Integrand size = 191, antiderivative size = 23 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=x+\frac {x}{9 \left (-1+4 x+\frac {-5+\log (4)}{\log (3)}\right )^2} \]
Leaf count is larger than twice the leaf count of optimal. \(220\) vs. \(2(23)=46\).
Time = 0.15 (sec) , antiderivative size = 220, normalized size of antiderivative = 9.57 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=\frac {2304 x^2 \left (-5+\log \left (\frac {4}{3}\right )\right ) \log ^3(3) \log ^2(81)+27 \log (3) (-5+\log (4))^2 \left (20+\log \left (\frac {6561}{256}\right )\right ) \log ^2(81)+4 \log ^2(3) (-5+\log (4)) \left (-270+54 \log \left (\frac {4}{3}\right )-7 \log (81)\right ) \log ^2(81)+1152 x^3 \log ^3(3) \log ^3(81)-9 (-5+\log (4))^3 \log ^3(81)-8 x \log (3) \log (81) \left (-54 \log (3) (-5+\log (4)) \log ^2(81)+27 (-5+\log (4))^2 \log ^2(81)+\log ^2(3) \left (-14400+5760 \log \left (\frac {4}{3}\right )-576 \log ^2\left (\frac {4}{3}\right )+26 \log ^2(81)\right )\right )+2 \log ^3(3) \left (-17280 \log ^2\left (\frac {4}{3}\right )+1152 \log ^3\left (\frac {4}{3}\right )+\log \left (\frac {4}{3}\right ) \left (86400-52 \log ^2(81)\right )+5 \left (-28800+52 \log ^2(81)+\log ^3(81)\right )\right )}{18 \log ^4(81) \left (-5+\log \left (\frac {4}{3}\right )+x \log (81)\right )^2} \]
Integrate[(-1125 + (-675 + 2700*x)*Log[3] + (-140 + 1080*x - 2160*x^2)*Log [3]^2 + (-10 + 104*x - 432*x^2 + 576*x^3)*Log[3]^3 + (675 + (270 - 1080*x) *Log[3] + (28 - 216*x + 432*x^2)*Log[3]^2)*Log[4] + (-135 + (-27 + 108*x)* Log[3])*Log[4]^2 + 9*Log[4]^3)/(-1125 + (-675 + 2700*x)*Log[3] + (-135 + 1 080*x - 2160*x^2)*Log[3]^2 + (-9 + 108*x - 432*x^2 + 576*x^3)*Log[3]^3 + ( 675 + (270 - 1080*x)*Log[3] + (27 - 216*x + 432*x^2)*Log[3]^2)*Log[4] + (- 135 + (-27 + 108*x)*Log[3])*Log[4]^2 + 9*Log[4]^3),x]
(2304*x^2*(-5 + Log[4/3])*Log[3]^3*Log[81]^2 + 27*Log[3]*(-5 + Log[4])^2*( 20 + Log[6561/256])*Log[81]^2 + 4*Log[3]^2*(-5 + Log[4])*(-270 + 54*Log[4/ 3] - 7*Log[81])*Log[81]^2 + 1152*x^3*Log[3]^3*Log[81]^3 - 9*(-5 + Log[4])^ 3*Log[81]^3 - 8*x*Log[3]*Log[81]*(-54*Log[3]*(-5 + Log[4])*Log[81]^2 + 27* (-5 + Log[4])^2*Log[81]^2 + Log[3]^2*(-14400 + 5760*Log[4/3] - 576*Log[4/3 ]^2 + 26*Log[81]^2)) + 2*Log[3]^3*(-17280*Log[4/3]^2 + 1152*Log[4/3]^3 + L og[4/3]*(86400 - 52*Log[81]^2) + 5*(-28800 + 52*Log[81]^2 + Log[81]^3)))/( 18*Log[81]^4*(-5 + Log[4/3] + x*Log[81])^2)
Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(23)=46\).
Time = 0.40 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.78, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2007, 2389, 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.
| \(\displaystyle \int \frac {\log (4) \left (\left (432 x^2-216 x+28\right ) \log ^2(3)+(270-1080 x) \log (3)+675\right )+\left (-2160 x^2+1080 x-140\right ) \log ^2(3)+\left (576 x^3-432 x^2+104 x-10\right ) \log ^3(3)+\log ^2(4) ((108 x-27) \log (3)-135)+(2700 x-675) \log (3)-1125+9 \log ^3(4)}{\log (4) \left (\left (432 x^2-216 x+27\right ) \log ^2(3)+(270-1080 x) \log (3)+675\right )+\left (-2160 x^2+1080 x-135\right ) \log ^2(3)+\left (576 x^3-432 x^2+108 x-9\right ) \log ^3(3)+\log ^2(4) ((108 x-27) \log (3)-135)+(2700 x-675) \log (3)-1125+9 \log ^3(4)} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {\log (4) \left (\left (432 x^2-216 x+28\right ) \log ^2(3)+(270-1080 x) \log (3)+675\right )+\left (-2160 x^2+1080 x-140\right ) \log ^2(3)+\left (576 x^3-432 x^2+104 x-10\right ) \log ^3(3)+\log ^2(4) ((108 x-27) \log (3)-135)+(2700 x-675) \log (3)-1125+9 \log ^3(4)}{\left (4\ 3^{2/3} x \log (3)-3^{2/3} (5+\log (3)-\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 2389 |
| \(\displaystyle \int \left (-\frac {\log ^2(3)}{9 \left (x \log (81)-5+\log \left (\frac {4}{3}\right )\right )^2}+\frac {2 \left (\log \left (\frac {4}{3}\right )-5\right ) \log ^2(3)}{9 \left (x \log (81)-5+\log \left (\frac {4}{3}\right )\right )^3}+1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x-\frac {\log ^2(3)}{9 \log (81) \left (x (-\log (81))+5-\log \left (\frac {4}{3}\right )\right )}+\frac {\left (5-\log \left (\frac {4}{3}\right )\right ) \log ^2(3)}{9 \log (81) \left (x (-\log (81))+5-\log \left (\frac {4}{3}\right )\right )^2}\) |
Int[(-1125 + (-675 + 2700*x)*Log[3] + (-140 + 1080*x - 2160*x^2)*Log[3]^2 + (-10 + 104*x - 432*x^2 + 576*x^3)*Log[3]^3 + (675 + (270 - 1080*x)*Log[3 ] + (28 - 216*x + 432*x^2)*Log[3]^2)*Log[4] + (-135 + (-27 + 108*x)*Log[3] )*Log[4]^2 + 9*Log[4]^3)/(-1125 + (-675 + 2700*x)*Log[3] + (-135 + 1080*x - 2160*x^2)*Log[3]^2 + (-9 + 108*x - 432*x^2 + 576*x^3)*Log[3]^3 + (675 + (270 - 1080*x)*Log[3] + (27 - 216*x + 432*x^2)*Log[3]^2)*Log[4] + (-135 + (-27 + 108*x)*Log[3])*Log[4]^2 + 9*Log[4]^3),x]
x + ((5 - Log[4/3])*Log[3]^2)/(9*Log[81]*(5 - Log[4/3] - x*Log[81])^2) - L og[3]^2/(9*Log[81]*(5 - Log[4/3] - x*Log[81]))
3.8.40.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand [Pq*(a + b*x^n)^p, x], x] /; FreeQ[{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p , 0] || EqQ[n, 1])
Time = 0.84 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.39
| method | result | size |
| default | \(x -\frac {\left (2 \ln \left (2\right )-\ln \left (3\right )-5\right ) \ln \left (3\right )}{36 \left (4 x \ln \left (3\right )+2 \ln \left (2\right )-\ln \left (3\right )-5\right )^{2}}+\frac {\ln \left (3\right )}{144 x \ln \left (3\right )+72 \ln \left (2\right )-36 \ln \left (3\right )-180}\) | \(55\) |
| risch | \(x +\frac {x \ln \left (3\right )^{2}}{144 x^{2} \ln \left (3\right )^{2}+144 x \ln \left (2\right ) \ln \left (3\right )-72 x \ln \left (3\right )^{2}+36 \ln \left (2\right )^{2}-36 \ln \left (2\right ) \ln \left (3\right )+9 \ln \left (3\right )^{2}-360 x \ln \left (3\right )-180 \ln \left (2\right )+90 \ln \left (3\right )+225}\) | \(66\) |
| norman | \(\frac {\left (-12 \ln \left (2\right )^{2}+12 \ln \left (2\right ) \ln \left (3\right )-\frac {26 \ln \left (3\right )^{2}}{9}+60 \ln \left (2\right )-30 \ln \left (3\right )-75\right ) x +16 x^{3} \ln \left (3\right )^{2}-\frac {8 \ln \left (2\right )^{3}-12 \ln \left (2\right )^{2} \ln \left (3\right )+6 \ln \left (2\right ) \ln \left (3\right )^{2}-\ln \left (3\right )^{3}-60 \ln \left (2\right )^{2}+60 \ln \left (2\right ) \ln \left (3\right )-15 \ln \left (3\right )^{2}+150 \ln \left (2\right )-75 \ln \left (3\right )-125}{2 \ln \left (3\right )}}{\left (4 x \ln \left (3\right )+2 \ln \left (2\right )-\ln \left (3\right )-5\right )^{2}}\) | \(121\) |
| gosper | \(-\frac {-288 x^{3} \ln \left (3\right )^{3}+216 \ln \left (2\right )^{2} \ln \left (3\right ) x -216 x \ln \left (2\right ) \ln \left (3\right )^{2}+52 x \ln \left (3\right )^{3}+72 \ln \left (2\right )^{3}-108 \ln \left (2\right )^{2} \ln \left (3\right )+54 \ln \left (2\right ) \ln \left (3\right )^{2}-1080 x \ln \left (2\right ) \ln \left (3\right )-9 \ln \left (3\right )^{3}+540 x \ln \left (3\right )^{2}-540 \ln \left (2\right )^{2}+540 \ln \left (2\right ) \ln \left (3\right )-135 \ln \left (3\right )^{2}+1350 x \ln \left (3\right )+1350 \ln \left (2\right )-675 \ln \left (3\right )-1125}{18 \ln \left (3\right ) \left (16 x^{2} \ln \left (3\right )^{2}+16 x \ln \left (2\right ) \ln \left (3\right )-8 x \ln \left (3\right )^{2}+4 \ln \left (2\right )^{2}-4 \ln \left (2\right ) \ln \left (3\right )+\ln \left (3\right )^{2}-40 x \ln \left (3\right )-20 \ln \left (2\right )+10 \ln \left (3\right )+25\right )}\) | \(172\) |
| parallelrisch | \(-\frac {-8640 x \ln \left (2\right ) \ln \left (3\right )^{2}-4320 \ln \left (2\right )^{2} \ln \left (3\right )+4320 x \ln \left (3\right )^{3}-864 \ln \left (3\right )^{2} \ln \left (2\right )^{2}+10800 x \ln \left (3\right )^{2}+416 x \ln \left (3\right )^{4}+10800 \ln \left (2\right ) \ln \left (3\right )+4320 \ln \left (2\right ) \ln \left (3\right )^{2}-72 \ln \left (3\right )^{4}-1080 \ln \left (3\right )^{3}-5400 \ln \left (3\right )^{2}-9000 \ln \left (3\right )+432 \ln \left (2\right ) \ln \left (3\right )^{3}+576 \ln \left (3\right ) \ln \left (2\right )^{3}+1728 \ln \left (2\right )^{2} \ln \left (3\right )^{2} x -1728 \ln \left (2\right ) \ln \left (3\right )^{3} x -2304 \ln \left (3\right )^{4} x^{3}}{144 \ln \left (3\right )^{2} \left (16 x^{2} \ln \left (3\right )^{2}+16 x \ln \left (2\right ) \ln \left (3\right )-8 x \ln \left (3\right )^{2}+4 \ln \left (2\right )^{2}-4 \ln \left (2\right ) \ln \left (3\right )+\ln \left (3\right )^{2}-40 x \ln \left (3\right )-20 \ln \left (2\right )+10 \ln \left (3\right )+25\right )}\) | \(193\) |
int((72*ln(2)^3+4*((108*x-27)*ln(3)-135)*ln(2)^2+2*((432*x^2-216*x+28)*ln( 3)^2+(-1080*x+270)*ln(3)+675)*ln(2)+(576*x^3-432*x^2+104*x-10)*ln(3)^3+(-2 160*x^2+1080*x-140)*ln(3)^2+(2700*x-675)*ln(3)-1125)/(72*ln(2)^3+4*((108*x -27)*ln(3)-135)*ln(2)^2+2*((432*x^2-216*x+27)*ln(3)^2+(-1080*x+270)*ln(3)+ 675)*ln(2)+(576*x^3-432*x^2+108*x-9)*ln(3)^3+(-2160*x^2+1080*x-135)*ln(3)^ 2+(2700*x-675)*ln(3)-1125),x,method=_RETURNVERBOSE)
x-1/36*(2*ln(2)-ln(3)-5)*ln(3)/(4*x*ln(3)+2*ln(2)-ln(3)-5)^2+1/36*ln(3)/(4 *x*ln(3)+2*ln(2)-ln(3)-5)
Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (23) = 46\).
Time = 0.24 (sec) , antiderivative size = 111, normalized size of antiderivative = 4.83 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=\frac {2 \, {\left (72 \, x^{3} - 36 \, x^{2} + 5 \, x\right )} \log \left (3\right )^{2} + 36 \, x \log \left (2\right )^{2} - 18 \, {\left (20 \, x^{2} - 2 \, {\left (4 \, x^{2} - x\right )} \log \left (2\right ) - 5 \, x\right )} \log \left (3\right ) - 180 \, x \log \left (2\right ) + 225 \, x}{9 \, {\left ({\left (16 \, x^{2} - 8 \, x + 1\right )} \log \left (3\right )^{2} + 2 \, {\left (2 \, {\left (4 \, x - 1\right )} \log \left (2\right ) - 20 \, x + 5\right )} \log \left (3\right ) + 4 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 25\right )}} \]
integrate((72*log(2)^3+4*((108*x-27)*log(3)-135)*log(2)^2+2*((432*x^2-216* x+28)*log(3)^2+(-1080*x+270)*log(3)+675)*log(2)+(576*x^3-432*x^2+104*x-10) *log(3)^3+(-2160*x^2+1080*x-140)*log(3)^2+(2700*x-675)*log(3)-1125)/(72*lo g(2)^3+4*((108*x-27)*log(3)-135)*log(2)^2+2*((432*x^2-216*x+27)*log(3)^2+( -1080*x+270)*log(3)+675)*log(2)+(576*x^3-432*x^2+108*x-9)*log(3)^3+(-2160* x^2+1080*x-135)*log(3)^2+(2700*x-675)*log(3)-1125),x, algorithm=\
1/9*(2*(72*x^3 - 36*x^2 + 5*x)*log(3)^2 + 36*x*log(2)^2 - 18*(20*x^2 - 2*( 4*x^2 - x)*log(2) - 5*x)*log(3) - 180*x*log(2) + 225*x)/((16*x^2 - 8*x + 1 )*log(3)^2 + 2*(2*(4*x - 1)*log(2) - 20*x + 5)*log(3) + 4*log(2)^2 - 20*lo g(2) + 25)
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (34) = 68\).
Time = 0.61 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.17 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=x + \frac {x \log {\left (3 \right )}^{2}}{144 x^{2} \log {\left (3 \right )}^{2} + x \left (- 360 \log {\left (3 \right )} - 72 \log {\left (3 \right )}^{2} + 144 \log {\left (2 \right )} \log {\left (3 \right )}\right ) - 180 \log {\left (2 \right )} - 36 \log {\left (2 \right )} \log {\left (3 \right )} + 9 \log {\left (3 \right )}^{2} + 36 \log {\left (2 \right )}^{2} + 90 \log {\left (3 \right )} + 225} \]
integrate((72*ln(2)**3+4*((108*x-27)*ln(3)-135)*ln(2)**2+2*((432*x**2-216* x+28)*ln(3)**2+(-1080*x+270)*ln(3)+675)*ln(2)+(576*x**3-432*x**2+104*x-10) *ln(3)**3+(-2160*x**2+1080*x-140)*ln(3)**2+(2700*x-675)*ln(3)-1125)/(72*ln (2)**3+4*((108*x-27)*ln(3)-135)*ln(2)**2+2*((432*x**2-216*x+27)*ln(3)**2+( -1080*x+270)*ln(3)+675)*ln(2)+(576*x**3-432*x**2+108*x-9)*ln(3)**3+(-2160* x**2+1080*x-135)*ln(3)**2+(2700*x-675)*ln(3)-1125),x)
x + x*log(3)**2/(144*x**2*log(3)**2 + x*(-360*log(3) - 72*log(3)**2 + 144* log(2)*log(3)) - 180*log(2) - 36*log(2)*log(3) + 9*log(3)**2 + 36*log(2)** 2 + 90*log(3) + 225)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (23) = 46\).
Time = 0.19 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.83 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=\frac {x \log \left (3\right )^{2}}{9 \, {\left (16 \, x^{2} \log \left (3\right )^{2} + 8 \, {\left ({\left (2 \, \log \left (2\right ) - 5\right )} \log \left (3\right ) - \log \left (3\right )^{2}\right )} x - 2 \, {\left (2 \, \log \left (2\right ) - 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 4 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 25\right )}} + x \]
integrate((72*log(2)^3+4*((108*x-27)*log(3)-135)*log(2)^2+2*((432*x^2-216* x+28)*log(3)^2+(-1080*x+270)*log(3)+675)*log(2)+(576*x^3-432*x^2+104*x-10) *log(3)^3+(-2160*x^2+1080*x-140)*log(3)^2+(2700*x-675)*log(3)-1125)/(72*lo g(2)^3+4*((108*x-27)*log(3)-135)*log(2)^2+2*((432*x^2-216*x+27)*log(3)^2+( -1080*x+270)*log(3)+675)*log(2)+(576*x^3-432*x^2+108*x-9)*log(3)^3+(-2160* x^2+1080*x-135)*log(3)^2+(2700*x-675)*log(3)-1125),x, algorithm=\
1/9*x*log(3)^2/(16*x^2*log(3)^2 + 8*((2*log(2) - 5)*log(3) - log(3)^2)*x - 2*(2*log(2) - 5)*log(3) + log(3)^2 + 4*log(2)^2 - 20*log(2) + 25) + x
Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=x + \frac {x \log \left (3\right )^{2}}{9 \, {\left (4 \, x \log \left (3\right ) - \log \left (3\right ) + 2 \, \log \left (2\right ) - 5\right )}^{2}} \]
integrate((72*log(2)^3+4*((108*x-27)*log(3)-135)*log(2)^2+2*((432*x^2-216* x+28)*log(3)^2+(-1080*x+270)*log(3)+675)*log(2)+(576*x^3-432*x^2+104*x-10) *log(3)^3+(-2160*x^2+1080*x-140)*log(3)^2+(2700*x-675)*log(3)-1125)/(72*lo g(2)^3+4*((108*x-27)*log(3)-135)*log(2)^2+2*((432*x^2-216*x+27)*log(3)^2+( -1080*x+270)*log(3)+675)*log(2)+(576*x^3-432*x^2+108*x-9)*log(3)^3+(-2160* x^2+1080*x-135)*log(3)^2+(2700*x-675)*log(3)-1125),x, algorithm=\
Time = 10.59 (sec) , antiderivative size = 923, normalized size of antiderivative = 40.13 \[ \int \frac {-1125+(-675+2700 x) \log (3)+\left (-140+1080 x-2160 x^2\right ) \log ^2(3)+\left (-10+104 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (28-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)}{-1125+(-675+2700 x) \log (3)+\left (-135+1080 x-2160 x^2\right ) \log ^2(3)+\left (-9+108 x-432 x^2+576 x^3\right ) \log ^3(3)+\left (675+(270-1080 x) \log (3)+\left (27-216 x+432 x^2\right ) \log ^2(3)\right ) \log (4)+(-135+(-27+108 x) \log (3)) \log ^2(4)+9 \log ^3(4)} \, dx=\text {Too large to display} \]
int((log(3)*(2700*x - 675) + 4*log(2)^2*(log(3)*(108*x - 27) - 135) - log( 3)^2*(2160*x^2 - 1080*x + 140) + 2*log(2)*(log(3)^2*(432*x^2 - 216*x + 28) - log(3)*(1080*x - 270) + 675) + 72*log(2)^3 + log(3)^3*(104*x - 432*x^2 + 576*x^3 - 10) - 1125)/(log(3)*(2700*x - 675) + 4*log(2)^2*(log(3)*(108*x - 27) - 135) - log(3)^2*(2160*x^2 - 1080*x + 135) + 2*log(2)*(log(3)^2*(4 32*x^2 - 216*x + 27) - log(3)*(1080*x - 270) + 675) + 72*log(2)^3 + log(3) ^3*(108*x - 432*x^2 + 576*x^3 - 9) - 1125),x)
x + symsum(log((51200*root(480*log(2)^2*log(3)^6 + 96*log(2)^2*log(3)^7 - 64*log(2)^3*log(3)^6 - 1200*log(2)*log(3)^6 - 480*log(2)*log(3)^7 - 48*log (2)*log(3)^8 + 1000*log(3)^6 + 600*log(3)^7 + 120*log(3)^8 + 8*log(3)^9, z , k)*log(3)^7)/3 + (20480*root(480*log(2)^2*log(3)^6 + 96*log(2)^2*log(3)^ 7 - 64*log(2)^3*log(3)^6 - 1200*log(2)*log(3)^6 - 480*log(2)*log(3)^7 - 48 *log(2)*log(3)^8 + 1000*log(3)^6 + 600*log(3)^7 + 120*log(3)^8 + 8*log(3)^ 9, z, k)*log(3)^8)/3 + (2048*root(480*log(2)^2*log(3)^6 + 96*log(2)^2*log( 3)^7 - 64*log(2)^3*log(3)^6 - 1200*log(2)*log(3)^6 - 480*log(2)*log(3)^7 - 48*log(2)*log(3)^8 + 1000*log(3)^6 + 600*log(3)^7 + 120*log(3)^8 + 8*log( 3)^9, z, k)*log(3)^9)/3 - (512*log(2)*log(3)^8)/81 + (1024*x*log(3)^9)/81 + (1280*log(3)^8)/81 + (256*log(3)^9)/81 + (8192*root(480*log(2)^2*log(3)^ 6 + 96*log(2)^2*log(3)^7 - 64*log(2)^3*log(3)^6 - 1200*log(2)*log(3)^6 - 4 80*log(2)*log(3)^7 - 48*log(2)*log(3)^8 + 1000*log(3)^6 + 600*log(3)^7 + 1 20*log(3)^8 + 8*log(3)^9, z, k)*log(2)^2*log(3)^7)/3 - (40960*root(480*log (2)^2*log(3)^6 + 96*log(2)^2*log(3)^7 - 64*log(2)^3*log(3)^6 - 1200*log(2) *log(3)^6 - 480*log(2)*log(3)^7 - 48*log(2)*log(3)^8 + 1000*log(3)^6 + 600 *log(3)^7 + 120*log(3)^8 + 8*log(3)^9, z, k)*log(2)*log(3)^7)/3 - (8192*ro ot(480*log(2)^2*log(3)^6 + 96*log(2)^2*log(3)^7 - 64*log(2)^3*log(3)^6 - 1 200*log(2)*log(3)^6 - 480*log(2)*log(3)^7 - 48*log(2)*log(3)^8 + 1000*log( 3)^6 + 600*log(3)^7 + 120*log(3)^8 + 8*log(3)^9, z, k)*log(2)*log(3)^8)...