Integrand size = 375, antiderivative size = 24 \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=x+\frac {x}{-2+x+\frac {x^4 (-4+x+\log (x))}{(2+\log (5))^2}} \end {dmath*}
Time = 0.10 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=x+\frac {x (2+\log (5))^2}{-4 x^4+x^5-2 (2+\log (5))^2+x (2+\log (5))^2+x^4 \log (x)} \end {dmath*}
Integrate[(32 - 64*x + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (64 - 128*x + 32*x^2 + 108*x^4 - 64*x^5 + 8*x^6)*Log[5] + (48 - 9 6*x + 24*x^2 + 27*x^4 - 16*x^5 + 2*x^6)*Log[5]^2 + (16 - 32*x + 8*x^2)*Log [5]^3 + (2 - 4*x + x^2)*Log[5]^4 + (-28*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-28 *x^4 + 8*x^5)*Log[5] + (-7*x^4 + 2*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2)/( 64 - 64*x + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (12 8 - 128*x + 32*x^2 + 64*x^4 - 48*x^5 + 8*x^6)*Log[5] + (96 - 96*x + 24*x^2 + 16*x^4 - 12*x^5 + 2*x^6)*Log[5]^2 + (32 - 32*x + 8*x^2)*Log[5]^3 + (4 - 4*x + x^2)*Log[5]^4 + (-16*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-16*x^4 + 8*x^5 )*Log[5] + (-4*x^4 + 2*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {x^{10}-8 x^9+16 x^8+x^8 \log ^2(x)+8 x^6-64 x^5+108 x^4+16 x^2+\left (x^2-4 x+2\right ) \log ^4(5)+\left (8 x^2-32 x+16\right ) \log ^3(5)+\left (2 x^9-8 x^8+8 x^5-28 x^4+\left (2 x^5-7 x^4\right ) \log ^2(5)+\left (8 x^5-28 x^4\right ) \log (5)\right ) \log (x)+\left (2 x^6-16 x^5+27 x^4+24 x^2-96 x+48\right ) \log ^2(5)+\left (8 x^6-64 x^5+108 x^4+32 x^2-128 x+64\right ) \log (5)-64 x+32}{x^{10}-8 x^9+16 x^8+x^8 \log ^2(x)+8 x^6-48 x^5+64 x^4+16 x^2+\left (x^2-4 x+4\right ) \log ^4(5)+\left (8 x^2-32 x+32\right ) \log ^3(5)+\left (2 x^9-8 x^8+8 x^5-16 x^4+\left (2 x^5-4 x^4\right ) \log ^2(5)+\left (8 x^5-16 x^4\right ) \log (5)\right ) \log (x)+\left (2 x^6-12 x^5+16 x^4+24 x^2-96 x+96\right ) \log ^2(5)+\left (8 x^6-48 x^5+64 x^4+32 x^2-128 x+128\right ) \log (5)-64 x+64} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^{10}-8 x^9+16 x^8+x^8 \log ^2(x)+2 x^6 (2+\log (5))^2-16 x^5 (2+\log (5))^2+27 x^4 (2+\log (5))^2+x^2 (2+\log (5))^4+x^4 \left (2 x^5-8 x^4+2 x (2+\log (5))^2-7 (2+\log (5))^2\right ) \log (x)-4 x (2+\log (5))^4+2 (2+\log (5))^4}{\left (-x^5+4 x^4-x^4 \log (x)-x (2+\log (5))^2+2 (2+\log (5))^2\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {(2+\log (5))^2 \left (-x^5-x^4+12 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-32 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )}{\left (-x^5+4 x^4-x^4 \log (x)-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )^2}+\frac {3 (2+\log (5))^2}{-x^5+4 x^4-x^4 \log (x)-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )}+1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -8 (2+\log (5))^4 \int \frac {1}{\left (-x^5-\log (x) x^4+4 x^4-4 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right ) x+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )^2}dx+3 (2+\log (5))^4 \int \frac {x}{\left (-x^5-\log (x) x^4+4 x^4-4 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right ) x+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )^2}dx-(2+\log (5))^2 \int \frac {x^4}{\left (-x^5-\log (x) x^4+4 x^4-4 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right ) x+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )^2}dx-(2+\log (5))^2 \int \frac {x^5}{\left (-x^5-\log (x) x^4+4 x^4-4 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right ) x+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )^2}dx+3 (2+\log (5))^2 \int \frac {1}{-x^5-\log (x) x^4+4 x^4-4 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right ) x+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )}dx+x\) |
Int[(32 - 64*x + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (64 - 128*x + 32*x^2 + 108*x^4 - 64*x^5 + 8*x^6)*Log[5] + (48 - 96*x + 24*x^2 + 27*x^4 - 16*x^5 + 2*x^6)*Log[5]^2 + (16 - 32*x + 8*x^2)*Log[5]^3 + (2 - 4*x + x^2)*Log[5]^4 + (-28*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-28*x^4 + 8*x^5)*Log[5] + (-7*x^4 + 2*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2)/(64 - 6 4*x + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (128 - 12 8*x + 32*x^2 + 64*x^4 - 48*x^5 + 8*x^6)*Log[5] + (96 - 96*x + 24*x^2 + 16* x^4 - 12*x^5 + 2*x^6)*Log[5]^2 + (32 - 32*x + 8*x^2)*Log[5]^3 + (4 - 4*x + x^2)*Log[5]^4 + (-16*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-16*x^4 + 8*x^5)*Log[ 5] + (-4*x^4 + 2*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2),x]
3.12.3.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(56\) vs. \(2(24)=48\).
Time = 2.62 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38
| method | result | size |
| default | \(x +\frac {\left (\ln \left (5\right )^{2}+4 \ln \left (5\right )+4\right ) x}{x^{4} \ln \left (x \right )+x^{5}-4 x^{4}+x \ln \left (5\right )^{2}-2 \ln \left (5\right )^{2}+4 x \ln \left (5\right )-8 \ln \left (5\right )+4 x -8}\) | \(57\) |
| risch | \(x +\frac {\left (\ln \left (5\right )^{2}+4 \ln \left (5\right )+4\right ) x}{x^{4} \ln \left (x \right )+x^{5}-4 x^{4}+x \ln \left (5\right )^{2}-2 \ln \left (5\right )^{2}+4 x \ln \left (5\right )-8 \ln \left (5\right )+4 x -8}\) | \(57\) |
| parallelrisch | \(\frac {-4 x +x^{5} \ln \left (x \right )-4 x \ln \left (5\right )+x^{2} \ln \left (5\right )^{2}-x \ln \left (5\right )^{2}+4 x^{2} \ln \left (5\right )+x^{6}-4 x^{5}+4 x^{2}}{x^{4} \ln \left (x \right )+x^{5}-4 x^{4}+x \ln \left (5\right )^{2}-2 \ln \left (5\right )^{2}+4 x \ln \left (5\right )-8 \ln \left (5\right )+4 x -8}\) | \(94\) |
int((x^8*ln(x)^2+((2*x^5-7*x^4)*ln(5)^2+(8*x^5-28*x^4)*ln(5)+2*x^9-8*x^8+8 *x^5-28*x^4)*ln(x)+(x^2-4*x+2)*ln(5)^4+(8*x^2-32*x+16)*ln(5)^3+(2*x^6-16*x ^5+27*x^4+24*x^2-96*x+48)*ln(5)^2+(8*x^6-64*x^5+108*x^4+32*x^2-128*x+64)*l n(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/(x^8*ln(x)^2+( (2*x^5-4*x^4)*ln(5)^2+(8*x^5-16*x^4)*ln(5)+2*x^9-8*x^8+8*x^5-16*x^4)*ln(x) +(x^2-4*x+4)*ln(5)^4+(8*x^2-32*x+32)*ln(5)^3+(2*x^6-12*x^5+16*x^4+24*x^2-9 6*x+96)*ln(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128)*ln(5)+x^10-8*x^9+16 *x^8+8*x^6-48*x^5+64*x^4+16*x^2-64*x+64),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.46 \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=\frac {x^{6} + x^{5} \log \left (x\right ) - 4 \, x^{5} + {\left (x^{2} - x\right )} \log \left (5\right )^{2} + 4 \, x^{2} + 4 \, {\left (x^{2} - x\right )} \log \left (5\right ) - 4 \, x}{x^{5} + x^{4} \log \left (x\right ) - 4 \, x^{4} + {\left (x - 2\right )} \log \left (5\right )^{2} + 4 \, {\left (x - 2\right )} \log \left (5\right ) + 4 \, x - 8} \end {dmath*}
integrate((x^8*log(x)^2+((2*x^5-7*x^4)*log(5)^2+(8*x^5-28*x^4)*log(5)+2*x^ 9-8*x^8+8*x^5-28*x^4)*log(x)+(x^2-4*x+2)*log(5)^4+(8*x^2-32*x+16)*log(5)^3 +(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*log(5)^2+(8*x^6-64*x^5+108*x^4+32*x^ 2-128*x+64)*log(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/ (x^8*log(x)^2+((2*x^5-4*x^4)*log(5)^2+(8*x^5-16*x^4)*log(5)+2*x^9-8*x^8+8* x^5-16*x^4)*log(x)+(x^2-4*x+4)*log(5)^4+(8*x^2-32*x+32)*log(5)^3+(2*x^6-12 *x^5+16*x^4+24*x^2-96*x+96)*log(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128 )*log(5)+x^10-8*x^9+16*x^8+8*x^6-48*x^5+64*x^4+16*x^2-64*x+64),x, algorith m=\
(x^6 + x^5*log(x) - 4*x^5 + (x^2 - x)*log(5)^2 + 4*x^2 + 4*(x^2 - x)*log(5 ) - 4*x)/(x^5 + x^4*log(x) - 4*x^4 + (x - 2)*log(5)^2 + 4*(x - 2)*log(5) + 4*x - 8)
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (22) = 44\).
Time = 0.31 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.62 \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=x + \frac {x \log {\left (5 \right )}^{2} + 4 x + 4 x \log {\left (5 \right )}}{x^{5} + x^{4} \log {\left (x \right )} - 4 x^{4} + x \log {\left (5 \right )}^{2} + 4 x + 4 x \log {\left (5 \right )} - 8 \log {\left (5 \right )} - 8 - 2 \log {\left (5 \right )}^{2}} \end {dmath*}
integrate((x**8*ln(x)**2+((2*x**5-7*x**4)*ln(5)**2+(8*x**5-28*x**4)*ln(5)+ 2*x**9-8*x**8+8*x**5-28*x**4)*ln(x)+(x**2-4*x+2)*ln(5)**4+(8*x**2-32*x+16) *ln(5)**3+(2*x**6-16*x**5+27*x**4+24*x**2-96*x+48)*ln(5)**2+(8*x**6-64*x** 5+108*x**4+32*x**2-128*x+64)*ln(5)+x**10-8*x**9+16*x**8+8*x**6-64*x**5+108 *x**4+16*x**2-64*x+32)/(x**8*ln(x)**2+((2*x**5-4*x**4)*ln(5)**2+(8*x**5-16 *x**4)*ln(5)+2*x**9-8*x**8+8*x**5-16*x**4)*ln(x)+(x**2-4*x+4)*ln(5)**4+(8* x**2-32*x+32)*ln(5)**3+(2*x**6-12*x**5+16*x**4+24*x**2-96*x+96)*ln(5)**2+( 8*x**6-48*x**5+64*x**4+32*x**2-128*x+128)*ln(5)+x**10-8*x**9+16*x**8+8*x** 6-48*x**5+64*x**4+16*x**2-64*x+64),x)
x + (x*log(5)**2 + 4*x + 4*x*log(5))/(x**5 + x**4*log(x) - 4*x**4 + x*log( 5)**2 + 4*x + 4*x*log(5) - 8*log(5) - 8 - 2*log(5)**2)
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (24) = 48\).
Time = 0.39 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.46 \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=\frac {x^{6} + x^{5} \log \left (x\right ) - 4 \, x^{5} + {\left (\log \left (5\right )^{2} + 4 \, \log \left (5\right ) + 4\right )} x^{2} - {\left (\log \left (5\right )^{2} + 4 \, \log \left (5\right ) + 4\right )} x}{x^{5} + x^{4} \log \left (x\right ) - 4 \, x^{4} + {\left (\log \left (5\right )^{2} + 4 \, \log \left (5\right ) + 4\right )} x - 2 \, \log \left (5\right )^{2} - 8 \, \log \left (5\right ) - 8} \end {dmath*}
integrate((x^8*log(x)^2+((2*x^5-7*x^4)*log(5)^2+(8*x^5-28*x^4)*log(5)+2*x^ 9-8*x^8+8*x^5-28*x^4)*log(x)+(x^2-4*x+2)*log(5)^4+(8*x^2-32*x+16)*log(5)^3 +(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*log(5)^2+(8*x^6-64*x^5+108*x^4+32*x^ 2-128*x+64)*log(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/ (x^8*log(x)^2+((2*x^5-4*x^4)*log(5)^2+(8*x^5-16*x^4)*log(5)+2*x^9-8*x^8+8* x^5-16*x^4)*log(x)+(x^2-4*x+4)*log(5)^4+(8*x^2-32*x+32)*log(5)^3+(2*x^6-12 *x^5+16*x^4+24*x^2-96*x+96)*log(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128 )*log(5)+x^10-8*x^9+16*x^8+8*x^6-48*x^5+64*x^4+16*x^2-64*x+64),x, algorith m=\
(x^6 + x^5*log(x) - 4*x^5 + (log(5)^2 + 4*log(5) + 4)*x^2 - (log(5)^2 + 4* log(5) + 4)*x)/(x^5 + x^4*log(x) - 4*x^4 + (log(5)^2 + 4*log(5) + 4)*x - 2 *log(5)^2 - 8*log(5) - 8)
Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (24) = 48\).
Time = 0.33 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.50 \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=x + \frac {x \log \left (5\right )^{2} + 4 \, x \log \left (5\right ) + 4 \, x}{x^{5} + x^{4} \log \left (x\right ) - 4 \, x^{4} + x \log \left (5\right )^{2} + 4 \, x \log \left (5\right ) - 2 \, \log \left (5\right )^{2} + 4 \, x - 8 \, \log \left (5\right ) - 8} \end {dmath*}
integrate((x^8*log(x)^2+((2*x^5-7*x^4)*log(5)^2+(8*x^5-28*x^4)*log(5)+2*x^ 9-8*x^8+8*x^5-28*x^4)*log(x)+(x^2-4*x+2)*log(5)^4+(8*x^2-32*x+16)*log(5)^3 +(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*log(5)^2+(8*x^6-64*x^5+108*x^4+32*x^ 2-128*x+64)*log(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/ (x^8*log(x)^2+((2*x^5-4*x^4)*log(5)^2+(8*x^5-16*x^4)*log(5)+2*x^9-8*x^8+8* x^5-16*x^4)*log(x)+(x^2-4*x+4)*log(5)^4+(8*x^2-32*x+32)*log(5)^3+(2*x^6-12 *x^5+16*x^4+24*x^2-96*x+96)*log(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128 )*log(5)+x^10-8*x^9+16*x^8+8*x^6-48*x^5+64*x^4+16*x^2-64*x+64),x, algorith m=\
x + (x*log(5)^2 + 4*x*log(5) + 4*x)/(x^5 + x^4*log(x) - 4*x^4 + x*log(5)^2 + 4*x*log(5) - 2*log(5)^2 + 4*x - 8*log(5) - 8)
Timed out. \begin {dmath*} \int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx=\int \frac {{\ln \left (5\right )}^4\,\left (x^2-4\,x+2\right )-\ln \left (x\right )\,\left (\ln \left (5\right )\,\left (28\,x^4-8\,x^5\right )+28\,x^4-8\,x^5+8\,x^8-2\,x^9+{\ln \left (5\right )}^2\,\left (7\,x^4-2\,x^5\right )\right )-64\,x+{\ln \left (5\right )}^2\,\left (2\,x^6-16\,x^5+27\,x^4+24\,x^2-96\,x+48\right )+x^8\,{\ln \left (x\right )}^2+{\ln \left (5\right )}^3\,\left (8\,x^2-32\,x+16\right )+16\,x^2+108\,x^4-64\,x^5+8\,x^6+16\,x^8-8\,x^9+x^{10}+\ln \left (5\right )\,\left (8\,x^6-64\,x^5+108\,x^4+32\,x^2-128\,x+64\right )+32}{{\ln \left (5\right )}^4\,\left (x^2-4\,x+4\right )-\ln \left (x\right )\,\left (\ln \left (5\right )\,\left (16\,x^4-8\,x^5\right )+16\,x^4-8\,x^5+8\,x^8-2\,x^9+{\ln \left (5\right )}^2\,\left (4\,x^4-2\,x^5\right )\right )-64\,x+{\ln \left (5\right )}^2\,\left (2\,x^6-12\,x^5+16\,x^4+24\,x^2-96\,x+96\right )+x^8\,{\ln \left (x\right )}^2+{\ln \left (5\right )}^3\,\left (8\,x^2-32\,x+32\right )+16\,x^2+64\,x^4-48\,x^5+8\,x^6+16\,x^8-8\,x^9+x^{10}+\ln \left (5\right )\,\left (8\,x^6-48\,x^5+64\,x^4+32\,x^2-128\,x+128\right )+64} \,d x \end {dmath*}
int((log(5)^4*(x^2 - 4*x + 2) - log(x)*(log(5)*(28*x^4 - 8*x^5) + 28*x^4 - 8*x^5 + 8*x^8 - 2*x^9 + log(5)^2*(7*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x ^2 - 96*x + 27*x^4 - 16*x^5 + 2*x^6 + 48) + x^8*log(x)^2 + log(5)^3*(8*x^2 - 32*x + 16) + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*(32*x^2 - 128*x + 108*x^4 - 64*x^5 + 8*x^6 + 64) + 32)/(log(5)^4* (x^2 - 4*x + 4) - log(x)*(log(5)*(16*x^4 - 8*x^5) + 16*x^4 - 8*x^5 + 8*x^8 - 2*x^9 + log(5)^2*(4*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x^2 - 96*x + 16 *x^4 - 12*x^5 + 2*x^6 + 96) + x^8*log(x)^2 + log(5)^3*(8*x^2 - 32*x + 32) + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*(32*x^ 2 - 128*x + 64*x^4 - 48*x^5 + 8*x^6 + 128) + 64),x)
int((log(5)^4*(x^2 - 4*x + 2) - log(x)*(log(5)*(28*x^4 - 8*x^5) + 28*x^4 - 8*x^5 + 8*x^8 - 2*x^9 + log(5)^2*(7*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x ^2 - 96*x + 27*x^4 - 16*x^5 + 2*x^6 + 48) + x^8*log(x)^2 + log(5)^3*(8*x^2 - 32*x + 16) + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*(32*x^2 - 128*x + 108*x^4 - 64*x^5 + 8*x^6 + 64) + 32)/(log(5)^4* (x^2 - 4*x + 4) - log(x)*(log(5)*(16*x^4 - 8*x^5) + 16*x^4 - 8*x^5 + 8*x^8 - 2*x^9 + log(5)^2*(4*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x^2 - 96*x + 16 *x^4 - 12*x^5 + 2*x^6 + 96) + x^8*log(x)^2 + log(5)^3*(8*x^2 - 32*x + 32) + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*(32*x^ 2 - 128*x + 64*x^4 - 48*x^5 + 8*x^6 + 128) + 64), x)