Integrand size = 62, antiderivative size = 23 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=x \left (4-\frac {\log (x)}{-3-e}\right )^2 (4+\log (80 x)) \] Output:
(4+ln(80*x))*(4-ln(x)/(-3-exp(1)))^2*x
Time = 0.15 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=\frac {x (4 (3+e)+\log (x))^2 (4+\log (80 x))}{(3+e)^2} \] Input:
Integrate[(816 + 512*E + 80*E^2 + (128 + 40*E)*Log[x] + 5*Log[x]^2 + (168 + 104*E + 16*E^2 + (26 + 8*E)*Log[x] + Log[x]^2)*Log[80*x])/(9 + 6*E + E^2 ),x]
Output:
(x*(4*(3 + E) + Log[x])^2*(4 + Log[80*x]))/(3 + E)^2
Leaf count is larger than twice the leaf count of optimal. \(147\) vs. \(2(23)=46\).
Time = 0.37 (sec) , antiderivative size = 147, normalized size of antiderivative = 6.39, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {27, 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.
| \(\displaystyle \int \frac {5 \log ^2(x)+\left (\log ^2(x)+(26+8 e) \log (x)+16 e^2+104 e+168\right ) \log (80 x)+(128+40 e) \log (x)+80 e^2+512 e+816}{9+6 e+e^2} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \left (5 \log ^2(x)+8 (16+5 e) \log (x)+\left (\log ^2(x)+2 (13+4 e) \log (x)+8 (3+e) (7+2 e)\right ) \log (80 x)+16 (3+e) (17+5 e)\right )dx}{(3+e)^2}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {16 (3+e) (17+5 e) x-8 (16+5 e) x+4 (13+4 e) x-8 (3+e) (7+2 e) x+4 x+4 x \log ^2(x)+x \log (80 x) \log ^2(x)+8 (16+5 e) x \log (x)-2 (13+4 e) x \log (x)-6 x \log (x)+2 (13+4 e) x \log (80 x) \log (x)-2 x \log (80 x) \log (x)-2 (13+4 e) x \log (80 x)+8 (3+e) (7+2 e) x \log (80 x)+2 x \log (80 x)}{(3+e)^2}\) |
Input:
Int[(816 + 512*E + 80*E^2 + (128 + 40*E)*Log[x] + 5*Log[x]^2 + (168 + 104* E + 16*E^2 + (26 + 8*E)*Log[x] + Log[x]^2)*Log[80*x])/(9 + 6*E + E^2),x]
Output:
(4*x - 8*(3 + E)*(7 + 2*E)*x + 4*(13 + 4*E)*x - 8*(16 + 5*E)*x + 16*(3 + E )*(17 + 5*E)*x - 6*x*Log[x] - 2*(13 + 4*E)*x*Log[x] + 8*(16 + 5*E)*x*Log[x ] + 4*x*Log[x]^2 + 2*x*Log[80*x] + 8*(3 + E)*(7 + 2*E)*x*Log[80*x] - 2*(13 + 4*E)*x*Log[80*x] - 2*x*Log[x]*Log[80*x] + 2*(13 + 4*E)*x*Log[x]*Log[80* x] + x*Log[x]^2*Log[80*x])/(3 + E)^2
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(71\) vs. \(2(24)=48\).
Time = 0.53 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.13
| method | result | size |
| norman | \(\frac {\left (64 \,{\mathrm e}+192\right ) x +\left (16 \,{\mathrm e}+48\right ) x \ln \left (80 x \right )+\frac {x \ln \left (x \right )^{2} \ln \left (80 x \right )}{3+{\mathrm e}}+32 x \ln \left (x \right )+8 x \ln \left (x \right ) \ln \left (80 x \right )+\frac {4 x \ln \left (x \right )^{2}}{3+{\mathrm e}}}{3+{\mathrm e}}\) | \(72\) |
| parallelrisch | \(\frac {-240 x +4 x \ln \left (x \right )^{2}-16 \,{\mathrm e}^{2} x +96 x \ln \left (x \right )-128 x \,{\mathrm e}+8 \,{\mathrm e} x \ln \left (x \right ) \ln \left (80 x \right )+32 x \,{\mathrm e} \ln \left (x \right )+144 \ln \left (80 x \right ) x +24 x \ln \left (x \right ) \ln \left (80 x \right )+x \ln \left (x \right )^{2} \ln \left (80 x \right )+96 \,{\mathrm e} x \ln \left (80 x \right )+16 \,{\mathrm e}^{2} x \ln \left (80 x \right )+\left (816+80 \,{\mathrm e}^{2}+512 \,{\mathrm e}\right ) x}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}\) | \(120\) |
| default | \(\frac {704 x +\left (40 \,{\mathrm e}+128\right ) \left (x \ln \left (x \right )-x \right )+16 \,{\mathrm e}^{2} \ln \left (80\right ) x +16 x \,{\mathrm e}^{2} \ln \left (x \right )+64 \,{\mathrm e}^{2} x +8 \,{\mathrm e} \ln \left (80\right ) \ln \left (x \right ) x +96 \,{\mathrm e} \ln \left (80\right ) x +8 \,{\mathrm e} \ln \left (x \right )^{2} x +88 x \,{\mathrm e} \ln \left (x \right )+424 x \,{\mathrm e}+\ln \left (80\right ) \ln \left (x \right )^{2} x +24 \ln \left (80\right ) \ln \left (x \right ) x +144 \ln \left (80\right ) x +x \ln \left (x \right )^{3}+28 x \ln \left (x \right )^{2}+112 x \ln \left (x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}\) | \(133\) |
| risch | \(\frac {x \ln \left (x \right )^{3}}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {x \left (56+2 \ln \left (5\right )+16 \,{\mathrm e}+8 \ln \left (2\right )\right ) \ln \left (x \right )^{2}}{2 \,{\mathrm e}^{2}+12 \,{\mathrm e}+18}+\frac {4 x \left (60+2 \ln \left (5\right ) {\mathrm e}+4 \,{\mathrm e}^{2}+8 \,{\mathrm e} \ln \left (2\right )+6 \ln \left (5\right )+32 \,{\mathrm e}+24 \ln \left (2\right )\right ) \ln \left (x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {16 x \,{\mathrm e}^{2} \ln \left (5\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {64 x \,{\mathrm e}^{2} \ln \left (2\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {96 x \ln \left (5\right ) {\mathrm e}}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {384 x \,{\mathrm e} \ln \left (2\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {64 x \,{\mathrm e}^{2}}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {144 x \ln \left (5\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {384 x \,{\mathrm e}}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {576 x \ln \left (2\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {576 x}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}\) | \(235\) |
| parts | \(\frac {\ln \left (80\right ) \left (x \ln \left (x \right )^{2}-2 x \ln \left (x \right )+2 x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {x \ln \left (x \right )^{3}-3 x \ln \left (x \right )^{2}+6 x \ln \left (x \right )-6 x}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {31 x \ln \left (x \right )^{2}-62 x \ln \left (x \right )+62 x}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {8 \,{\mathrm e} \ln \left (80\right ) \left (x \ln \left (x \right )-x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {8 \,{\mathrm e} \left (x \ln \left (x \right )^{2}-2 x \ln \left (x \right )+2 x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {40 \,{\mathrm e} \left (x \ln \left (x \right )-x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {26 \ln \left (80\right ) \left (x \ln \left (x \right )-x \right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {128 x \ln \left (x \right )-128 x}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}+\frac {16 \left (5 \,{\mathrm e}+17\right ) x}{3+{\mathrm e}}+\frac {8 \left (2 \,{\mathrm e}+7\right ) \left (\ln \left (80 x \right ) x -x \right )}{3+{\mathrm e}}\) | \(262\) |
| orering | \(\frac {\left (\left (\ln \left (x \right )^{2}+\left (8 \,{\mathrm e}+26\right ) \ln \left (x \right )+16 \,{\mathrm e}^{2}+104 \,{\mathrm e}+168\right ) \ln \left (80 x \right )+5 \ln \left (x \right )^{2}+\left (40 \,{\mathrm e}+128\right ) \ln \left (x \right )+80 \,{\mathrm e}^{2}+512 \,{\mathrm e}+816\right ) x}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}-\frac {x^{2} \left (\left (\frac {2 \ln \left (x \right )}{x}+\frac {8 \,{\mathrm e}+26}{x}\right ) \ln \left (80 x \right )+\frac {\ln \left (x \right )^{2}+\left (8 \,{\mathrm e}+26\right ) \ln \left (x \right )+16 \,{\mathrm e}^{2}+104 \,{\mathrm e}+168}{x}+\frac {10 \ln \left (x \right )}{x}+\frac {40 \,{\mathrm e}+128}{x}\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}-\frac {2 x^{3} \left (\left (\frac {2}{x^{2}}-\frac {2 \ln \left (x \right )}{x^{2}}-\frac {8 \,{\mathrm e}+26}{x^{2}}\right ) \ln \left (80 x \right )+\frac {\frac {4 \ln \left (x \right )}{x}+\frac {2 \left (8 \,{\mathrm e}+26\right )}{x}}{x}-\frac {\ln \left (x \right )^{2}+\left (8 \,{\mathrm e}+26\right ) \ln \left (x \right )+16 \,{\mathrm e}^{2}+104 \,{\mathrm e}+168}{x^{2}}+\frac {10}{x^{2}}-\frac {10 \ln \left (x \right )}{x^{2}}-\frac {40 \,{\mathrm e}+128}{x^{2}}\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}-\frac {x^{4} \left (\left (-\frac {6}{x^{3}}+\frac {4 \ln \left (x \right )}{x^{3}}+\frac {16 \,{\mathrm e}+52}{x^{3}}\right ) \ln \left (80 x \right )+\frac {\frac {6}{x^{2}}-\frac {6 \ln \left (x \right )}{x^{2}}-\frac {3 \left (8 \,{\mathrm e}+26\right )}{x^{2}}}{x}-\frac {3 \left (\frac {2 \ln \left (x \right )}{x}+\frac {8 \,{\mathrm e}+26}{x}\right )}{x^{2}}+\frac {2 \ln \left (x \right )^{2}+2 \left (8 \,{\mathrm e}+26\right ) \ln \left (x \right )+32 \,{\mathrm e}^{2}+208 \,{\mathrm e}+336}{x^{3}}-\frac {30}{x^{3}}+\frac {20 \ln \left (x \right )}{x^{3}}+\frac {80 \,{\mathrm e}+256}{x^{3}}\right )}{{\mathrm e}^{2}+6 \,{\mathrm e}+9}\) | \(435\) |
Input:
int(((ln(x)^2+(8*exp(1)+26)*ln(x)+16*exp(1)^2+104*exp(1)+168)*ln(80*x)+5*l n(x)^2+(40*exp(1)+128)*ln(x)+80*exp(1)^2+512*exp(1)+816)/(exp(1)^2+6*exp(1 )+9),x,method=_RETURNVERBOSE)
Output:
((64*exp(1)+192)*x+(16*exp(1)+48)*x*ln(80*x)+1/(3+exp(1))*x*ln(x)^2*ln(80* x)+32*x*ln(x)+8*x*ln(x)*ln(80*x)+4/(3+exp(1))*x*ln(x)^2)/(3+exp(1))
Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (21) = 42\).
Time = 0.07 (sec) , antiderivative size = 95, normalized size of antiderivative = 4.13 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=\frac {x \log \left (x\right )^{3} + {\left (8 \, x e + x \log \left (80\right ) + 28 \, x\right )} \log \left (x\right )^{2} + 64 \, x e^{2} + 384 \, x e + 16 \, {\left (x e^{2} + 6 \, x e + 9 \, x\right )} \log \left (80\right ) + 8 \, {\left (2 \, x e^{2} + 16 \, x e + {\left (x e + 3 \, x\right )} \log \left (80\right ) + 30 \, x\right )} \log \left (x\right ) + 576 \, x}{e^{2} + 6 \, e + 9} \] Input:
integrate(((log(x)^2+(8*exp(1)+26)*log(x)+16*exp(1)^2+104*exp(1)+168)*log( 80*x)+5*log(x)^2+(40*exp(1)+128)*log(x)+80*exp(1)^2+512*exp(1)+816)/(exp(1 )^2+6*exp(1)+9),x, algorithm="fricas")
Output:
(x*log(x)^3 + (8*x*e + x*log(80) + 28*x)*log(x)^2 + 64*x*e^2 + 384*x*e + 1 6*(x*e^2 + 6*x*e + 9*x)*log(80) + 8*(2*x*e^2 + 16*x*e + (x*e + 3*x)*log(80 ) + 30*x)*log(x) + 576*x)/(e^2 + 6*e + 9)
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (20) = 40\).
Time = 0.16 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.48 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=\frac {x \log {\left (x \right )}^{3}}{e^{2} + 9 + 6 e} + x \left (64 + 16 \log {\left (80 \right )}\right ) + \frac {\left (x \log {\left (80 \right )} + 8 e x + 28 x\right ) \log {\left (x \right )}^{2}}{e^{2} + 9 + 6 e} + \frac {\left (8 x \log {\left (80 \right )} + 16 e x + 80 x\right ) \log {\left (x \right )}}{e + 3} \] Input:
integrate(((ln(x)**2+(8*exp(1)+26)*ln(x)+16*exp(1)**2+104*exp(1)+168)*ln(8 0*x)+5*ln(x)**2+(40*exp(1)+128)*ln(x)+80*exp(1)**2+512*exp(1)+816)/(exp(1) **2+6*exp(1)+9),x)
Output:
x*log(x)**3/(exp(2) + 9 + 6*E) + x*(64 + 16*log(80)) + (x*log(80) + 8*E*x + 28*x)*log(x)**2/(exp(2) + 9 + 6*E) + (8*x*log(80) + 16*E*x + 80*x)*log(x )/(E + 3)
Leaf count of result is larger than twice the leaf count of optimal. 133 vs. \(2 (21) = 42\).
Time = 0.04 (sec) , antiderivative size = 133, normalized size of antiderivative = 5.78 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=-\frac {2 \, x {\left (4 \, e + 11\right )} \log \left (x\right ) + x \log \left (x\right )^{2} - 5 \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + 2 \, x {\left (8 \, e^{2} + 44 \, e + 61\right )} - 8 \, {\left (x \log \left (x\right ) - x\right )} {\left (5 \, e + 16\right )} - 80 \, x e^{2} - 512 \, x e - {\left ({\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + 2 \, {\left (x \log \left (x\right ) - x\right )} {\left (4 \, e + 13\right )} + 16 \, x e^{2} + 104 \, x e + 168 \, x\right )} \log \left (80 \, x\right ) - 816 \, x}{e^{2} + 6 \, e + 9} \] Input:
integrate(((log(x)^2+(8*exp(1)+26)*log(x)+16*exp(1)^2+104*exp(1)+168)*log( 80*x)+5*log(x)^2+(40*exp(1)+128)*log(x)+80*exp(1)^2+512*exp(1)+816)/(exp(1 )^2+6*exp(1)+9),x, algorithm="maxima")
Output:
-(2*x*(4*e + 11)*log(x) + x*log(x)^2 - 5*(log(x)^2 - 2*log(x) + 2)*x + 2*x *(8*e^2 + 44*e + 61) - 8*(x*log(x) - x)*(5*e + 16) - 80*x*e^2 - 512*x*e - ((log(x)^2 - 2*log(x) + 2)*x + 2*(x*log(x) - x)*(4*e + 13) + 16*x*e^2 + 10 4*x*e + 168*x)*log(80*x) - 816*x)/(e^2 + 6*e + 9)
Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (21) = 42\).
Time = 0.11 (sec) , antiderivative size = 125, normalized size of antiderivative = 5.43 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=\frac {8 \, x e \log \left (80\right ) \log \left (x\right ) + 8 \, x e \log \left (x\right )^{2} + x \log \left (80\right ) \log \left (x\right )^{2} + x \log \left (x\right )^{3} + 16 \, x e^{2} \log \left (80\right ) + 96 \, x e \log \left (80\right ) + 16 \, x e^{2} \log \left (x\right ) + 88 \, x e \log \left (x\right ) + 24 \, x \log \left (80\right ) \log \left (x\right ) + 28 \, x \log \left (x\right )^{2} + 8 \, {\left (x \log \left (x\right ) - x\right )} {\left (5 \, e + 16\right )} + 64 \, x e^{2} + 424 \, x e + 144 \, x \log \left (80\right ) + 112 \, x \log \left (x\right ) + 704 \, x}{e^{2} + 6 \, e + 9} \] Input:
integrate(((log(x)^2+(8*exp(1)+26)*log(x)+16*exp(1)^2+104*exp(1)+168)*log( 80*x)+5*log(x)^2+(40*exp(1)+128)*log(x)+80*exp(1)^2+512*exp(1)+816)/(exp(1 )^2+6*exp(1)+9),x, algorithm="giac")
Output:
(8*x*e*log(80)*log(x) + 8*x*e*log(x)^2 + x*log(80)*log(x)^2 + x*log(x)^3 + 16*x*e^2*log(80) + 96*x*e*log(80) + 16*x*e^2*log(x) + 88*x*e*log(x) + 24* x*log(80)*log(x) + 28*x*log(x)^2 + 8*(x*log(x) - x)*(5*e + 16) + 64*x*e^2 + 424*x*e + 144*x*log(80) + 112*x*log(x) + 704*x)/(e^2 + 6*e + 9)
Time = 0.51 (sec) , antiderivative size = 76, normalized size of antiderivative = 3.30 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=\frac {x\,\left ({\ln \left (x\right )}^3+{\ln \left (x\right )}^2\,\left (\ln \left (80\,x\right )+8\,\mathrm {e}-\ln \left (x\right )+28\right )+16\,{\left (\mathrm {e}+3\right )}^2\,\left (\ln \left (80\,x\right )-\ln \left (x\right )+4\right )+8\,\ln \left (x\right )\,\left (\mathrm {e}+3\right )\,\left (\ln \left (80\,x\right )+2\,\mathrm {e}-\ln \left (x\right )+10\right )\right )}{6\,\mathrm {e}+{\mathrm {e}}^2+9} \] Input:
int((512*exp(1) + 80*exp(2) + log(80*x)*(104*exp(1) + 16*exp(2) + log(x)^2 + log(x)*(8*exp(1) + 26) + 168) + 5*log(x)^2 + log(x)*(40*exp(1) + 128) + 816)/(6*exp(1) + exp(2) + 9),x)
Output:
(x*(log(x)^3 + log(x)^2*(log(80*x) + 8*exp(1) - log(x) + 28) + 16*(exp(1) + 3)^2*(log(80*x) - log(x) + 4) + 8*log(x)*(exp(1) + 3)*(log(80*x) + 2*exp (1) - log(x) + 10)))/(6*exp(1) + exp(2) + 9)
Time = 0.26 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.70 \[ \int \frac {816+512 e+80 e^2+(128+40 e) \log (x)+5 \log ^2(x)+\left (168+104 e+16 e^2+(26+8 e) \log (x)+\log ^2(x)\right ) \log (80 x)}{9+6 e+e^2} \, dx=\frac {x \left (\mathrm {log}\left (80 x \right ) \mathrm {log}\left (x \right )^{2}+8 \,\mathrm {log}\left (80 x \right ) \mathrm {log}\left (x \right ) e +24 \,\mathrm {log}\left (80 x \right ) \mathrm {log}\left (x \right )+16 \,\mathrm {log}\left (80 x \right ) e^{2}+96 \,\mathrm {log}\left (80 x \right ) e +144 \,\mathrm {log}\left (80 x \right )+4 \mathrm {log}\left (x \right )^{2}+32 \,\mathrm {log}\left (x \right ) e +96 \,\mathrm {log}\left (x \right )+64 e^{2}+384 e +576\right )}{e^{2}+6 e +9} \] Input:
int(((log(x)^2+(8*exp(1)+26)*log(x)+16*exp(1)^2+104*exp(1)+168)*log(80*x)+ 5*log(x)^2+(40*exp(1)+128)*log(x)+80*exp(1)^2+512*exp(1)+816)/(exp(1)^2+6* exp(1)+9),x)
Output:
(x*(log(80*x)*log(x)**2 + 8*log(80*x)*log(x)*e + 24*log(80*x)*log(x) + 16* log(80*x)*e**2 + 96*log(80*x)*e + 144*log(80*x) + 4*log(x)**2 + 32*log(x)* e + 96*log(x) + 64*e**2 + 384*e + 576))/(e**2 + 6*e + 9)