Integrand size = 111, antiderivative size = 26 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx=5 x (5+2 x) \left (x^2+\log \left (-4+\frac {e^3}{1-x}\right )\right ) \]
Leaf count is larger than twice the leaf count of optimal. \(162\) vs. \(2(26)=52\).
Time = 0.14 (sec) , antiderivative size = 162, normalized size of antiderivative = 6.23 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx=5 \left (5 x^3+2 x^4+5 \log \left (4-e^3-4 x\right )-\frac {5}{4} e^3 \log \left (4-e^3-4 x\right )-5 \log \left (-\frac {4-e^3-4 x}{1-x}\right )+\frac {5}{4} e^3 \log \left (-\frac {4-e^3-4 x}{1-x}\right )+5 x \log \left (-\frac {4-e^3-4 x}{1-x}\right )+2 x^2 \log \left (-\frac {4-e^3-4 x}{1-x}\right )-5 \log (1-x)+\frac {5}{4} e^3 \log (1-x)\right ) \]
Integrate[(300*x^2 - 440*x^3 - 20*x^4 + 160*x^5 + E^3*(-25*x - 85*x^2 + 35 *x^3 + 40*x^4) + (100 - 120*x - 60*x^2 + 80*x^3 + E^3*(-25 + 5*x + 20*x^2) )*Log[(4 - E^3 - 4*x)/(-1 + x)])/(4 + E^3*(-1 + x) - 8*x + 4*x^2),x]
5*(5*x^3 + 2*x^4 + 5*Log[4 - E^3 - 4*x] - (5*E^3*Log[4 - E^3 - 4*x])/4 - 5 *Log[-((4 - E^3 - 4*x)/(1 - x))] + (5*E^3*Log[-((4 - E^3 - 4*x)/(1 - x))]) /4 + 5*x*Log[-((4 - E^3 - 4*x)/(1 - x))] + 2*x^2*Log[-((4 - E^3 - 4*x)/(1 - x))] - 5*Log[1 - x] + (5*E^3*Log[1 - x])/4)
Leaf count is larger than twice the leaf count of optimal. \(380\) vs. \(2(26)=52\).
Time = 1.59 (sec) , antiderivative size = 380, normalized size of antiderivative = 14.62, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {7292, 7279, 2009}
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.
| \(\displaystyle \int \frac {160 x^5-20 x^4-440 x^3+300 x^2+\left (80 x^3-60 x^2+e^3 \left (20 x^2+5 x-25\right )-120 x+100\right ) \log \left (\frac {-4 x-e^3+4}{x-1}\right )+e^3 \left (40 x^4+35 x^3-85 x^2-25 x\right )}{4 x^2-8 x+e^3 (x-1)+4} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {160 x^5-20 x^4-440 x^3+300 x^2+\left (80 x^3-60 x^2+e^3 \left (20 x^2+5 x-25\right )-120 x+100\right ) \log \left (\frac {-4 x-e^3+4}{x-1}\right )+e^3 \left (40 x^4+35 x^3-85 x^2-25 x\right )}{4 x^2-\left (8-e^3\right ) x-e^3+4}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle \int \left (\frac {160 x^5}{(x-1) \left (4 x+e^3-4\right )}-\frac {20 x^4}{(x-1) \left (4 x+e^3-4\right )}-\frac {440 x^3}{(x-1) \left (4 x+e^3-4\right )}+\frac {300 x^2}{(x-1) \left (4 x+e^3-4\right )}+\frac {5 e^3 \left (8 x^3+7 x^2-17 x-5\right ) x}{(x-1) \left (4 x+e^3-4\right )}+5 (4 x+5) \log \left (-\frac {4 x+e^3-4}{x-1}\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 10 x^4+\frac {10}{3} \left (8-e^3\right ) x^3+\frac {10 e^3 x^3}{3}-\frac {5 x^3}{3}+\frac {5}{4} \left (48-12 e^3+e^6\right ) x^2-\frac {5}{8} \left (8-e^3\right ) x^2+\frac {5}{8} e^3 \left (23-2 e^3\right ) x^2-55 x^2+\frac {5}{8} \left (256-96 e^3+16 e^6-e^9\right ) x+\frac {5}{16} e^3 \left (84-31 e^3+2 e^6\right ) x-\frac {5}{16} \left (48-12 e^3+e^6\right ) x-\frac {55}{2} \left (8-e^3\right ) x+\frac {5 e^3 x}{2}+75 x+\frac {5}{64} \left (448+224 e^3-208 e^6+39 e^9-2 e^{12}\right ) \log \left (-4 x-e^3+4\right )-\frac {5}{8} \left (9-e^3\right )^2 \log \left (-4 x-e^3+4\right )-\frac {5 \left (4-e^3\right )^5 \log \left (-4 x-e^3+4\right )}{32 e^3}+\frac {5 \left (4-e^3\right )^4 \log \left (-4 x-e^3+4\right )}{64 e^3}+\frac {55 \left (4-e^3\right )^3 \log \left (-4 x-e^3+4\right )}{8 e^3}-\frac {75 \left (4-e^3\right )^2 \log \left (-4 x-e^3+4\right )}{4 e^3}+\frac {5}{8} (4 x+5)^2 \log \left (-\frac {-4 x-e^3+4}{1-x}\right )+\frac {125}{8} \log (1-x)\) |
Int[(300*x^2 - 440*x^3 - 20*x^4 + 160*x^5 + E^3*(-25*x - 85*x^2 + 35*x^3 + 40*x^4) + (100 - 120*x - 60*x^2 + 80*x^3 + E^3*(-25 + 5*x + 20*x^2))*Log[ (4 - E^3 - 4*x)/(-1 + x)])/(4 + E^3*(-1 + x) - 8*x + 4*x^2),x]
75*x + (5*E^3*x)/2 - (55*(8 - E^3)*x)/2 - (5*(48 - 12*E^3 + E^6)*x)/16 + ( 5*E^3*(84 - 31*E^3 + 2*E^6)*x)/16 + (5*(256 - 96*E^3 + 16*E^6 - E^9)*x)/8 - 55*x^2 + (5*E^3*(23 - 2*E^3)*x^2)/8 - (5*(8 - E^3)*x^2)/8 + (5*(48 - 12* E^3 + E^6)*x^2)/4 - (5*x^3)/3 + (10*E^3*x^3)/3 + (10*(8 - E^3)*x^3)/3 + 10 *x^4 - (75*(4 - E^3)^2*Log[4 - E^3 - 4*x])/(4*E^3) + (55*(4 - E^3)^3*Log[4 - E^3 - 4*x])/(8*E^3) + (5*(4 - E^3)^4*Log[4 - E^3 - 4*x])/(64*E^3) - (5* (4 - E^3)^5*Log[4 - E^3 - 4*x])/(32*E^3) - (5*(9 - E^3)^2*Log[4 - E^3 - 4* x])/8 + (5*(448 + 224*E^3 - 208*E^6 + 39*E^9 - 2*E^12)*Log[4 - E^3 - 4*x]) /64 + (5*(5 + 4*x)^2*Log[-((4 - E^3 - 4*x)/(1 - x))])/8 + (125*Log[1 - x]) /8
3.7.77.3.1 Defintions of rubi rules used
Int[(u_)/((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.)), x_Symbol] :> With[ {v = RationalFunctionExpand[u/(a + b*x^n + c*x^(2*n)), x]}, Int[v, x] /; Su mQ[v]] /; FreeQ[{a, b, c}, x] && EqQ[n2, 2*n] && IGtQ[n, 0]
Time = 0.32 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.46
| method | result | size |
| risch | \(\left (10 x^{2}+25 x \right ) \ln \left (\frac {-{\mathrm e}^{3}-4 x +4}{-1+x}\right )+10 x^{4}+25 x^{3}\) | \(38\) |
| norman | \(25 x^{3}+10 x^{4}+25 x \ln \left (\frac {-{\mathrm e}^{3}-4 x +4}{-1+x}\right )+10 x^{2} \ln \left (\frac {-{\mathrm e}^{3}-4 x +4}{-1+x}\right )\) | \(52\) |
| parallelrisch | \(10 x^{4}-\frac {5 \,{\mathrm e}^{6} \ln \left (-1+x \right )}{8}+\frac {5 \,{\mathrm e}^{6} \ln \left (x +\frac {{\mathrm e}^{3}}{4}-1\right )}{8}-\frac {5 \,{\mathrm e}^{6} \ln \left (-\frac {{\mathrm e}^{3}+4 x -4}{-1+x}\right )}{8}+25 x^{3}+10 \ln \left (-\frac {{\mathrm e}^{3}+4 x -4}{-1+x}\right ) x^{2}+\frac {5 \,{\mathrm e}^{6}}{2}+\frac {5 \,{\mathrm e}^{3} \ln \left (-1+x \right )}{2}-\frac {5 \,{\mathrm e}^{3} \ln \left (x +\frac {{\mathrm e}^{3}}{4}-1\right )}{2}+\frac {5 \,{\mathrm e}^{3} \ln \left (-\frac {{\mathrm e}^{3}+4 x -4}{-1+x}\right )}{2}+90+25 \ln \left (-\frac {{\mathrm e}^{3}+4 x -4}{-1+x}\right ) x -\frac {65 \,{\mathrm e}^{3}}{2}+40 \ln \left (-1+x \right )-40 \ln \left (x +\frac {{\mathrm e}^{3}}{4}-1\right )+40 \ln \left (-\frac {{\mathrm e}^{3}+4 x -4}{-1+x}\right )\) | \(178\) |
| parts | \(5 \,{\mathrm e}^{3} \left (-4 \,{\mathrm e}^{3} \left (-\frac {\left (-1+x \right ) {\mathrm e}^{-3}}{8}-\frac {\ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )}{32}+\frac {\ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-\frac {{\mathrm e}^{3}}{-1+x}+4\right ) \left (-1+x \right )^{2} {\mathrm e}^{-6}}{32}\right )-\frac {9 \ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )}{4}-\frac {9 \ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-1+x \right ) {\mathrm e}^{-3}}{4}\right )+10 x^{4}+25 x^{3}-\frac {5 x \,{\mathrm e}^{3}}{2}-35 \,{\mathrm e}^{3} {\mathrm e}^{-3} \ln \left (-1+x \right )+\frac {5 \left (-18 \,{\mathrm e}^{6}+{\mathrm e}^{6} {\mathrm e}^{3}+56 \,{\mathrm e}^{3}\right ) {\mathrm e}^{-3} \ln \left ({\mathrm e}^{3}+4 x -4\right )}{8}\) | \(194\) |
| derivativedivides | \({\mathrm e}^{3} \left (-\frac {45 \ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )}{4}-\frac {45 \ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-1+x \right ) {\mathrm e}^{-3}}{4}-20 \,{\mathrm e}^{3} \left (-\frac {\left (-1+x \right ) {\mathrm e}^{-3}}{8}-\frac {\ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )}{32}+\frac {\ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-\frac {{\mathrm e}^{3}}{-1+x}+4\right ) \left (-1+x \right )^{2} {\mathrm e}^{-6}}{32}\right )-5 \,{\mathrm e}^{-3} \left (\left (-\frac {9 \,{\mathrm e}^{3}}{4}+\frac {{\mathrm e}^{6}}{8}\right ) \ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )+\left (\frac {{\mathrm e}^{6}}{2}-23 \,{\mathrm e}^{3}\right ) \left (-1+x \right ) {\mathrm e}^{-3}-27 \,{\mathrm e}^{6} \left (-1+x \right )^{2} {\mathrm e}^{-6}-13 \,{\mathrm e}^{9} \left (-1+x \right )^{3} {\mathrm e}^{-9}-2 \,{\mathrm e}^{12} \left (-1+x \right )^{4} {\mathrm e}^{-12}+\left (\frac {9 \,{\mathrm e}^{3}}{4}-\frac {{\mathrm e}^{6}}{8}-7\right ) \ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right )\right )\right )\) | \(226\) |
| default | \({\mathrm e}^{3} \left (-\frac {45 \ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )}{4}-\frac {45 \ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-1+x \right ) {\mathrm e}^{-3}}{4}-20 \,{\mathrm e}^{3} \left (-\frac {\left (-1+x \right ) {\mathrm e}^{-3}}{8}-\frac {\ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )}{32}+\frac {\ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right ) \left (-\frac {{\mathrm e}^{3}}{-1+x}+4\right ) \left (-1+x \right )^{2} {\mathrm e}^{-6}}{32}\right )-5 \,{\mathrm e}^{-3} \left (\left (-\frac {9 \,{\mathrm e}^{3}}{4}+\frac {{\mathrm e}^{6}}{8}\right ) \ln \left (-\frac {{\mathrm e}^{3}}{-1+x}\right )+\left (\frac {{\mathrm e}^{6}}{2}-23 \,{\mathrm e}^{3}\right ) \left (-1+x \right ) {\mathrm e}^{-3}-27 \,{\mathrm e}^{6} \left (-1+x \right )^{2} {\mathrm e}^{-6}-13 \,{\mathrm e}^{9} \left (-1+x \right )^{3} {\mathrm e}^{-9}-2 \,{\mathrm e}^{12} \left (-1+x \right )^{4} {\mathrm e}^{-12}+\left (\frac {9 \,{\mathrm e}^{3}}{4}-\frac {{\mathrm e}^{6}}{8}-7\right ) \ln \left (-4-\frac {{\mathrm e}^{3}}{-1+x}\right )\right )\right )\) | \(226\) |
int((((20*x^2+5*x-25)*exp(3)+80*x^3-60*x^2-120*x+100)*ln((-exp(3)-4*x+4)/( -1+x))+(40*x^4+35*x^3-85*x^2-25*x)*exp(3)+160*x^5-20*x^4-440*x^3+300*x^2)/ ((-1+x)*exp(3)+4*x^2-8*x+4),x,method=_RETURNVERBOSE)
Time = 0.23 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx=10 \, x^{4} + 25 \, x^{3} + 5 \, {\left (2 \, x^{2} + 5 \, x\right )} \log \left (-\frac {4 \, x + e^{3} - 4}{x - 1}\right ) \]
integrate((((20*x^2+5*x-25)*exp(3)+80*x^3-60*x^2-120*x+100)*log((-exp(3)-4 *x+4)/(-1+x))+(40*x^4+35*x^3-85*x^2-25*x)*exp(3)+160*x^5-20*x^4-440*x^3+30 0*x^2)/((-1+x)*exp(3)+4*x^2-8*x+4),x, algorithm=\
Time = 0.12 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx=10 x^{4} + 25 x^{3} + \left (10 x^{2} + 25 x\right ) \log {\left (\frac {- 4 x - e^{3} + 4}{x - 1} \right )} \]
integrate((((20*x**2+5*x-25)*exp(3)+80*x**3-60*x**2-120*x+100)*ln((-exp(3) -4*x+4)/(-1+x))+(40*x**4+35*x**3-85*x**2-25*x)*exp(3)+160*x**5-20*x**4-440 *x**3+300*x**2)/((-1+x)*exp(3)+4*x**2-8*x+4),x)
Leaf count of result is larger than twice the leaf count of optimal. 641 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 641, normalized size of antiderivative = 24.65 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx=\text {Too large to display} \]
integrate((((20*x^2+5*x-25)*exp(3)+80*x^3-60*x^2-120*x+100)*log((-exp(3)-4 *x+4)/(-1+x))+(40*x^4+35*x^3-85*x^2-25*x)*exp(3)+160*x^5-20*x^4-440*x^3+30 0*x^2)/((-1+x)*exp(3)+4*x^2-8*x+4),x, algorithm=\
10*x^4 - 10/3*x^3*(e^3 - 8) - 5/3*x^3 + 5/4*x^2*(e^6 - 12*e^3 + 48) + 5/8* x^2*(e^3 - 8) + 5/32*(e^15 - 20*e^12 + 160*e^9 - 640*e^6 + 1280*e^3 - 1024 )*e^(-3)*log(4*x + e^3 - 4) + 5/64*(e^12 - 16*e^9 + 96*e^6 - 256*e^3 + 256 )*e^(-3)*log(4*x + e^3 - 4) - 55/8*(e^9 - 12*e^6 + 48*e^3 - 64)*e^(-3)*log (4*x + e^3 - 4) - 75/4*(e^6 - 8*e^3 + 16)*e^(-3)*log(4*x + e^3 - 4) + 25*( e^(-3)*log(4*x + e^3 - 4) - e^(-3)*log(x - 1))*e^3*log(-4*x/(x - 1) - e^3/ (x - 1) + 4/(x - 1)) - 55*x^2 - 5/8*x*(e^9 - 16*e^6 + 96*e^3 - 256) - 5/16 *x*(e^6 - 12*e^3 + 48) + 55/2*x*(e^3 - 8) + 5/96*(64*x^3 - 24*x^2*(e^3 - 8 ) - 3*(e^12 - 16*e^9 + 96*e^6 - 256*e^3 + 256)*e^(-3)*log(4*x + e^3 - 4) + 12*x*(e^6 - 12*e^3 + 48) + 768*e^(-3)*log(x - 1))*e^3 + 35/64*((e^9 - 12* e^6 + 48*e^3 - 64)*e^(-3)*log(4*x + e^3 - 4) + 8*x^2 - 4*x*(e^3 - 8) + 64* e^(-3)*log(x - 1))*e^3 + 85/16*((e^6 - 8*e^3 + 16)*e^(-3)*log(4*x + e^3 - 4) - 16*e^(-3)*log(x - 1) - 4*x)*e^3 - 25/4*((e^3 - 4)*e^(-3)*log(4*x + e^ 3 - 4) + 4*e^(-3)*log(x - 1))*e^3 - 5/8*(20*(e^3 - 4)*log(x - 1)^2 + 20*(e ^3 - 4)*log(-4*x - e^3 + 4)^2 - 4*x*e^6 + 8*(2*x^2*e^3 + 5*x*e^3 - 7*e^3)* log(x - 1) - (16*x^2*e^3 + 40*x*e^3 + 40*(e^3 - 4)*log(x - 1) - e^9 + 18*e ^6 - 56*e^3)*log(-4*x - e^3 + 4))*e^(-3) + 50*(log(4*x + e^3 - 4)^2 - 2*lo g(4*x + e^3 - 4)*log(x - 1) + log(x - 1)^2)*e^(-3) - 25/2*log(4*x + e^3 - 4)^2 + 25*log(4*x + e^3 - 4)*log(x - 1) - 25/2*log(x - 1)^2 - 100*(e^(-3)* log(4*x + e^3 - 4) - e^(-3)*log(x - 1))*log(-4*x/(x - 1) - e^3/(x - 1) ...
Leaf count of result is larger than twice the leaf count of optimal. 546 vs. \(2 (24) = 48\).
Time = 0.39 (sec) , antiderivative size = 546, normalized size of antiderivative = 21.00 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx =\text {Too large to display} \]
integrate((((20*x^2+5*x-25)*exp(3)+80*x^3-60*x^2-120*x+100)*log((-exp(3)-4 *x+4)/(-1+x))+(40*x^4+35*x^3-85*x^2-25*x)*exp(3)+160*x^5-20*x^4-440*x^3+30 0*x^2)/((-1+x)*exp(3)+4*x^2-8*x+4),x, algorithm=\
5*((e^3 - 4)*e^(-6) + 4*e^(-6))*(2*(4*x + e^3 - 4)^2*e^9*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1)^2 - 16*(4*x + e^3 - 4)*e^9*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1) + 32*e^9*log(-(4*x + e^3 - 4)/(x - 1)) + 9*(4*x + e^3 - 4)^3*e ^6*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1)^3 - 108*(4*x + e^3 - 4)^2*e^6*log (-(4*x + e^3 - 4)/(x - 1))/(x - 1)^2 + 432*(4*x + e^3 - 4)*e^6*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1) - 576*e^6*log(-(4*x + e^3 - 4)/(x - 1)) + 7*(4* x + e^3 - 4)^4*e^3*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1)^4 - 112*(4*x + e^ 3 - 4)^3*e^3*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1)^3 + 672*(4*x + e^3 - 4) ^2*e^3*log(-(4*x + e^3 - 4)/(x - 1))/(x - 1)^2 - 1792*(4*x + e^3 - 4)*e^3* log(-(4*x + e^3 - 4)/(x - 1))/(x - 1) + 1792*e^3*log(-(4*x + e^3 - 4)/(x - 1)) + 13*(4*x + e^3 - 4)*e^12/(x - 1) + 27*(4*x + e^3 - 4)^2*e^9/(x - 1)^ 2 - 216*(4*x + e^3 - 4)*e^9/(x - 1) + 23*(4*x + e^3 - 4)^3*e^6/(x - 1)^3 - 276*(4*x + e^3 - 4)^2*e^6/(x - 1)^2 + 1104*(4*x + e^3 - 4)*e^6/(x - 1) + 2*e^15 - 52*e^12 + 432*e^9 - 1472*e^6)/((4*x + e^3 - 4)^4/(x - 1)^4 - 16*( 4*x + e^3 - 4)^3/(x - 1)^3 + 96*(4*x + e^3 - 4)^2/(x - 1)^2 - 256*(4*x + e ^3 - 4)/(x - 1) + 256)
Time = 1.37 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.04 \[ \int \frac {300 x^2-440 x^3-20 x^4+160 x^5+e^3 \left (-25 x-85 x^2+35 x^3+40 x^4\right )+\left (100-120 x-60 x^2+80 x^3+e^3 \left (-25+5 x+20 x^2\right )\right ) \log \left (\frac {4-e^3-4 x}{-1+x}\right )}{4+e^3 (-1+x)-8 x+4 x^2} \, dx=5\,x\,\left (2\,x+5\right )\,\left (\ln \left (-\frac {4\,x+{\mathrm {e}}^3-4}{x-1}\right )+x^2\right ) \]