Integrand size = 146, antiderivative size = 28 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\left (-(1+x)^2+2 x \log \left ((-1+5 (2 x-\log (3)))^2\right )\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(72\) vs. \(2(28)=56\).
Time = 0.09 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\frac {1}{250} x \left (1000+1500 x+1000 x^2+250 x^3-5655 \log (3)+1131 \log (243)-160 \log (3) \log (243)+32 \log ^2(243)-1000 (1+x)^2 \log \left ((1-10 x+\log (243))^2\right )+1000 x \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \]
Integrate[(4 + 52*x + 52*x^2 - 36*x^3 - 40*x^4 + (20 + 60*x + 60*x^2 + 20* x^3)*Log[3] + (-4 + 24*x - 12*x^2 + 120*x^3 + (-20 - 80*x - 60*x^2)*Log[3] )*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2] + (8*x - 80* x^2 + 40*x*Log[3])*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3 ]^2]^2)/(1 - 10*x + 5*Log[3]),x]
(x*(1000 + 1500*x + 1000*x^2 + 250*x^3 - 5655*Log[3] + 1131*Log[243] - 160 *Log[3]*Log[243] + 32*Log[243]^2 - 1000*(1 + x)^2*Log[(1 - 10*x + Log[243] )^2] + 1000*x*Log[(1 - 10*x + Log[243])^2]^2))/250
Time = 0.59 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.82, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {7292, 27, 7237}
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.
| \(\displaystyle \int \frac {-40 x^4-36 x^3+52 x^2+\left (-80 x^2+8 x+40 x \log (3)\right ) \log ^2\left (100 x^2-20 x+(10-100 x) \log (3)+1+25 \log ^2(3)\right )+\left (120 x^3-12 x^2+\left (-60 x^2-80 x-20\right ) \log (3)+24 x-4\right ) \log \left (100 x^2-20 x+(10-100 x) \log (3)+1+25 \log ^2(3)\right )+\left (20 x^3+60 x^2+60 x+20\right ) \log (3)+52 x+4}{-10 x+1+5 \log (3)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {4 \left (x^2+2 x-2 x \log \left ((-10 x+1+\log (243))^2\right )+1\right ) \left (-10 x^2+10 x \log \left ((-10 x+1+\log (243))^2\right )+11 x \left (1+\frac {5 \log (3)}{11}\right )-(1+\log (243)) \log \left ((-10 x+1+\log (243))^2\right )+1+\log (243)\right )}{-10 x+1+5 \log (3)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {\left (x^2-2 \log \left ((-10 x+\log (243)+1)^2\right ) x+2 x+1\right ) \left (-10 x^2+10 \log \left ((-10 x+\log (243)+1)^2\right ) x+(11+\log (243)) x-(1+\log (243)) \log \left ((-10 x+\log (243)+1)^2\right )+\log (243)+1\right )}{-10 x+\log (243)+1}dx\) |
| \(\Big \downarrow \) 7237 |
| \(\displaystyle \left (x^2+2 x-2 x \log \left ((-10 x+1+\log (243))^2\right )+1\right )^2\) |
Int[(4 + 52*x + 52*x^2 - 36*x^3 - 40*x^4 + (20 + 60*x + 60*x^2 + 20*x^3)*L og[3] + (-4 + 24*x - 12*x^2 + 120*x^3 + (-20 - 80*x - 60*x^2)*Log[3])*Log[ 1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2] + (8*x - 80*x^2 + 40*x*Log[3])*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2]^2 )/(1 - 10*x + 5*Log[3]),x]
3.11.45.3.1 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_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Si mp[q*(y^(m + 1)/(m + 1)), x] /; !FalseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]
Leaf count of result is larger than twice the leaf count of optimal. \(78\) vs. \(2(25)=50\).
Time = 0.58 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.82
| method | result | size |
| risch | \(4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+\left (-4 x^{3}-8 x^{2}-4 x \right ) \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+\left (1+x \right )^{4}\) | \(79\) |
| norman | \(x^{4}+4 x +6 x^{2}+4 x^{3}-4 x \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )-8 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}-4 x^{3} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )\) | \(138\) |
| parallelrisch | \(x^{4}-4 x^{3} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+4 x^{3}-8 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )-\frac {3 \ln \left (3\right )^{2}}{2}+\frac {37}{50}+6 x^{2}-4 x \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+\frac {17 \ln \left (3\right )}{5}+4 x\) | \(149\) |
| parts | \(-4 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right ) x^{3}-\frac {12 x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{5}+\left (-\ln \left (3\right )^{2}-\frac {2 \ln \left (3\right )}{5}-\frac {1}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+\left (6 \ln \left (3\right )^{2}+\frac {12 \ln \left (3\right )}{5}+\frac {6}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )-\frac {4 x}{5}-8 x \ln \left (3\right )+x^{4}+4 x^{3}+6 x^{2}+80 \left (\frac {\ln \left (3\right )^{3}}{80}+\frac {3 \ln \left (3\right )^{2}}{400}+\frac {3 \ln \left (3\right )}{2000}+\frac {1}{10000}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+48 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+8 \left (x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )-2 x -20 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )\right ) \ln \left (3\right )-\frac {4 \left (\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{10}-\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right )^{2}}{10}\right ) \left (-50 \ln \left (3\right )^{2}-20 \ln \left (3\right )-2\right )}{5}+4 \left (-\frac {\ln \left (3\right )^{3}}{4}-\frac {23 \ln \left (3\right )^{2}}{20}-\frac {143 \ln \left (3\right )}{100}-\frac {121}{500}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+\left (24 \ln \left (3\right )+\frac {24}{5}\right ) x -8 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+\left (-8 \ln \left (3\right )-\frac {8}{5}\right ) x \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )\) | \(463\) |
| default | \(\left (-8 \ln \left (3\right )-\frac {8}{5}\right ) x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )+4 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )^{2} x^{2}-4 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right ) x^{3}-8 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right ) x^{2}-\frac {12 x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{5}-\frac {4 x}{5}-8 x \ln \left (3\right )+x^{4}+4 x^{3}+6 x^{2}+\left (-\ln \left (3\right )^{2}-\frac {2 \ln \left (3\right )}{5}-\frac {1}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )^{2}+\left (6 \ln \left (3\right )^{2}+\frac {12 \ln \left (3\right )}{5}+\frac {6}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )+80 \left (\frac {\ln \left (3\right )^{3}}{80}+\frac {3 \ln \left (3\right )^{2}}{400}+\frac {3 \ln \left (3\right )}{2000}+\frac {1}{10000}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+48 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+8 \left (x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )-2 x -20 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )\right ) \ln \left (3\right )-\frac {4 \left (\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{10}-\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right )^{2}}{10}\right ) \left (-50 \ln \left (3\right )^{2}-20 \ln \left (3\right )-2\right )}{5}+4 \left (-\frac {\ln \left (3\right )^{3}}{4}-\frac {23 \ln \left (3\right )^{2}}{20}-\frac {143 \ln \left (3\right )}{100}-\frac {121}{500}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+\left (24 \ln \left (3\right )+\frac {24}{5}\right ) x\) | \(468\) |
int(((40*x*ln(3)-80*x^2+8*x)*ln(25*ln(3)^2+(-100*x+10)*ln(3)+100*x^2-20*x+ 1)^2+((-60*x^2-80*x-20)*ln(3)+120*x^3-12*x^2+24*x-4)*ln(25*ln(3)^2+(-100*x +10)*ln(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*ln(3)-40*x^4-36*x^3+52* x^2+52*x+4)/(5*ln(3)-10*x+1),x,method=_RETURNVERBOSE)
4*x^2*ln(25*ln(3)^2+(-100*x+10)*ln(3)+100*x^2-20*x+1)^2+(-4*x^3-8*x^2-4*x) *ln(25*ln(3)^2+(-100*x+10)*ln(3)+100*x^2-20*x+1)+(1+x)^4
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (23) = 46\).
Time = 0.25 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^{4} + 4 \, x^{2} \log \left (100 \, x^{2} - 10 \, {\left (10 \, x - 1\right )} \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 1\right )^{2} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (100 \, x^{2} - 10 \, {\left (10 \, x - 1\right )} \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 1\right ) + 4 \, x \]
integrate(((40*x*log(3)-80*x^2+8*x)*log(25*log(3)^2+(-100*x+10)*log(3)+100 *x^2-20*x+1)^2+((-60*x^2-80*x-20)*log(3)+120*x^3-12*x^2+24*x-4)*log(25*log (3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*log(3)-40 *x^4-36*x^3+52*x^2+52*x+4)/(5*log(3)-10*x+1),x, algorithm=\
x^4 + 4*x^2*log(100*x^2 - 10*(10*x - 1)*log(3) + 25*log(3)^2 - 20*x + 1)^2 + 4*x^3 + 6*x^2 - 4*(x^3 + 2*x^2 + x)*log(100*x^2 - 10*(10*x - 1)*log(3) + 25*log(3)^2 - 20*x + 1) + 4*x
Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (22) = 44\).
Time = 0.14 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.29 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^{4} + 4 x^{3} + 4 x^{2} \log {\left (100 x^{2} - 20 x + \left (10 - 100 x\right ) \log {\left (3 \right )} + 1 + 25 \log {\left (3 \right )}^{2} \right )}^{2} + 6 x^{2} + 4 x + \left (- 4 x^{3} - 8 x^{2} - 4 x\right ) \log {\left (100 x^{2} - 20 x + \left (10 - 100 x\right ) \log {\left (3 \right )} + 1 + 25 \log {\left (3 \right )}^{2} \right )} \]
integrate(((40*x*ln(3)-80*x**2+8*x)*ln(25*ln(3)**2+(-100*x+10)*ln(3)+100*x **2-20*x+1)**2+((-60*x**2-80*x-20)*ln(3)+120*x**3-12*x**2+24*x-4)*ln(25*ln (3)**2+(-100*x+10)*ln(3)+100*x**2-20*x+1)+(20*x**3+60*x**2+60*x+20)*ln(3)- 40*x**4-36*x**3+52*x**2+52*x+4)/(5*ln(3)-10*x+1),x)
x**4 + 4*x**3 + 4*x**2*log(100*x**2 - 20*x + (10 - 100*x)*log(3) + 1 + 25* log(3)**2)**2 + 6*x**2 + 4*x + (-4*x**3 - 8*x**2 - 4*x)*log(100*x**2 - 20* x + (10 - 100*x)*log(3) + 1 + 25*log(3)**2)
Leaf count of result is larger than twice the leaf count of optimal. 1507 vs. \(2 (23) = 46\).
Time = 0.31 (sec) , antiderivative size = 1507, normalized size of antiderivative = 53.82 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\text {Too large to display} \]
integrate(((40*x*log(3)-80*x^2+8*x)*log(25*log(3)^2+(-100*x+10)*log(3)+100 *x^2-20*x+1)^2+((-60*x^2-80*x-20)*log(3)+120*x^3-12*x^2+24*x-4)*log(25*log (3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*log(3)-40 *x^4-36*x^3+52*x^2+52*x+4)/(5*log(3)-10*x+1),x, algorithm=\
x^4 + 2/15*x^3*(5*log(3) + 1) - 2/5*((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(3)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log (3) + 1)^2 + 8/75*(25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1)^3 - 8/75*(5*log(3) + 1)*log(10*x - 5*log(3) - 1)^3 + 1/50*(25*log(3)^2 + 10 *log(3) + 1)*x^2 + 58/15*x^3 + 59/50*x^2*(5*log(3) + 1) + 3/50*(50*x^2 + 1 0*x*(5*log(3) + 1) + (25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1 ))*log(3)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 4/5*((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(3)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 2/25*(50*x^2 + 10* x*(5*log(3) + 1) + (25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1)) *log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)^2 - 2/25 *((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(100*x^2 - 100*x*log( 3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)^2 + 2*log(3)*log(100*x^2 - 100*x* log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)*log(10*x - 5*log(3) - 1) + 3/ 250*(125*log(3)^3 + 75*log(3)^2 + 15*log(3) + 1)*log(10*x - 5*log(3) - 1)^ 2 + 117/250*(25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 - 2/2 5*(5*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 + 1/250*(125*log(3)^3 + 75*log (3)^2 + 15*log(3) + 1)*x + 119/250*(25*log(3)^2 + 10*log(3) + 1)*x + 24/5* x^2 + 258/25*x*(5*log(3) + 1) - 4/15*(2*(5*log(3) + 1)*log(10*x - 5*log(3) - 1)^3 + 6*(5*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 - 3*((5*log(3) + ...
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (23) = 46\).
Time = 0.54 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^{4} + 4 \, x^{2} \log \left (100 \, x^{2} - 100 \, x \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 10 \, \log \left (3\right ) + 1\right )^{2} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (100 \, x^{2} - 100 \, x \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 10 \, \log \left (3\right ) + 1\right ) + 4 \, x \]
integrate(((40*x*log(3)-80*x^2+8*x)*log(25*log(3)^2+(-100*x+10)*log(3)+100 *x^2-20*x+1)^2+((-60*x^2-80*x-20)*log(3)+120*x^3-12*x^2+24*x-4)*log(25*log (3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*log(3)-40 *x^4-36*x^3+52*x^2+52*x+4)/(5*log(3)-10*x+1),x, algorithm=\
x^4 + 4*x^2*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)^2 + 4*x^3 + 6*x^2 - 4*(x^3 + 2*x^2 + x)*log(100*x^2 - 100*x*log(3) + 25 *log(3)^2 - 20*x + 10*log(3) + 1) + 4*x
Timed out. \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\int \frac {52\,x-\ln \left (25\,{\ln \left (3\right )}^2-\ln \left (3\right )\,\left (100\,x-10\right )-20\,x+100\,x^2+1\right )\,\left (\ln \left (3\right )\,\left (60\,x^2+80\,x+20\right )-24\,x+12\,x^2-120\,x^3+4\right )+\ln \left (3\right )\,\left (20\,x^3+60\,x^2+60\,x+20\right )+{\ln \left (25\,{\ln \left (3\right )}^2-\ln \left (3\right )\,\left (100\,x-10\right )-20\,x+100\,x^2+1\right )}^2\,\left (8\,x+40\,x\,\ln \left (3\right )-80\,x^2\right )+52\,x^2-36\,x^3-40\,x^4+4}{5\,\ln \left (3\right )-10\,x+1} \,d x \]
int((52*x - log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x + 100*x^2 + 1)*(l og(3)*(80*x + 60*x^2 + 20) - 24*x + 12*x^2 - 120*x^3 + 4) + log(3)*(60*x + 60*x^2 + 20*x^3 + 20) + log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x + 10 0*x^2 + 1)^2*(8*x + 40*x*log(3) - 80*x^2) + 52*x^2 - 36*x^3 - 40*x^4 + 4)/ (5*log(3) - 10*x + 1),x)
int((52*x - log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x + 100*x^2 + 1)*(l og(3)*(80*x + 60*x^2 + 20) - 24*x + 12*x^2 - 120*x^3 + 4) + log(3)*(60*x + 60*x^2 + 20*x^3 + 20) + log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x + 10 0*x^2 + 1)^2*(8*x + 40*x*log(3) - 80*x^2) + 52*x^2 - 36*x^3 - 40*x^4 + 4)/ (5*log(3) - 10*x + 1), x)