Integrand size = 182, antiderivative size = 28 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\frac {\log ^2(8)}{9 \left (x^3-\log (x)\right )^2 \log ^2\left (\frac {x}{(-5+x)^2}\right )} \]
Time = 0.51 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\frac {\log ^2(8)}{9 \left (x^3-\log (x)\right )^2 \log ^2\left (\frac {x}{(-5+x)^2}\right )} \]
Integrate[((-10*x^3 - 2*x^4)*Log[8]^2 + (10 + 2*x)*Log[8]^2*Log[x] + (10 - 2*x - 30*x^3 + 6*x^4)*Log[8]^2*Log[x/(25 - 10*x + x^2)])/((45*x^10 - 9*x^ 11)*Log[x/(25 - 10*x + x^2)]^3 + (-135*x^7 + 27*x^8)*Log[x]*Log[x/(25 - 10 *x + x^2)]^3 + (135*x^4 - 27*x^5)*Log[x]^2*Log[x/(25 - 10*x + x^2)]^3 + (- 45*x + 9*x^2)*Log[x]^3*Log[x/(25 - 10*x + x^2)]^3),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.
| \(\displaystyle \int \frac {\left (-2 x^4-10 x^3\right ) \log ^2(8)+\left (6 x^4-30 x^3-2 x+10\right ) \log ^2(8) \log \left (\frac {x}{x^2-10 x+25}\right )+(2 x+10) \log ^2(8) \log (x)}{\left (9 x^2-45 x\right ) \log ^3(x) \log ^3\left (\frac {x}{x^2-10 x+25}\right )+\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{x^2-10 x+25}\right )+\left (27 x^8-135 x^7\right ) \log (x) \log ^3\left (\frac {x}{x^2-10 x+25}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{x^2-10 x+25}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \log ^2(8) \left (-\left ((x+5) x^3\right )+\left (3 x^4-15 x^3-x+5\right ) \log \left (\frac {x}{(x-5)^2}\right )+(x+5) \log (x)\right )}{9 (5-x) x \left (x^3-\log (x)\right )^3 \log ^3\left (\frac {x}{(x-5)^2}\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{9} \log ^2(8) \int -\frac {(x+5) x^3-(x+5) \log (x)-\left (3 x^4-15 x^3-x+5\right ) \log \left (\frac {x}{(5-x)^2}\right )}{(5-x) x \left (x^3-\log (x)\right )^3 \log ^3\left (\frac {x}{(5-x)^2}\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {2}{9} \log ^2(8) \int \frac {(x+5) x^3-(x+5) \log (x)-\left (3 x^4-15 x^3-x+5\right ) \log \left (\frac {x}{(5-x)^2}\right )}{(5-x) x \left (x^3-\log (x)\right )^3 \log ^3\left (\frac {x}{(5-x)^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {2}{9} \log ^2(8) \int \left (\frac {-x-5}{(x-5) x \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(x-5)^2}\right )}+\frac {3 x^3-1}{x \left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(x-5)^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2}{9} \log ^2(8) \left (-2 \int \frac {1}{(x-5) \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(x-5)^2}\right )}dx+\int \frac {1}{x \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(x-5)^2}\right )}dx-\int \frac {1}{x \left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(x-5)^2}\right )}dx+3 \int \frac {x^2}{\left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(x-5)^2}\right )}dx\right )\) |
Int[((-10*x^3 - 2*x^4)*Log[8]^2 + (10 + 2*x)*Log[8]^2*Log[x] + (10 - 2*x - 30*x^3 + 6*x^4)*Log[8]^2*Log[x/(25 - 10*x + x^2)])/((45*x^10 - 9*x^11)*Lo g[x/(25 - 10*x + x^2)]^3 + (-135*x^7 + 27*x^8)*Log[x]*Log[x/(25 - 10*x + x ^2)]^3 + (135*x^4 - 27*x^5)*Log[x]^2*Log[x/(25 - 10*x + x^2)]^3 + (-45*x + 9*x^2)*Log[x]^3*Log[x/(25 - 10*x + x^2)]^3),x]
3.9.29.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 45.08 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.36
| method | result | size |
| parallelrisch | \(\frac {\ln \left (2\right )^{2}}{\left (x^{6}-2 x^{3} \ln \left (x \right )+\ln \left (x \right )^{2}\right ) \ln \left (\frac {x}{x^{2}-10 x +25}\right )^{2}}\) | \(38\) |
| risch | \(-\frac {4 \ln \left (2\right )^{2}}{{\left (-\pi \,\operatorname {csgn}\left (\frac {i}{\left (-5+x \right )^{2}}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\left (-5+x \right )^{2}}\right )+\pi \,\operatorname {csgn}\left (\frac {i}{\left (-5+x \right )^{2}}\right ) \operatorname {csgn}\left (\frac {i x}{\left (-5+x \right )^{2}}\right )^{2}+\pi \operatorname {csgn}\left (i \left (-5+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-5+x \right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (-5+x \right )\right ) \operatorname {csgn}\left (i \left (-5+x \right )^{2}\right )^{2}+\pi \operatorname {csgn}\left (i \left (-5+x \right )^{2}\right )^{3}+\pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\left (-5+x \right )^{2}}\right )^{2}-\pi \operatorname {csgn}\left (\frac {i x}{\left (-5+x \right )^{2}}\right )^{3}+4 i \ln \left (-5+x \right )-2 i \ln \left (x \right )\right )}^{2} \left (x^{6}-2 x^{3} \ln \left (x \right )+\ln \left (x \right )^{2}\right )}\) | \(177\) |
int((9*(2*x+10)*ln(2)^2*ln(x)+9*(6*x^4-30*x^3-2*x+10)*ln(2)^2*ln(x/(x^2-10 *x+25))+9*(-2*x^4-10*x^3)*ln(2)^2)/((9*x^2-45*x)*ln(x/(x^2-10*x+25))^3*ln( x)^3+(-27*x^5+135*x^4)*ln(x/(x^2-10*x+25))^3*ln(x)^2+(27*x^8-135*x^7)*ln(x /(x^2-10*x+25))^3*ln(x)+(-9*x^11+45*x^10)*ln(x/(x^2-10*x+25))^3),x,method= _RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (25) = 50\).
Time = 0.24 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.46 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\frac {\log \left (2\right )^{2}}{x^{6} \log \left (\frac {x}{x^{2} - 10 \, x + 25}\right )^{2} - 2 \, x^{3} \log \left (x\right ) \log \left (\frac {x}{x^{2} - 10 \, x + 25}\right )^{2} + \log \left (x\right )^{2} \log \left (\frac {x}{x^{2} - 10 \, x + 25}\right )^{2}} \]
integrate((9*(2*x+10)*log(2)^2*log(x)+9*(6*x^4-30*x^3-2*x+10)*log(2)^2*log (x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*log(2)^2)/((9*x^2-45*x)*log(x/(x^2-10* x+25))^3*log(x)^3+(-27*x^5+135*x^4)*log(x/(x^2-10*x+25))^3*log(x)^2+(27*x^ 8-135*x^7)*log(x/(x^2-10*x+25))^3*log(x)+(-9*x^11+45*x^10)*log(x/(x^2-10*x +25))^3),x, algorithm=\
log(2)^2/(x^6*log(x/(x^2 - 10*x + 25))^2 - 2*x^3*log(x)*log(x/(x^2 - 10*x + 25))^2 + log(x)^2*log(x/(x^2 - 10*x + 25))^2)
Time = 0.14 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\frac {\log {\left (2 \right )}^{2}}{\left (x^{6} - 2 x^{3} \log {\left (x \right )} + \log {\left (x \right )}^{2}\right ) \log {\left (\frac {x}{x^{2} - 10 x + 25} \right )}^{2}} \]
integrate((9*(2*x+10)*ln(2)**2*ln(x)+9*(6*x**4-30*x**3-2*x+10)*ln(2)**2*ln (x/(x**2-10*x+25))+9*(-2*x**4-10*x**3)*ln(2)**2)/((9*x**2-45*x)*ln(x/(x**2 -10*x+25))**3*ln(x)**3+(-27*x**5+135*x**4)*ln(x/(x**2-10*x+25))**3*ln(x)** 2+(27*x**8-135*x**7)*ln(x/(x**2-10*x+25))**3*ln(x)+(-9*x**11+45*x**10)*ln( x/(x**2-10*x+25))**3),x)
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (25) = 50\).
Time = 0.34 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.79 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\frac {\log \left (2\right )^{2}}{x^{6} \log \left (x\right )^{2} - 2 \, x^{3} \log \left (x\right )^{3} + \log \left (x\right )^{4} + 4 \, {\left (x^{6} - 2 \, x^{3} \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (x - 5\right )^{2} - 4 \, {\left (x^{6} \log \left (x\right ) - 2 \, x^{3} \log \left (x\right )^{2} + \log \left (x\right )^{3}\right )} \log \left (x - 5\right )} \]
integrate((9*(2*x+10)*log(2)^2*log(x)+9*(6*x^4-30*x^3-2*x+10)*log(2)^2*log (x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*log(2)^2)/((9*x^2-45*x)*log(x/(x^2-10* x+25))^3*log(x)^3+(-27*x^5+135*x^4)*log(x/(x^2-10*x+25))^3*log(x)^2+(27*x^ 8-135*x^7)*log(x/(x^2-10*x+25))^3*log(x)+(-9*x^11+45*x^10)*log(x/(x^2-10*x +25))^3),x, algorithm=\
log(2)^2/(x^6*log(x)^2 - 2*x^3*log(x)^3 + log(x)^4 + 4*(x^6 - 2*x^3*log(x) + log(x)^2)*log(x - 5)^2 - 4*(x^6*log(x) - 2*x^3*log(x)^2 + log(x)^3)*log (x - 5))
Leaf count of result is larger than twice the leaf count of optimal. 264 vs. \(2 (25) = 50\).
Time = 2.97 (sec) , antiderivative size = 264, normalized size of antiderivative = 9.43 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\frac {x \log \left (2\right )^{2} + 5 \, \log \left (2\right )^{2}}{x^{7} \log \left (x^{2} - 10 \, x + 25\right )^{2} - 2 \, x^{7} \log \left (x^{2} - 10 \, x + 25\right ) \log \left (x\right ) + x^{7} \log \left (x\right )^{2} + 5 \, x^{6} \log \left (x^{2} - 10 \, x + 25\right )^{2} - 10 \, x^{6} \log \left (x^{2} - 10 \, x + 25\right ) \log \left (x\right ) + 5 \, x^{6} \log \left (x\right )^{2} - 2 \, x^{4} \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \left (x\right ) + 4 \, x^{4} \log \left (x^{2} - 10 \, x + 25\right ) \log \left (x\right )^{2} - 2 \, x^{4} \log \left (x\right )^{3} - 10 \, x^{3} \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \left (x\right ) + 20 \, x^{3} \log \left (x^{2} - 10 \, x + 25\right ) \log \left (x\right )^{2} - 10 \, x^{3} \log \left (x\right )^{3} + x \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \left (x\right )^{2} - 2 \, x \log \left (x^{2} - 10 \, x + 25\right ) \log \left (x\right )^{3} + x \log \left (x\right )^{4} + 5 \, \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \left (x\right )^{2} - 10 \, \log \left (x^{2} - 10 \, x + 25\right ) \log \left (x\right )^{3} + 5 \, \log \left (x\right )^{4}} \]
integrate((9*(2*x+10)*log(2)^2*log(x)+9*(6*x^4-30*x^3-2*x+10)*log(2)^2*log (x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*log(2)^2)/((9*x^2-45*x)*log(x/(x^2-10* x+25))^3*log(x)^3+(-27*x^5+135*x^4)*log(x/(x^2-10*x+25))^3*log(x)^2+(27*x^ 8-135*x^7)*log(x/(x^2-10*x+25))^3*log(x)+(-9*x^11+45*x^10)*log(x/(x^2-10*x +25))^3),x, algorithm=\
(x*log(2)^2 + 5*log(2)^2)/(x^7*log(x^2 - 10*x + 25)^2 - 2*x^7*log(x^2 - 10 *x + 25)*log(x) + x^7*log(x)^2 + 5*x^6*log(x^2 - 10*x + 25)^2 - 10*x^6*log (x^2 - 10*x + 25)*log(x) + 5*x^6*log(x)^2 - 2*x^4*log(x^2 - 10*x + 25)^2*l og(x) + 4*x^4*log(x^2 - 10*x + 25)*log(x)^2 - 2*x^4*log(x)^3 - 10*x^3*log( x^2 - 10*x + 25)^2*log(x) + 20*x^3*log(x^2 - 10*x + 25)*log(x)^2 - 10*x^3* log(x)^3 + x*log(x^2 - 10*x + 25)^2*log(x)^2 - 2*x*log(x^2 - 10*x + 25)*lo g(x)^3 + x*log(x)^4 + 5*log(x^2 - 10*x + 25)^2*log(x)^2 - 10*log(x^2 - 10* x + 25)*log(x)^3 + 5*log(x)^4)
Time = 14.46 (sec) , antiderivative size = 2546, normalized size of antiderivative = 90.93 \[ \int \frac {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx=\text {Too large to display} \]
int(-(9*log(2)^2*(10*x^3 + 2*x^4) - 9*log(2)^2*log(x)*(2*x + 10) + 9*log(2 )^2*log(x/(x^2 - 10*x + 25))*(2*x + 30*x^3 - 6*x^4 - 10))/(log(x/(x^2 - 10 *x + 25))^3*(45*x^10 - 9*x^11) - log(x/(x^2 - 10*x + 25))^3*log(x)^3*(45*x - 9*x^2) - log(x/(x^2 - 10*x + 25))^3*log(x)*(135*x^7 - 27*x^8) + log(x/( x^2 - 10*x + 25))^3*log(x)^2*(135*x^4 - 27*x^5)),x)
((log(2)^2*(600*x^2 + 67500*x^3 + 2238*x^4 - 5400*x^5 - 151965*x^6 - 13142 *x^7 + 11950*x^8 + 68050*x^9 + 12507*x^10 - 4800*x^11 - 570*x^12 + 108*x^1 3 - 7500))/(4*(3*x^3 - 1)*(x + 5)^4) + (x*log(2)^2*log(x)^2*(16885*x^2 - 2 00*x - 7500*x^3 - 750*x^4 + 240*x^5 + 27*x^6 + 250))/(4*(3*x^3 - 1)*(x + 5 )^4) + (x*log(2)^2*log(x)*(13000*x^3 - 50535*x^2 + 4450*x^4 + 117565*x^5 - 5331*x^6 - 10650*x^7 + 330*x^8 + 189*x^9 - 2250))/(4*(3*x^3 - 1)*(x + 5)^ 4))/(log(x)^4 - 4*x^9*log(x) - 4*x^3*log(x)^3 + 6*x^6*log(x)^2 + x^12) - ( (x*log(x)*(589575*x^2*log(2)^2 - 194305*x^3*log(2)^2 - 52750*x^4*log(2)^2 - 3026950*x^5*log(2)^2 + 628435*x^6*log(2)^2 + 390939*x^7*log(2)^2 + 52941 75*x^8*log(2)^2 - 681405*x^9*log(2)^2 - 799722*x^10*log(2)^2 - 2250*x^11*l og(2)^2 + 21825*x^12*log(2)^2 + 1701*x^13*log(2)^2 - 5250*x*log(2)^2 + 875 0*log(2)^2))/(12*(3*x^3 - 1)^3*(x + 5)^5) - (x*(421125*x^2*log(2)^2 - 1320 25*x^3*log(2)^2 - 84000*x^4*log(2)^2 - 3205050*x^5*log(2)^2 + 60045*x^6*lo g(2)^2 + 456385*x^7*log(2)^2 + 8130250*x^8*log(2)^2 + 1026770*x^9*log(2)^2 - 909276*x^10*log(2)^2 - 6201150*x^11*log(2)^2 - 1722900*x^12*log(2)^2 + 463842*x^13*log(2)^2 + 134550*x^14*log(2)^2 - 7650*x^15*log(2)^2 - 1944*x^ 16*log(2)^2 + 3750*x*log(2)^2 + 18750*log(2)^2))/(12*(3*x^3 - 1)^3*(x + 5) ^5) + (x*log(2)^2*log(x)^2*(2750*x - 253675*x^2 + 159385*x^3 + 17250*x^4 - 3450*x^5 - 316545*x^6 + 44919*x^7 + 15300*x^8 + 900*x^9 - 1250))/(12*(3*x ^3 - 1)^3*(x + 5)^5))/(3*x^6*log(x) + log(x)^3 - 3*x^3*log(x)^2 - x^9) ...