e}^{x} x +8 x +16 \,{\mathrm e}^{x}-16\right ) \ln \left (x \right )}{x^{2}+2 \ln \left (-2+x \right )-8 x +16}\)	\(57\)

[In]

int((((60*x^2-120*x)*exp(x)*ln(-2+x)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*ln(-2+x)
+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*ln(x)+((60*x-120)*exp(x)-60*x+120)*ln(-2+x)^2+((30*x^3-30
0*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*ln(-2+x))/((4*x^2-8*x)*ln(-2+x)^2+(4*x^4-40*x^3+128*x^2-128*
x)*ln(-2+x)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x,method=_RETURNVERBOSE)

[Out]

1/8*(240*ln(-2+x)*ln(x)*exp(x)-240*ln(x)*ln(-2+x))/(x^2+2*ln(-2+x)-8*x+16)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\frac {30 \, {\left (e^{x} - 1\right )} \log \left (x - 2\right ) \log \left (x\right )}{x^{2} - 8 \, x + 2 \, \log \left (x - 2\right ) + 16} \]

[In]

integrate((((60*x^2-120*x)*exp(x)*log(-2+x)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*l
og(-2+x)+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*log(x)+((60*x-120)*exp(x)-60*x+120)*log(-2+x)^2+(
(30*x^3-300*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*log(-2+x))/((4*x^2-8*x)*log(-2+x)^2+(4*x^4-40*x^3+
128*x^2-128*x)*log(-2+x)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x, algorithm="fricas")

[Out]

30*(e^x - 1)*log(x - 2)*log(x)/(x^2 - 8*x + 2*log(x - 2) + 16)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (20) = 40\).

Time = 0.28 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\frac {15 x^{2} \log {\left (x \right )} - 120 x \log {\left (x \right )} + 240 \log {\left (x \right )}}{x^{2} - 8 x + 2 \log {\left (x - 2 \right )} + 16} - 15 \log {\left (x \right )} + \frac {30 e^{x} \log {\left (x \right )} \log {\left (x - 2 \right )}}{x^{2} - 8 x + 2 \log {\left (x - 2 \right )} + 16} \]

[In]

integrate((((60*x**2-120*x)*exp(x)*ln(-2+x)**2+((30*x**4-360*x**3+1320*x**2-1440*x)*exp(x)+60*x**3-360*x**2+48
0*x)*ln(-2+x)+(30*x**3-240*x**2+480*x)*exp(x)-30*x**3+240*x**2-480*x)*ln(x)+((60*x-120)*exp(x)-60*x+120)*ln(-2
+x)**2+((30*x**3-300*x**2+960*x-960)*exp(x)-30*x**3+300*x**2-960*x+960)*ln(-2+x))/((4*x**2-8*x)*ln(-2+x)**2+(4
*x**4-40*x**3+128*x**2-128*x)*ln(-2+x)+x**6-18*x**5+128*x**4-448*x**3+768*x**2-512*x),x)

[Out]

(15*x**2*log(x) - 120*x*log(x) + 240*log(x))/(x**2 - 8*x + 2*log(x - 2) + 16) - 15*log(x) + 30*exp(x)*log(x)*l
og(x - 2)/(x**2 - 8*x + 2*log(x - 2) + 16)

Maxima [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.80 \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\frac {15 \, {\left (2 \, e^{x} \log \left (x - 2\right ) \log \left (x\right ) + {\left (x^{2} - 8 \, x + 16\right )} \log \left (x\right )\right )}}{x^{2} - 8 \, x + 2 \, \log \left (x - 2\right ) + 16} - 15 \, \log \left (x\right ) \]

[In]

integrate((((60*x^2-120*x)*exp(x)*log(-2+x)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*l
og(-2+x)+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*log(x)+((60*x-120)*exp(x)-60*x+120)*log(-2+x)^2+(
(30*x^3-300*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*log(-2+x))/((4*x^2-8*x)*log(-2+x)^2+(4*x^4-40*x^3+
128*x^2-128*x)*log(-2+x)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x, algorithm="maxima")

[Out]

15*(2*e^x*log(x - 2)*log(x) + (x^2 - 8*x + 16)*log(x))/(x^2 - 8*x + 2*log(x - 2) + 16) - 15*log(x)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.44 \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\frac {30 \, {\left (e^{x} \log \left (x - 2\right ) \log \left (x\right ) - \log \left (x - 2\right ) \log \left (x\right )\right )}}{x^{2} - 8 \, x + 2 \, \log \left (x - 2\right ) + 16} \]

[In]

integrate((((60*x^2-120*x)*exp(x)*log(-2+x)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*l
og(-2+x)+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*log(x)+((60*x-120)*exp(x)-60*x+120)*log(-2+x)^2+(
(30*x^3-300*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*log(-2+x))/((4*x^2-8*x)*log(-2+x)^2+(4*x^4-40*x^3+
128*x^2-128*x)*log(-2+x)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x, algorithm="giac")

[Out]

30*(e^x*log(x - 2)*log(x) - log(x - 2)*log(x))/(x^2 - 8*x + 2*log(x - 2) + 16)

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (960-960 x+300 x^2-30 x^3+e^x \left (-960+960 x-300 x^2+30 x^3\right )\right ) \log (-2+x)+\left (120-60 x+e^x (-120+60 x)\right ) \log ^2(-2+x)+\left (-480 x+240 x^2-30 x^3+e^x \left (480 x-240 x^2+30 x^3\right )+\left (480 x-360 x^2+60 x^3+e^x \left (-1440 x+1320 x^2-360 x^3+30 x^4\right )\right ) \log (-2+x)+e^x \left (-120 x+60 x^2\right ) \log ^2(-2+x)\right ) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+\left (-128 x+128 x^2-40 x^3+4 x^4\right ) \log (-2+x)+\left (-8 x+4 x^2\right ) \log ^2(-2+x)} \, dx=\int -\frac {\ln \left (x-2\right )\,\left (300\,x^2-960\,x-30\,x^3+{\mathrm {e}}^x\,\left (30\,x^3-300\,x^2+960\,x-960\right )+960\right )-\ln \left (x\right )\,\left (480\,x-\ln \left (x-2\right )\,\left (480\,x-{\mathrm {e}}^x\,\left (-30\,x^4+360\,x^3-1320\,x^2+1440\,x\right )-360\,x^2+60\,x^3\right )-240\,x^2+30\,x^3-{\mathrm {e}}^x\,\left (30\,x^3-240\,x^2+480\,x\right )+{\ln \left (x-2\right )}^2\,{\mathrm {e}}^x\,\left (120\,x-60\,x^2\right )\right )+{\ln \left (x-2\right )}^2\,\left ({\mathrm {e}}^x\,\left (60\,x-120\right )-60\,x+120\right )}{512\,x+{\ln \left (x-2\right )}^2\,\left (8\,x-4\,x^2\right )+\ln \left (x-2\right )\,\left (-4\,x^4+40\,x^3-128\,x^2+128\,x\right )-768\,x^2+448\,x^3-128\,x^4+18\,x^5-x^6} \,d x \]

[In]

int(-(log(x - 2)*(300*x^2 - 960*x - 30*x^3 + exp(x)*(960*x - 300*x^2 + 30*x^3 - 960) + 960) - log(x)*(480*x -
log(x - 2)*(480*x - exp(x)*(1440*x - 1320*x^2 + 360*x^3 - 30*x^4) - 360*x^2 + 60*x^3) - 240*x^2 + 30*x^3 - exp
(x)*(480*x - 240*x^2 + 30*x^3) + log(x - 2)^2*exp(x)*(120*x - 60*x^2)) + log(x - 2)^2*(exp(x)*(60*x - 120) - 6
0*x + 120))/(512*x + log(x - 2)^2*(8*x - 4*x^2) + log(x - 2)*(128*x - 128*x^2 + 40*x^3 - 4*x^4) - 768*x^2 + 44
8*x^3 - 128*x^4 + 18*x^5 - x^6),x)

[Out]

int(-(log(x - 2)*(300*x^2 - 960*x - 30*x^3 + exp(x)*(960*x - 300*x^2 + 30*x^3 - 960) + 960) - log(x)*(480*x -
log(x - 2)*(480*x - exp(x)*(1440*x - 1320*x^2 + 360*x^3 - 30*x^4) - 360*x^2 + 60*x^3) - 240*x^2 + 30*x^3 - exp
(x)*(480*x - 240*x^2 + 30*x^3) + log(x - 2)^2*exp(x)*(120*x - 60*x^2)) + log(x - 2)^2*(exp(x)*(60*x - 120) - 6
0*x + 120))/(512*x + log(x - 2)^2*(8*x - 4*x^2) + log(x - 2)*(128*x - 128*x^2 + 40*x^3 - 4*x^4) - 768*x^2 + 44
8*x^3 - 128*x^4 + 18*x^5 - x^6), x)