Integrand size = 180, antiderivative size = 28 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=x+(2+3 x)^2+\frac {2 x}{\log \left (-9+\frac {x}{(-5+x) \log (x)}\right )} \] Output:
2*x/ln(x/ln(x)/(-5+x)-9)+(2+3*x)^2+x
Time = 0.10 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=13 x+9 x^2+\frac {2 x}{\log \left (-9+\frac {x}{(-5+x) \log (x)}\right )} \] Input:
Integrate[(10*x - 2*x^2 - 10*x*Log[x] + ((10*x - 2*x^2)*Log[x] + (450 - 18 0*x + 18*x^2)*Log[x]^2)*Log[(x + (45 - 9*x)*Log[x])/((-5 + x)*Log[x])] + ( (65*x + 77*x^2 - 18*x^3)*Log[x] + (2925 + 2880*x - 1503*x^2 + 162*x^3)*Log [x]^2)*Log[(x + (45 - 9*x)*Log[x])/((-5 + x)*Log[x])]^2)/(((5*x - x^2)*Log [x] + (225 - 90*x + 9*x^2)*Log[x]^2)*Log[(x + (45 - 9*x)*Log[x])/((-5 + x) *Log[x])]^2),x]
Output:
13*x + 9*x^2 + (2*x)/Log[-9 + x/((-5 + x)*Log[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.
| \(\displaystyle \int \frac {-2 x^2+\left (\left (18 x^2-180 x+450\right ) \log ^2(x)+\left (10 x-2 x^2\right ) \log (x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(x-5) \log (x)}\right )+\left (\left (162 x^3-1503 x^2+2880 x+2925\right ) \log ^2(x)+\left (-18 x^3+77 x^2+65 x\right ) \log (x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(x-5) \log (x)}\right )+10 x-10 x \log (x)}{\left (\left (9 x^2-90 x+225\right ) \log ^2(x)+\left (5 x-x^2\right ) \log (x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(x-5) \log (x)}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-2 x^2+\left (\left (18 x^2-180 x+450\right ) \log ^2(x)+\left (10 x-2 x^2\right ) \log (x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(x-5) \log (x)}\right )+\left (\left (162 x^3-1503 x^2+2880 x+2925\right ) \log ^2(x)+\left (-18 x^3+77 x^2+65 x\right ) \log (x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(x-5) \log (x)}\right )+10 x-10 x \log (x)}{(5-x) \log (x) (x-9 x \log (x)+45 \log (x)) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(x-5) \log (x)}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (18 x-\frac {2 x (x+5 \log (x)-5)}{(x-5) \log (x) (-x+9 x \log (x)-45 \log (x)) \log ^2\left (\frac {x}{(x-5) \log (x)}-9\right )}+\frac {2}{\log \left (\frac {x}{(x-5) \log (x)}-9\right )}+13\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -10 \int \frac {1}{(9 \log (x) x-x-45 \log (x)) \log ^2\left (\frac {x}{(x-5) \log (x)}-9\right )}dx-50 \int \frac {1}{(x-5) (9 \log (x) x-x-45 \log (x)) \log ^2\left (\frac {x}{(x-5) \log (x)}-9\right )}dx-2 \int \frac {x}{\log (x) (9 \log (x) x-x-45 \log (x)) \log ^2\left (\frac {x}{(x-5) \log (x)}-9\right )}dx+2 \int \frac {1}{\log \left (\frac {x}{(x-5) \log (x)}-9\right )}dx+9 x^2+13 x\) |
Input:
Int[(10*x - 2*x^2 - 10*x*Log[x] + ((10*x - 2*x^2)*Log[x] + (450 - 180*x + 18*x^2)*Log[x]^2)*Log[(x + (45 - 9*x)*Log[x])/((-5 + x)*Log[x])] + ((65*x + 77*x^2 - 18*x^3)*Log[x] + (2925 + 2880*x - 1503*x^2 + 162*x^3)*Log[x]^2) *Log[(x + (45 - 9*x)*Log[x])/((-5 + x)*Log[x])]^2)/(((5*x - x^2)*Log[x] + (225 - 90*x + 9*x^2)*Log[x]^2)*Log[(x + (45 - 9*x)*Log[x])/((-5 + x)*Log[x ])]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(28)=56\).
Time = 3.02 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.68
| method | result | size |
| parallelrisch | \(\frac {14580 x^{2} \ln \left (\frac {\left (-9 x +45\right ) \ln \left (x \right )+x}{\ln \left (x \right ) \left (-5+x \right )}\right )+21060 \ln \left (\frac {\left (-9 x +45\right ) \ln \left (x \right )+x}{\ln \left (x \right ) \left (-5+x \right )}\right ) x +3240 x -206550 \ln \left (\frac {\left (-9 x +45\right ) \ln \left (x \right )+x}{\ln \left (x \right ) \left (-5+x \right )}\right )}{1620 \ln \left (\frac {\left (-9 x +45\right ) \ln \left (x \right )+x}{\ln \left (x \right ) \left (-5+x \right )}\right )}\) | \(103\) |
| risch | \(9 x^{2}+13 x -\frac {4 i x}{-2 \pi \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{\ln \left (x \right ) \left (-5+x \right )}\right )^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{-5+x}\right ) \operatorname {csgn}\left (i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{-5+x}\right )+\pi \,\operatorname {csgn}\left (\frac {i}{-5+x}\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{-5+x}\right )^{2}+\pi \,\operatorname {csgn}\left (i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{-5+x}\right )^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{-5+x}\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{\ln \left (x \right ) \left (-5+x \right )}\right )+\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{\ln \left (x \right ) \left (-5+x \right )}\right )^{2}-\pi \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{-5+x}\right )^{3}+\pi \,\operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{-5+x}\right ) \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{\ln \left (x \right ) \left (-5+x \right )}\right )^{2}+\pi \operatorname {csgn}\left (\frac {i \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )}{\ln \left (x \right ) \left (-5+x \right )}\right )^{3}+2 \pi -2 i \ln \left (\left (\ln \left (x \right )-\frac {1}{9}\right ) x -5 \ln \left (x \right )\right )-4 i \ln \left (3\right )+2 i \ln \left (-5+x \right )+2 i \ln \left (\ln \left (x \right )\right )}\) | \(393\) |
Input:
int((((162*x^3-1503*x^2+2880*x+2925)*ln(x)^2+(-18*x^3+77*x^2+65*x)*ln(x))* ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x))^2+((18*x^2-180*x+450)*ln(x)^2+(-2*x^2 +10*x)*ln(x))*ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x))-10*x*ln(x)-2*x^2+10*x)/ ((9*x^2-90*x+225)*ln(x)^2+(-x^2+5*x)*ln(x))/ln(((-9*x+45)*ln(x)+x)/ln(x)/( -5+x))^2,x,method=_RETURNVERBOSE)
Output:
1/1620*(14580*x^2*ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x))+21060*ln(((-9*x+45) *ln(x)+x)/ln(x)/(-5+x))*x+3240*x-206550*ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x )))/ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x))
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (28) = 56\).
Time = 0.10 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=\frac {{\left (9 \, x^{2} + 13 \, x\right )} \log \left (-\frac {9 \, {\left (x - 5\right )} \log \left (x\right ) - x}{{\left (x - 5\right )} \log \left (x\right )}\right ) + 2 \, x}{\log \left (-\frac {9 \, {\left (x - 5\right )} \log \left (x\right ) - x}{{\left (x - 5\right )} \log \left (x\right )}\right )} \] Input:
integrate((((162*x^3-1503*x^2+2880*x+2925)*log(x)^2+(-18*x^3+77*x^2+65*x)* log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))^2+((18*x^2-180*x+450)*log( x)^2+(-2*x^2+10*x)*log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))-10*x*lo g(x)-2*x^2+10*x)/((9*x^2-90*x+225)*log(x)^2+(-x^2+5*x)*log(x))/log(((-9*x+ 45)*log(x)+x)/log(x)/(-5+x))^2,x, algorithm="fricas")
Output:
((9*x^2 + 13*x)*log(-(9*(x - 5)*log(x) - x)/((x - 5)*log(x))) + 2*x)/log(- (9*(x - 5)*log(x) - x)/((x - 5)*log(x)))
Time = 0.20 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=9 x^{2} + 13 x + \frac {2 x}{\log {\left (\frac {x + \left (45 - 9 x\right ) \log {\left (x \right )}}{\left (x - 5\right ) \log {\left (x \right )}} \right )}} \] Input:
integrate((((162*x**3-1503*x**2+2880*x+2925)*ln(x)**2+(-18*x**3+77*x**2+65 *x)*ln(x))*ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x))**2+((18*x**2-180*x+450)*ln (x)**2+(-2*x**2+10*x)*ln(x))*ln(((-9*x+45)*ln(x)+x)/ln(x)/(-5+x))-10*x*ln( x)-2*x**2+10*x)/((9*x**2-90*x+225)*ln(x)**2+(-x**2+5*x)*ln(x))/ln(((-9*x+4 5)*ln(x)+x)/ln(x)/(-5+x))**2,x)
Output:
9*x**2 + 13*x + 2*x/log((x + (45 - 9*x)*log(x))/((x - 5)*log(x)))
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (28) = 56\).
Time = 0.10 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.79 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=\frac {{\left (9 \, x^{2} + 13 \, x\right )} \log \left (-9 \, {\left (x - 5\right )} \log \left (x\right ) + x\right ) - {\left (9 \, x^{2} + 13 \, x\right )} \log \left (x - 5\right ) - {\left (9 \, x^{2} + 13 \, x\right )} \log \left (\log \left (x\right )\right ) + 2 \, x}{\log \left (-9 \, {\left (x - 5\right )} \log \left (x\right ) + x\right ) - \log \left (x - 5\right ) - \log \left (\log \left (x\right )\right )} \] Input:
integrate((((162*x^3-1503*x^2+2880*x+2925)*log(x)^2+(-18*x^3+77*x^2+65*x)* log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))^2+((18*x^2-180*x+450)*log( x)^2+(-2*x^2+10*x)*log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))-10*x*lo g(x)-2*x^2+10*x)/((9*x^2-90*x+225)*log(x)^2+(-x^2+5*x)*log(x))/log(((-9*x+ 45)*log(x)+x)/log(x)/(-5+x))^2,x, algorithm="maxima")
Output:
((9*x^2 + 13*x)*log(-9*(x - 5)*log(x) + x) - (9*x^2 + 13*x)*log(x - 5) - ( 9*x^2 + 13*x)*log(log(x)) + 2*x)/(log(-9*(x - 5)*log(x) + x) - log(x - 5) - log(log(x)))
Time = 0.38 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=9 \, x^{2} + 13 \, x - \frac {2 \, x}{\log \left (x \log \left (x\right ) - 5 \, \log \left (x\right )\right ) - \log \left (-9 \, x \log \left (x\right ) + x + 45 \, \log \left (x\right )\right )} \] Input:
integrate((((162*x^3-1503*x^2+2880*x+2925)*log(x)^2+(-18*x^3+77*x^2+65*x)* log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))^2+((18*x^2-180*x+450)*log( x)^2+(-2*x^2+10*x)*log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))-10*x*lo g(x)-2*x^2+10*x)/((9*x^2-90*x+225)*log(x)^2+(-x^2+5*x)*log(x))/log(((-9*x+ 45)*log(x)+x)/log(x)/(-5+x))^2,x, algorithm="giac")
Output:
9*x^2 + 13*x - 2*x/(log(x*log(x) - 5*log(x)) - log(-9*x*log(x) + x + 45*lo g(x)))
Time = 4.29 (sec) , antiderivative size = 184, normalized size of antiderivative = 6.57 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=451\,x+90\,\ln \left (x\right )+\frac {14000}{x+5}-\frac {\frac {2\,{\left (x-5\right )}^2\,\left (27\,x^3-305\,x^2+1075\,x-1125\right )}{25\,\left (x+5\right )}+\frac {2\,x\,\ln \left (x\right )\,\left (36\,x^3-525\,x^2+2600\,x-4375\right )}{5\,\left (x+5\right )}}{x+5\,\ln \left (x\right )-5}+\frac {2\,x+\frac {2\,\ln \left (\frac {x-\ln \left (x\right )\,\left (9\,x-45\right )}{\ln \left (x\right )\,\left (x-5\right )}\right )\,\ln \left (x\right )\,\left (x-5\right )\,\left (x+45\,\ln \left (x\right )-9\,x\,\ln \left (x\right )\right )}{x+5\,\ln \left (x\right )-5}}{\ln \left (\frac {x-\ln \left (x\right )\,\left (9\,x-45\right )}{\ln \left (x\right )\,\left (x-5\right )}\right )}-\ln \left (x\right )\,\left (36\,x-\frac {18\,x^2}{5}\right )-37\,x^2+\frac {54\,x^3}{25} \] Input:
int((10*x + log((x - log(x)*(9*x - 45))/(log(x)*(x - 5)))*(log(x)^2*(18*x^ 2 - 180*x + 450) + log(x)*(10*x - 2*x^2)) - 10*x*log(x) - 2*x^2 + log((x - log(x)*(9*x - 45))/(log(x)*(x - 5)))^2*(log(x)^2*(2880*x - 1503*x^2 + 162 *x^3 + 2925) + log(x)*(65*x + 77*x^2 - 18*x^3)))/(log((x - log(x)*(9*x - 4 5))/(log(x)*(x - 5)))^2*(log(x)^2*(9*x^2 - 90*x + 225) + log(x)*(5*x - x^2 ))),x)
Output:
451*x + 90*log(x) + 14000/(x + 5) - ((2*(x - 5)^2*(1075*x - 305*x^2 + 27*x ^3 - 1125))/(25*(x + 5)) + (2*x*log(x)*(2600*x - 525*x^2 + 36*x^3 - 4375)) /(5*(x + 5)))/(x + 5*log(x) - 5) + (2*x + (2*log((x - log(x)*(9*x - 45))/( log(x)*(x - 5)))*log(x)*(x - 5)*(x + 45*log(x) - 9*x*log(x)))/(x + 5*log(x ) - 5))/log((x - log(x)*(9*x - 45))/(log(x)*(x - 5))) - log(x)*(36*x - (18 *x^2)/5) - 37*x^2 + (54*x^3)/25
Time = 0.16 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.96 \[ \int \frac {10 x-2 x^2-10 x \log (x)+\left (\left (10 x-2 x^2\right ) \log (x)+\left (450-180 x+18 x^2\right ) \log ^2(x)\right ) \log \left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )+\left (\left (65 x+77 x^2-18 x^3\right ) \log (x)+\left (2925+2880 x-1503 x^2+162 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )}{\left (\left (5 x-x^2\right ) \log (x)+\left (225-90 x+9 x^2\right ) \log ^2(x)\right ) \log ^2\left (\frac {x+(45-9 x) \log (x)}{(-5+x) \log (x)}\right )} \, dx=\frac {x \left (9 \,\mathrm {log}\left (\frac {-9 \,\mathrm {log}\left (x \right ) x +45 \,\mathrm {log}\left (x \right )+x}{\mathrm {log}\left (x \right ) x -5 \,\mathrm {log}\left (x \right )}\right ) x +13 \,\mathrm {log}\left (\frac {-9 \,\mathrm {log}\left (x \right ) x +45 \,\mathrm {log}\left (x \right )+x}{\mathrm {log}\left (x \right ) x -5 \,\mathrm {log}\left (x \right )}\right )+2\right )}{\mathrm {log}\left (\frac {-9 \,\mathrm {log}\left (x \right ) x +45 \,\mathrm {log}\left (x \right )+x}{\mathrm {log}\left (x \right ) x -5 \,\mathrm {log}\left (x \right )}\right )} \] Input:
int((((162*x^3-1503*x^2+2880*x+2925)*log(x)^2+(-18*x^3+77*x^2+65*x)*log(x) )*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))^2+((18*x^2-180*x+450)*log(x)^2+( -2*x^2+10*x)*log(x))*log(((-9*x+45)*log(x)+x)/log(x)/(-5+x))-10*x*log(x)-2 *x^2+10*x)/((9*x^2-90*x+225)*log(x)^2+(-x^2+5*x)*log(x))/log(((-9*x+45)*lo g(x)+x)/log(x)/(-5+x))^2,x)
Output:
(x*(9*log(( - 9*log(x)*x + 45*log(x) + x)/(log(x)*x - 5*log(x)))*x + 13*lo g(( - 9*log(x)*x + 45*log(x) + x)/(log(x)*x - 5*log(x))) + 2))/log(( - 9*l og(x)*x + 45*log(x) + x)/(log(x)*x - 5*log(x)))