\(\int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+(768 x-128 x^2+128 x^3-384 x^4) \log (-2+x)+(-512+256 x-1024 x^2+512 x^3) \log ^2(-2+x)+(-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+(-1280 x-128 x^2+256 x^3) \log (-2+x)) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+(-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8) \log (-2+x)+(3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6) \log ^2(-2+x)+(1536 x^2-256 x^3-256 x^4) \log ^3(-2+x)+(-512 x+256 x^2) \log ^4(-2+x)} \, dx\) [2491]

Optimal result

Integrand size = 293, antiderivative size = 31 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {x^2+\log (x)}{-3-x+\left (\frac {1}{4} x (3+x)-\log (-2+x)\right )^2} \]

[Out]

(ln(x)+x^2)/((1/4*(3+x)*x-ln(-2+x))^2-3-x)

Rubi [F]

\[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx \]

[In]

Int[(1536 - 256*x + 2528*x^2 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32*x^7 + (768*x - 128*x^2 + 128*x^3 - 3
84*x^4)*Log[-2 + x] + (-512 + 256*x - 1024*x^2 + 512*x^3)*Log[-2 + x]^2 + (-512*x + 1216*x^2 + 416*x^3 - 160*x
^4 - 64*x^5 + (-1280*x - 128*x^2 + 256*x^3)*Log[-2 + x])*Log[x])/(-4608*x - 768*x^2 + 2752*x^3 + 1120*x^4 - 45
0*x^5 - 359*x^6 - 32*x^7 + 30*x^8 + 10*x^9 + x^10 + (-4608*x^2 - 768*x^3 + 1888*x^4 + 688*x^5 - 144*x^6 - 112*
x^7 - 16*x^8)*Log[-2 + x] + (3072*x - 512*x^2 - 2240*x^3 - 288*x^4 + 384*x^5 + 96*x^6)*Log[-2 + x]^2 + (1536*x
^2 - 256*x^3 - 256*x^4)*Log[-2 + x]^3 + (-512*x + 256*x^2)*Log[-2 + x]^4),x]

[Out]

2560*Defer[Int][(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^(
-2), x] + 5120*Defer[Int][1/((-2 + x)*(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x]
+ 16*Log[-2 + x]^2)^2), x] + 1280*Defer[Int][x/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*L
og[-2 + x] + 16*Log[-2 + x]^2)^2, x] + 896*Defer[Int][x^2/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x]
- 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 160*Defer[Int][x^3/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*L
og[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 288*Defer[Int][x^4/(-48 - 16*x + 9*x^2 + 6*x^3 + x^
4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 64*Defer[Int][x^5/(-48 - 16*x + 9*x^2 + 6
*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 1024*Defer[Int][Log[-2 + x]/(-48
- 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 2048*Defer[In
t][Log[-2 + x]/((-2 + x)*(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2
+ x]^2)^2), x] - 512*Defer[Int][(x*Log[-2 + x])/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*L
og[-2 + x] + 16*Log[-2 + x]^2)^2, x] + 384*Defer[Int][(x^2*Log[-2 + x])/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24
*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] + 256*Defer[Int][(x^3*Log[-2 + x])/(-48 - 16*x +
9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] + 16*Defer[Int][1/(x*(-48
- 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)), x] + 32*Defer[Int][
x/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2), x] + 896*Defer
[Int][Log[x]/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x
] + 1280*Defer[Int][Log[x]/((-2 + x)*(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x]
+ 16*Log[-2 + x]^2)^2), x] - 160*Defer[Int][(x*Log[x])/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] -
8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 288*Defer[Int][(x^2*Log[x])/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 -
24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] - 64*Defer[Int][(x^3*Log[x])/(-48 - 16*x + 9*x^
2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] + 384*Defer[Int][(Log[-2 + x]
*Log[x])/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x] -
512*Defer[Int][(Log[-2 + x]*Log[x])/((-2 + x)*(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 24*x*Log[-2 + x] - 8*x^2*Log
[-2 + x] + 16*Log[-2 + x]^2)^2), x] + 256*Defer[Int][(x*Log[-2 + x]*Log[x])/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4
- 24*x*Log[-2 + x] - 8*x^2*Log[-2 + x] + 16*Log[-2 + x]^2)^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {16 \left (-96+16 x-158 x^2+67 x^3-12 x^4-21 x^5+2 x^6+2 x^7-16 \left (-2+x-4 x^2+2 x^3\right ) \log ^2(-2+x)+2 x \left (16-38 x-13 x^2+5 x^3+2 x^4\right ) \log (x)+8 x \log (-2+x) \left (-6+x-x^2+3 x^3+\left (10+x-2 x^2\right ) \log (x)\right )\right )}{(2-x) x \left (48+16 x-9 x^2-6 x^3-x^4+8 x (3+x) \log (-2+x)-16 \log ^2(-2+x)\right )^2} \, dx \\ & = 16 \int \frac {-96+16 x-158 x^2+67 x^3-12 x^4-21 x^5+2 x^6+2 x^7-16 \left (-2+x-4 x^2+2 x^3\right ) \log ^2(-2+x)+2 x \left (16-38 x-13 x^2+5 x^3+2 x^4\right ) \log (x)+8 x \log (-2+x) \left (-6+x-x^2+3 x^3+\left (10+x-2 x^2\right ) \log (x)\right )}{(2-x) x \left (48+16 x-9 x^2-6 x^3-x^4+8 x (3+x) \log (-2+x)-16 \log ^2(-2+x)\right )^2} \, dx \\ & = 16 \int \left (-\frac {16}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {96}{(-2+x) x \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {158 x}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}-\frac {67 x^2}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {12 x^3}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {21 x^4}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}-\frac {2 x^5}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}-\frac {2 x^6}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {48 \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}-\frac {8 x \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {8 x^2 \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}-\frac {24 x^3 \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}+\frac {16 \left (1+2 x^2\right ) \log ^2(-2+x)}{x \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}-\frac {2 \left (16-38 x-13 x^2+5 x^3+2 x^4+40 \log (-2+x)+4 x \log (-2+x)-8 x^2 \log (-2+x)\right ) \log (x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2}\right ) \, dx \\ & = -\left (32 \int \frac {x^5}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx\right )-32 \int \frac {x^6}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx-32 \int \frac {\left (16-38 x-13 x^2+5 x^3+2 x^4+40 \log (-2+x)+4 x \log (-2+x)-8 x^2 \log (-2+x)\right ) \log (x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx-128 \int \frac {x \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+128 \int \frac {x^2 \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+192 \int \frac {x^3}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx-256 \int \frac {1}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+256 \int \frac {\left (1+2 x^2\right ) \log ^2(-2+x)}{x \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+336 \int \frac {x^4}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx-384 \int \frac {x^3 \log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+768 \int \frac {\log (-2+x)}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx-1072 \int \frac {x^2}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+1536 \int \frac {1}{(-2+x) x \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx+2528 \int \frac {x}{(-2+x) \left (-48-16 x+9 x^2+6 x^3+x^4-24 x \log (-2+x)-8 x^2 \log (-2+x)+16 \log ^2(-2+x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.16 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \left (x^2+\log (x)\right )}{-48-16 x+9 x^2+6 x^3+x^4-8 x (3+x) \log (-2+x)+16 \log ^2(-2+x)} \]

[In]

Integrate[(1536 - 256*x + 2528*x^2 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32*x^7 + (768*x - 128*x^2 + 128*x
^3 - 384*x^4)*Log[-2 + x] + (-512 + 256*x - 1024*x^2 + 512*x^3)*Log[-2 + x]^2 + (-512*x + 1216*x^2 + 416*x^3 -
160*x^4 - 64*x^5 + (-1280*x - 128*x^2 + 256*x^3)*Log[-2 + x])*Log[x])/(-4608*x - 768*x^2 + 2752*x^3 + 1120*x^
4 - 450*x^5 - 359*x^6 - 32*x^7 + 30*x^8 + 10*x^9 + x^10 + (-4608*x^2 - 768*x^3 + 1888*x^4 + 688*x^5 - 144*x^6
- 112*x^7 - 16*x^8)*Log[-2 + x] + (3072*x - 512*x^2 - 2240*x^3 - 288*x^4 + 384*x^5 + 96*x^6)*Log[-2 + x]^2 + (
1536*x^2 - 256*x^3 - 256*x^4)*Log[-2 + x]^3 + (-512*x + 256*x^2)*Log[-2 + x]^4),x]

[Out]

(16*(x^2 + Log[x]))/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 8*x*(3 + x)*Log[-2 + x] + 16*Log[-2 + x]^2)

Maple [A] (verified)

Time = 7.42 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.71

method	result	size
risch	\(\frac {16 \ln \left (x \right )+16 x^{2}}{x^{4}-8 x^{2} \ln \left (-2+x \right )+6 x^{3}+16 \ln \left (-2+x \right )^{2}-24 x \ln \left (-2+x \right )+9 x^{2}-16 x -48}\)	\(53\)
parallelrisch	\(-\frac {-1024 x^{2}-1024 \ln \left (x \right )}{64 \left (x^{4}-8 x^{2} \ln \left (-2+x \right )+6 x^{3}+16 \ln \left (-2+x \right )^{2}-24 x \ln \left (-2+x \right )+9 x^{2}-16 x -48\right )}\)	\(57\)

[In]

int((((256*x^3-128*x^2-1280*x)*ln(-2+x)-64*x^5-160*x^4+416*x^3+1216*x^2-512*x)*ln(x)+(512*x^3-1024*x^2+256*x-5
12)*ln(-2+x)^2+(-384*x^4+128*x^3-128*x^2+768*x)*ln(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528*x^2-256*x
+1536)/((256*x^2-512*x)*ln(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*ln(-2+x)^3+(96*x^6+384*x^5-288*x^4-2240*x^3-512
*x^2+3072*x)*ln(-2+x)^2+(-16*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*ln(-2+x)+x^10+10*x^9+30*x^
8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x,method=_RETURNVERBOSE)

[Out]

16*(ln(x)+x^2)/(x^4-8*x^2*ln(-2+x)+6*x^3+16*ln(-2+x)^2-24*x*ln(-2+x)+9*x^2-16*x-48)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.58 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \, {\left (x^{2} + \log \left (x\right )\right )}}{x^{4} + 6 \, x^{3} + 9 \, x^{2} - 8 \, {\left (x^{2} + 3 \, x\right )} \log \left (x - 2\right ) + 16 \, \log \left (x - 2\right )^{2} - 16 \, x - 48} \]

[In]

integrate((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216*x^2-512*x)*log(x)+(512*x^3-1024*x^2
+256*x-512)*log(-2+x)^2+(-384*x^4+128*x^3-128*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528
*x^2-256*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*log(-2+x)^3+(96*x^6+384*x^5-288*x^4-
2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-16*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^1
0+10*x^9+30*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x, algorithm="fricas")

[Out]

16*(x^2 + log(x))/(x^4 + 6*x^3 + 9*x^2 - 8*(x^2 + 3*x)*log(x - 2) + 16*log(x - 2)^2 - 16*x - 48)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (24) = 48\).

Time = 0.21 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.65 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 x^{2} + 16 \log {\left (x \right )}}{x^{4} + 6 x^{3} + 9 x^{2} - 16 x + \left (- 8 x^{2} - 24 x\right ) \log {\left (x - 2 \right )} + 16 \log {\left (x - 2 \right )}^{2} - 48} \]

[In]

integrate((((256*x**3-128*x**2-1280*x)*ln(-2+x)-64*x**5-160*x**4+416*x**3+1216*x**2-512*x)*ln(x)+(512*x**3-102
4*x**2+256*x-512)*ln(-2+x)**2+(-384*x**4+128*x**3-128*x**2+768*x)*ln(-2+x)-32*x**7-32*x**6+336*x**5+192*x**4-1
072*x**3+2528*x**2-256*x+1536)/((256*x**2-512*x)*ln(-2+x)**4+(-256*x**4-256*x**3+1536*x**2)*ln(-2+x)**3+(96*x*
*6+384*x**5-288*x**4-2240*x**3-512*x**2+3072*x)*ln(-2+x)**2+(-16*x**8-112*x**7-144*x**6+688*x**5+1888*x**4-768
*x**3-4608*x**2)*ln(-2+x)+x**10+10*x**9+30*x**8-32*x**7-359*x**6-450*x**5+1120*x**4+2752*x**3-768*x**2-4608*x)
,x)

[Out]

(16*x**2 + 16*log(x))/(x**4 + 6*x**3 + 9*x**2 - 16*x + (-8*x**2 - 24*x)*log(x - 2) + 16*log(x - 2)**2 - 48)

Maxima [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.58 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \, {\left (x^{2} + \log \left (x\right )\right )}}{x^{4} + 6 \, x^{3} + 9 \, x^{2} - 8 \, {\left (x^{2} + 3 \, x\right )} \log \left (x - 2\right ) + 16 \, \log \left (x - 2\right )^{2} - 16 \, x - 48} \]

[In]

integrate((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216*x^2-512*x)*log(x)+(512*x^3-1024*x^2
+256*x-512)*log(-2+x)^2+(-384*x^4+128*x^3-128*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528
*x^2-256*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*log(-2+x)^3+(96*x^6+384*x^5-288*x^4-
2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-16*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^1
0+10*x^9+30*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x, algorithm="maxima")

[Out]

16*(x^2 + log(x))/(x^4 + 6*x^3 + 9*x^2 - 8*(x^2 + 3*x)*log(x - 2) + 16*log(x - 2)^2 - 16*x - 48)

Giac [A] (verification not implemented)

none

Time = 0.43 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.68 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \, {\left (x^{2} + \log \left (x\right )\right )}}{x^{4} + 6 \, x^{3} - 8 \, x^{2} \log \left (x - 2\right ) + 9 \, x^{2} - 24 \, x \log \left (x - 2\right ) + 16 \, \log \left (x - 2\right )^{2} - 16 \, x - 48} \]

[In]

integrate((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216*x^2-512*x)*log(x)+(512*x^3-1024*x^2
+256*x-512)*log(-2+x)^2+(-384*x^4+128*x^3-128*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528
*x^2-256*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*log(-2+x)^3+(96*x^6+384*x^5-288*x^4-
2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-16*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^1
0+10*x^9+30*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x, algorithm="giac")

[Out]

16*(x^2 + log(x))/(x^4 + 6*x^3 - 8*x^2*log(x - 2) + 9*x^2 - 24*x*log(x - 2) + 16*log(x - 2)^2 - 16*x - 48)

Mupad [F(-1)]

Timed out. \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=-\int \frac {\ln \left (x-2\right )\,\left (-384\,x^4+128\,x^3-128\,x^2+768\,x\right )-256\,x-\ln \left (x\right )\,\left (512\,x+\ln \left (x-2\right )\,\left (-256\,x^3+128\,x^2+1280\,x\right )-1216\,x^2-416\,x^3+160\,x^4+64\,x^5\right )+{\ln \left (x-2\right )}^2\,\left (512\,x^3-1024\,x^2+256\,x-512\right )+2528\,x^2-1072\,x^3+192\,x^4+336\,x^5-32\,x^6-32\,x^7+1536}{4608\,x+{\ln \left (x-2\right )}^3\,\left (256\,x^4+256\,x^3-1536\,x^2\right )-{\ln \left (x-2\right )}^2\,\left (96\,x^6+384\,x^5-288\,x^4-2240\,x^3-512\,x^2+3072\,x\right )+{\ln \left (x-2\right )}^4\,\left (512\,x-256\,x^2\right )+\ln \left (x-2\right )\,\left (16\,x^8+112\,x^7+144\,x^6-688\,x^5-1888\,x^4+768\,x^3+4608\,x^2\right )+768\,x^2-2752\,x^3-1120\,x^4+450\,x^5+359\,x^6+32\,x^7-30\,x^8-10\,x^9-x^{10}} \,d x \]

[In]

int(-(log(x - 2)*(768*x - 128*x^2 + 128*x^3 - 384*x^4) - 256*x - log(x)*(512*x + log(x - 2)*(1280*x + 128*x^2
- 256*x^3) - 1216*x^2 - 416*x^3 + 160*x^4 + 64*x^5) + log(x - 2)^2*(256*x - 1024*x^2 + 512*x^3 - 512) + 2528*x
^2 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32*x^7 + 1536)/(4608*x + log(x - 2)^3*(256*x^3 - 1536*x^2 + 256*x
^4) - log(x - 2)^2*(3072*x - 512*x^2 - 2240*x^3 - 288*x^4 + 384*x^5 + 96*x^6) + log(x - 2)^4*(512*x - 256*x^2)
+ log(x - 2)*(4608*x^2 + 768*x^3 - 1888*x^4 - 688*x^5 + 144*x^6 + 112*x^7 + 16*x^8) + 768*x^2 - 2752*x^3 - 11
20*x^4 + 450*x^5 + 359*x^6 + 32*x^7 - 30*x^8 - 10*x^9 - x^10),x)

[Out]

-int((log(x - 2)*(768*x - 128*x^2 + 128*x^3 - 384*x^4) - 256*x - log(x)*(512*x + log(x - 2)*(1280*x + 128*x^2
- 256*x^3) - 1216*x^2 - 416*x^3 + 160*x^4 + 64*x^5) + log(x - 2)^2*(256*x - 1024*x^2 + 512*x^3 - 512) + 2528*x
^2 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32*x^7 + 1536)/(4608*x + log(x - 2)^3*(256*x^3 - 1536*x^2 + 256*x
^4) - log(x - 2)^2*(3072*x - 512*x^2 - 2240*x^3 - 288*x^4 + 384*x^5 + 96*x^6) + log(x - 2)^4*(512*x - 256*x^2)
+ log(x - 2)*(4608*x^2 + 768*x^3 - 1888*x^4 - 688*x^5 + 144*x^6 + 112*x^7 + 16*x^8) + 768*x^2 - 2752*x^3 - 11
20*x^4 + 450*x^5 + 359*x^6 + 32*x^7 - 30*x^8 - 10*x^9 - x^10), x)