\(\int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+(680 x-320 x^2+30 x^3) \log (2)+(80 x-10 x^2) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+(2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8) \log (2)+(6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7) \log ^2(2)+(8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6) \log ^3(2)+(4096 x-2048 x^2+384 x^3-32 x^4+x^5) \log ^4(2)+(32 x-128 x^2+144 x^3-32 x^4+2 x^5+(128 x-272 x^2+64 x^3-4 x^4) \log (2)+(128 x-32 x^2+2 x^3) \log ^2(2)) \log (x)+x \log ^2(x)} \, dx\) [9408]

Optimal result

Integrand size = 312, antiderivative size = 21 \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{(-4+(-8+x) (-x+\log (2)))^2+\log (x)} \]

[Out]

5/(((-8+x)*(ln(2)-x)-4)^2+ln(x))

Rubi [F]

\[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx \]

[In]

Int[(-5 + 320*x - 720*x^2 + 240*x^3 - 20*x^4 + (680*x - 320*x^2 + 30*x^3)*Log[2] + (80*x - 10*x^2)*Log[2]^2)/(
256*x - 2048*x^2 + 6400*x^3 - 9728*x^4 + 7264*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + (2048*x - 12544*x^2 +
27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8)*Log[2] + (6144*x - 26112*x^2 + 33888*x^3 - 1344
0*x^4 + 2352*x^5 - 192*x^6 + 6*x^7)*Log[2]^2 + (8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6)*Lo
g[2]^3 + (4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)*Log[2]^4 + (32*x - 128*x^2 + 144*x^3 - 32*x^4 + 2*x^5 +
(128*x - 272*x^2 + 64*x^3 - 4*x^4)*Log[2] + (128*x - 32*x^2 + 2*x^3)*Log[2]^2)*Log[x] + x*Log[x]^2),x]

[Out]

40*(8 + Log[2])*(1 + Log[4])*Defer[Int][(x^4 - 16*x^3*(1 + Log[2]/8) + 72*x^2*(1 + (Log[2]*(32 + Log[2]))/72)
+ 16*(1 + (1 + Log[2])*Log[16]) - 64*x*(1 + (Log[2]*(1 + ((8 + Log[2])*Log[256])/Log[16]))/8) + Log[x])^(-2),
x] - 5*Defer[Int][1/(x*(x^4 - 16*x^3*(1 + Log[2]/8) + 72*x^2*(1 + (Log[2]*(32 + Log[2]))/72) + 16*(1 + (1 + Lo
g[2])*Log[16]) - 64*x*(1 + (Log[2]*(1 + ((8 + Log[2])*Log[256])/Log[16]))/8) + Log[x])^2), x] - 10*(72 + 32*Lo
g[2] + Log[2]^2)*Defer[Int][x/(x^4 - 16*x^3*(1 + Log[2]/8) + 72*x^2*(1 + (Log[2]*(32 + Log[2]))/72) + 16*(1 +
(1 + Log[2])*Log[16]) - 64*x*(1 + (Log[2]*(1 + ((8 + Log[2])*Log[256])/Log[16]))/8) + Log[x])^2, x] + 30*(8 +
Log[2])*Defer[Int][x^2/(x^4 - 16*x^3*(1 + Log[2]/8) + 72*x^2*(1 + (Log[2]*(32 + Log[2]))/72) + 16*(1 + (1 + Lo
g[2])*Log[16]) - 64*x*(1 + (Log[2]*(1 + ((8 + Log[2])*Log[256])/Log[16]))/8) + Log[x])^2, x] - 20*Defer[Int][x
^3/(x^4 - 16*x^3*(1 + Log[2]/8) + 72*x^2*(1 + (Log[2]*(32 + Log[2]))/72) + 16*(1 + (1 + Log[2])*Log[16]) - 64*
x*(1 + (Log[2]*(1 + ((8 + Log[2])*Log[256])/Log[16]))/8) + Log[x])^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {5 \left (-1-4 x^4+6 x^3 (8+\log (2))+8 x (8+\log (2)) (1+2 \log (2))-2 x^2 \left (72+32 \log (2)+\log ^2(2)\right )\right )}{x \left (\left (4+x^2-x (8+\log (2))+\log (256)\right )^2+\log (x)\right )^2} \, dx \\ & = 5 \int \frac {-1-4 x^4+6 x^3 (8+\log (2))+8 x (8+\log (2)) (1+2 \log (2))-2 x^2 \left (72+32 \log (2)+\log ^2(2)\right )}{x \left (\left (4+x^2-x (8+\log (2))+\log (256)\right )^2+\log (x)\right )^2} \, dx \\ & = 5 \int \frac {-1-4 x^4+6 x^3 (8+\log (2))-2 x^2 \left (72+32 \log (2)+\log ^2(2)\right )+8 x (8+\log (2)) (1+\log (4))}{x \left (\left (4+x^2-x (8+\log (2))+\log (256)\right )^2+\log (x)\right )^2} \, dx \\ & = 5 \int \left (-\frac {1}{x \left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2}-\frac {4 x^3}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2}+\frac {6 x^2 (8+\log (2))}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2}+\frac {2 x \left (-72-32 \log (2)-\log ^2(2)\right )}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2}+\frac {8 (8+\log (2)) (1+\log (4))}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2}\right ) \, dx \\ & = -\left (5 \int \frac {1}{x \left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2} \, dx\right )-20 \int \frac {x^3}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2} \, dx+(30 (8+\log (2))) \int \frac {x^2}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2} \, dx-\left (10 \left (72+32 \log (2)+\log ^2(2)\right )\right ) \int \frac {x}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2} \, dx+(40 (8+\log (2)) (1+\log (4))) \int \frac {1}{\left (x^4-16 x^3 \left (1+\frac {\log (2)}{8}\right )+72 x^2 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right )+16 (1+(1+\log (2)) \log (16))-64 x \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right )+\log (x)\right )^2} \, dx \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(21)=42\).

Time = 5.48 (sec) , antiderivative size = 113, normalized size of antiderivative = 5.38 \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=-\frac {5 \left (-1-4 x^4+6 x^3 (8+\log (2))-2 x^2 \left (72+32 \log (2)+\log ^2(2)\right )+8 x \left (8+17 \log (2)+2 \log ^2(2)\right )\right )}{\left (1+4 x^4-6 x^3 (8+\log (2))-2 x (8+\log (2)) (4+\log (256))+2 x^2 \left (72+\log ^2(2)+2 \log (65536)\right )\right ) \left (\left (4+x^2-x (8+\log (2))+\log (256)\right )^2+\log (x)\right )} \]

[In]

Integrate[(-5 + 320*x - 720*x^2 + 240*x^3 - 20*x^4 + (680*x - 320*x^2 + 30*x^3)*Log[2] + (80*x - 10*x^2)*Log[2
]^2)/(256*x - 2048*x^2 + 6400*x^3 - 9728*x^4 + 7264*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + (2048*x - 12544*
x^2 + 27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8)*Log[2] + (6144*x - 26112*x^2 + 33888*x^3
- 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7)*Log[2]^2 + (8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x
^6)*Log[2]^3 + (4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)*Log[2]^4 + (32*x - 128*x^2 + 144*x^3 - 32*x^4 + 2*
x^5 + (128*x - 272*x^2 + 64*x^3 - 4*x^4)*Log[2] + (128*x - 32*x^2 + 2*x^3)*Log[2]^2)*Log[x] + x*Log[x]^2),x]

[Out]

(-5*(-1 - 4*x^4 + 6*x^3*(8 + Log[2]) - 2*x^2*(72 + 32*Log[2] + Log[2]^2) + 8*x*(8 + 17*Log[2] + 2*Log[2]^2)))/
((1 + 4*x^4 - 6*x^3*(8 + Log[2]) - 2*x*(8 + Log[2])*(4 + Log[256]) + 2*x^2*(72 + Log[2]^2 + 2*Log[65536]))*((4
+ x^2 - x*(8 + Log[2]) + Log[256])^2 + Log[x]))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(68\) vs. \(2(21)=42\).

Time = 3.84 (sec) , antiderivative size = 69, normalized size of antiderivative = 3.29

method	result	size
default	\(\frac {5}{x^{2} \ln \left (2\right )^{2}-2 x^{3} \ln \left (2\right )+x^{4}-16 x \ln \left (2\right )^{2}+32 x^{2} \ln \left (2\right )-16 x^{3}+64 \ln \left (2\right )^{2}-136 x \ln \left (2\right )+72 x^{2}+\ln \left (x \right )+64 \ln \left (2\right )-64 x +16}\)	\(69\)
risch	\(\frac {5}{x^{2} \ln \left (2\right )^{2}-2 x^{3} \ln \left (2\right )+x^{4}-16 x \ln \left (2\right )^{2}+32 x^{2} \ln \left (2\right )-16 x^{3}+64 \ln \left (2\right )^{2}-136 x \ln \left (2\right )+72 x^{2}+\ln \left (x \right )+64 \ln \left (2\right )-64 x +16}\)	\(69\)
parallelrisch	\(\frac {5}{x^{2} \ln \left (2\right )^{2}-2 x^{3} \ln \left (2\right )+x^{4}-16 x \ln \left (2\right )^{2}+32 x^{2} \ln \left (2\right )-16 x^{3}+64 \ln \left (2\right )^{2}-136 x \ln \left (2\right )+72 x^{2}+\ln \left (x \right )+64 \ln \left (2\right )-64 x +16}\)	\(69\)

[In]

int(((-10*x^2+80*x)*ln(2)^2+(30*x^3-320*x^2+680*x)*ln(2)-20*x^4+240*x^3-720*x^2+320*x-5)/(x*ln(x)^2+((2*x^3-32
*x^2+128*x)*ln(2)^2+(-4*x^4+64*x^3-272*x^2+128*x)*ln(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*ln(x)+(x^5-32*x^4+3
84*x^3-2048*x^2+4096*x)*ln(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x^3-19456*x^2+8192*x)*ln(2)^3+(6*x^7-192*x^6+235
2*x^5-13440*x^4+33888*x^3-26112*x^2+6144*x)*ln(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4+27648*x^3-1254
4*x^2+2048*x)*ln(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728*x^4+6400*x^3-2048*x^2+256*x),x,method=_RETURNVER
BOSE)

[Out]

5/(x^2*ln(2)^2-2*x^3*ln(2)+x^4-16*x*ln(2)^2+32*x^2*ln(2)-16*x^3+64*ln(2)^2-136*x*ln(2)+72*x^2+ln(x)+64*ln(2)-6
4*x+16)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (21) = 42\).

Time = 0.27 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.57 \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 16 \, x^{3} + {\left (x^{2} - 16 \, x + 64\right )} \log \left (2\right )^{2} + 72 \, x^{2} - 2 \, {\left (x^{3} - 16 \, x^{2} + 68 \, x - 32\right )} \log \left (2\right ) - 64 \, x + \log \left (x\right ) + 16} \]

[In]

integrate(((-10*x^2+80*x)*log(2)^2+(30*x^3-320*x^2+680*x)*log(2)-20*x^4+240*x^3-720*x^2+320*x-5)/(x*log(x)^2+(
(2*x^3-32*x^2+128*x)*log(2)^2+(-4*x^4+64*x^3-272*x^2+128*x)*log(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*log(x)+(
x^5-32*x^4+384*x^3-2048*x^2+4096*x)*log(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x^3-19456*x^2+8192*x)*log(2)^3+(6*x
^7-192*x^6+2352*x^5-13440*x^4+33888*x^3-26112*x^2+6144*x)*log(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4
+27648*x^3-12544*x^2+2048*x)*log(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728*x^4+6400*x^3-2048*x^2+256*x),x,
algorithm="fricas")

[Out]

5/(x^4 - 16*x^3 + (x^2 - 16*x + 64)*log(2)^2 + 72*x^2 - 2*(x^3 - 16*x^2 + 68*x - 32)*log(2) - 64*x + log(x) +
16)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (15) = 30\).

Time = 0.15 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.57 \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 16 x^{3} - 2 x^{3} \log {\left (2 \right )} + x^{2} \log {\left (2 \right )}^{2} + 32 x^{2} \log {\left (2 \right )} + 72 x^{2} - 136 x \log {\left (2 \right )} - 64 x - 16 x \log {\left (2 \right )}^{2} + \log {\left (x \right )} + 16 + 64 \log {\left (2 \right )}^{2} + 64 \log {\left (2 \right )}} \]

[In]

integrate(((-10*x**2+80*x)*ln(2)**2+(30*x**3-320*x**2+680*x)*ln(2)-20*x**4+240*x**3-720*x**2+320*x-5)/(x*ln(x)
**2+((2*x**3-32*x**2+128*x)*ln(2)**2+(-4*x**4+64*x**3-272*x**2+128*x)*ln(2)+2*x**5-32*x**4+144*x**3-128*x**2+3
2*x)*ln(x)+(x**5-32*x**4+384*x**3-2048*x**2+4096*x)*ln(2)**4+(-4*x**6+128*x**5-1552*x**4+8576*x**3-19456*x**2+
8192*x)*ln(2)**3+(6*x**7-192*x**6+2352*x**5-13440*x**4+33888*x**3-26112*x**2+6144*x)*ln(2)**2+(-4*x**8+128*x**
7-1584*x**6+9344*x**5-25792*x**4+27648*x**3-12544*x**2+2048*x)*ln(2)+x**9-32*x**8+400*x**7-2432*x**6+7264*x**5
-9728*x**4+6400*x**3-2048*x**2+256*x),x)

[Out]

5/(x**4 - 16*x**3 - 2*x**3*log(2) + x**2*log(2)**2 + 32*x**2*log(2) + 72*x**2 - 136*x*log(2) - 64*x - 16*x*log
(2)**2 + log(x) + 16 + 64*log(2)**2 + 64*log(2))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (21) = 42\).

Time = 0.33 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.81 \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 2 \, x^{3} {\left (\log \left (2\right ) + 8\right )} + {\left (\log \left (2\right )^{2} + 32 \, \log \left (2\right ) + 72\right )} x^{2} - 8 \, {\left (2 \, \log \left (2\right )^{2} + 17 \, \log \left (2\right ) + 8\right )} x + 64 \, \log \left (2\right )^{2} + 64 \, \log \left (2\right ) + \log \left (x\right ) + 16} \]

[In]

integrate(((-10*x^2+80*x)*log(2)^2+(30*x^3-320*x^2+680*x)*log(2)-20*x^4+240*x^3-720*x^2+320*x-5)/(x*log(x)^2+(
(2*x^3-32*x^2+128*x)*log(2)^2+(-4*x^4+64*x^3-272*x^2+128*x)*log(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*log(x)+(
x^5-32*x^4+384*x^3-2048*x^2+4096*x)*log(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x^3-19456*x^2+8192*x)*log(2)^3+(6*x
^7-192*x^6+2352*x^5-13440*x^4+33888*x^3-26112*x^2+6144*x)*log(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4
+27648*x^3-12544*x^2+2048*x)*log(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728*x^4+6400*x^3-2048*x^2+256*x),x,
algorithm="maxima")

[Out]

5/(x^4 - 2*x^3*(log(2) + 8) + (log(2)^2 + 32*log(2) + 72)*x^2 - 8*(2*log(2)^2 + 17*log(2) + 8)*x + 64*log(2)^2
+ 64*log(2) + log(x) + 16)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (21) = 42\).

Time = 0.30 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.24 \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 2 \, x^{3} \log \left (2\right ) + x^{2} \log \left (2\right )^{2} - 16 \, x^{3} + 32 \, x^{2} \log \left (2\right ) - 16 \, x \log \left (2\right )^{2} + 72 \, x^{2} - 136 \, x \log \left (2\right ) + 64 \, \log \left (2\right )^{2} - 64 \, x + 64 \, \log \left (2\right ) + \log \left (x\right ) + 16} \]

[In]

integrate(((-10*x^2+80*x)*log(2)^2+(30*x^3-320*x^2+680*x)*log(2)-20*x^4+240*x^3-720*x^2+320*x-5)/(x*log(x)^2+(
(2*x^3-32*x^2+128*x)*log(2)^2+(-4*x^4+64*x^3-272*x^2+128*x)*log(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*log(x)+(
x^5-32*x^4+384*x^3-2048*x^2+4096*x)*log(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x^3-19456*x^2+8192*x)*log(2)^3+(6*x
^7-192*x^6+2352*x^5-13440*x^4+33888*x^3-26112*x^2+6144*x)*log(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4
+27648*x^3-12544*x^2+2048*x)*log(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728*x^4+6400*x^3-2048*x^2+256*x),x,
algorithm="giac")

[Out]

5/(x^4 - 2*x^3*log(2) + x^2*log(2)^2 - 16*x^3 + 32*x^2*log(2) - 16*x*log(2)^2 + 72*x^2 - 136*x*log(2) + 64*log
(2)^2 - 64*x + 64*log(2) + log(x) + 16)

Mupad [F(-1)]

Timed out. \[ \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\int \frac {320\,x+\ln \left (2\right )\,\left (30\,x^3-320\,x^2+680\,x\right )+{\ln \left (2\right )}^2\,\left (80\,x-10\,x^2\right )-720\,x^2+240\,x^3-20\,x^4-5}{256\,x+x\,{\ln \left (x\right )}^2+{\ln \left (2\right )}^3\,\left (-4\,x^6+128\,x^5-1552\,x^4+8576\,x^3-19456\,x^2+8192\,x\right )+\ln \left (2\right )\,\left (-4\,x^8+128\,x^7-1584\,x^6+9344\,x^5-25792\,x^4+27648\,x^3-12544\,x^2+2048\,x\right )+{\ln \left (2\right )}^2\,\left (6\,x^7-192\,x^6+2352\,x^5-13440\,x^4+33888\,x^3-26112\,x^2+6144\,x\right )+\ln \left (x\right )\,\left (32\,x+\ln \left (2\right )\,\left (-4\,x^4+64\,x^3-272\,x^2+128\,x\right )+{\ln \left (2\right )}^2\,\left (2\,x^3-32\,x^2+128\,x\right )-128\,x^2+144\,x^3-32\,x^4+2\,x^5\right )-2048\,x^2+6400\,x^3-9728\,x^4+7264\,x^5-2432\,x^6+400\,x^7-32\,x^8+x^9+{\ln \left (2\right )}^4\,\left (x^5-32\,x^4+384\,x^3-2048\,x^2+4096\,x\right )} \,d x \]

[In]

int((320*x + log(2)*(680*x - 320*x^2 + 30*x^3) + log(2)^2*(80*x - 10*x^2) - 720*x^2 + 240*x^3 - 20*x^4 - 5)/(2
56*x + x*log(x)^2 + log(2)^3*(8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6) + log(2)*(2048*x - 1
2544*x^2 + 27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8) + log(2)^2*(6144*x - 26112*x^2 + 338
88*x^3 - 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7) + log(x)*(32*x + log(2)*(128*x - 272*x^2 + 64*x^3 - 4*x^4) +
log(2)^2*(128*x - 32*x^2 + 2*x^3) - 128*x^2 + 144*x^3 - 32*x^4 + 2*x^5) - 2048*x^2 + 6400*x^3 - 9728*x^4 + 726
4*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + log(2)^4*(4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)),x)

[Out]

int((320*x + log(2)*(680*x - 320*x^2 + 30*x^3) + log(2)^2*(80*x - 10*x^2) - 720*x^2 + 240*x^3 - 20*x^4 - 5)/(2
56*x + x*log(x)^2 + log(2)^3*(8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6) + log(2)*(2048*x - 1
2544*x^2 + 27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8) + log(2)^2*(6144*x - 26112*x^2 + 338
88*x^3 - 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7) + log(x)*(32*x + log(2)*(128*x - 272*x^2 + 64*x^3 - 4*x^4) +
log(2)^2*(128*x - 32*x^2 + 2*x^3) - 128*x^2 + 144*x^3 - 32*x^4 + 2*x^5) - 2048*x^2 + 6400*x^3 - 9728*x^4 + 726
4*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + log(2)^4*(4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)), x)