Integrand size = 141, antiderivative size = 25 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=x \left (-\frac {x}{-1+x}+2 e^3 x^3-\log (x)\right )^2 \] Output:
x*(2*x^3*exp(3)-ln(x)-x/(-1+x))^2
Leaf count is larger than twice the leaf count of optimal. \(121\) vs. \(2(25)=50\).
Time = 0.07 (sec) , antiderivative size = 121, normalized size of antiderivative = 4.84 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=-3+17 e^3-4 e^6+\frac {1}{(-1+x)^2}+\frac {3}{-1+x}-\frac {4 e^3}{-1+x}+x-4 e^3 x-4 e^3 x^2-4 e^3 x^3-4 e^3 x^4+4 e^6 x^7-2 \log (1-x)+2 \log (-1+x)+2 \log (x)+\frac {2 \log (x)}{-1+x}+2 x \log (x)-4 e^3 x^4 \log (x)+x \log ^2(x) \] Input:
Integrate[(2*x - 7*x^2 + 3*x^3 + E^3*(4*x^3 - 32*x^4 + 48*x^5 - 20*x^6) + E^6*(-28*x^6 + 84*x^7 - 84*x^8 + 28*x^9) + (-2 + 10*x - 12*x^2 + 4*x^3 + E ^3*(16*x^3 - 48*x^4 + 48*x^5 - 16*x^6))*Log[x] + (-1 + 3*x - 3*x^2 + x^3)* Log[x]^2)/(-1 + 3*x - 3*x^2 + x^3),x]
Output:
-3 + 17*E^3 - 4*E^6 + (-1 + x)^(-2) + 3/(-1 + x) - (4*E^3)/(-1 + x) + x - 4*E^3*x - 4*E^3*x^2 - 4*E^3*x^3 - 4*E^3*x^4 + 4*E^6*x^7 - 2*Log[1 - x] + 2 *Log[-1 + x] + 2*Log[x] + (2*Log[x])/(-1 + x) + 2*x*Log[x] - 4*E^3*x^4*Log [x] + x*Log[x]^2
Leaf count is larger than twice the leaf count of optimal. \(115\) vs. \(2(25)=50\).
Time = 0.66 (sec) , antiderivative size = 115, normalized size of antiderivative = 4.60, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {2007, 7293, 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.
\(\displaystyle \int \frac {3 x^3-7 x^2+\left (x^3-3 x^2+3 x-1\right ) \log ^2(x)+e^6 \left (28 x^9-84 x^8+84 x^7-28 x^6\right )+e^3 \left (-20 x^6+48 x^5-32 x^4+4 x^3\right )+\left (4 x^3-12 x^2+e^3 \left (-16 x^6+48 x^5-48 x^4+16 x^3\right )+10 x-2\right ) \log (x)+2 x}{x^3-3 x^2+3 x-1} \, dx\) |
\(\Big \downarrow \) 2007 |
\(\displaystyle \int \frac {3 x^3-7 x^2+\left (x^3-3 x^2+3 x-1\right ) \log ^2(x)+e^6 \left (28 x^9-84 x^8+84 x^7-28 x^6\right )+e^3 \left (-20 x^6+48 x^5-32 x^4+4 x^3\right )+\left (4 x^3-12 x^2+e^3 \left (-16 x^6+48 x^5-48 x^4+16 x^3\right )+10 x-2\right ) \log (x)+2 x}{(x-1)^3}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (28 e^6 x^6+\frac {3 x^3}{(x-1)^3}-\frac {7 x^2}{(x-1)^3}-\frac {4 e^3 \left (5 x^2-7 x+1\right ) x^3}{(x-1)^2}-\frac {2 \left (8 e^3 x^5-16 e^3 x^4+8 e^3 x^3-2 x^2+4 x-1\right ) \log (x)}{(x-1)^2}+\frac {2 x}{(x-1)^3}+\log ^2(x)\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle 4 e^6 x^7-4 e^3 x^4-4 e^3 x^4 \log (x)-4 e^3 x^3-\frac {x^2}{(1-x)^2}-4 e^3 x^2-4 e^3 x+x+\frac {4 e^3}{1-x}-\frac {5}{1-x}+\frac {2}{(1-x)^2}+x \log ^2(x)-\frac {2 x \log (x)}{1-x}+2 x \log (x)\) |
Input:
Int[(2*x - 7*x^2 + 3*x^3 + E^3*(4*x^3 - 32*x^4 + 48*x^5 - 20*x^6) + E^6*(- 28*x^6 + 84*x^7 - 84*x^8 + 28*x^9) + (-2 + 10*x - 12*x^2 + 4*x^3 + E^3*(16 *x^3 - 48*x^4 + 48*x^5 - 16*x^6))*Log[x] + (-1 + 3*x - 3*x^2 + x^3)*Log[x] ^2)/(-1 + 3*x - 3*x^2 + x^3),x]
Output:
2/(1 - x)^2 - 5/(1 - x) + (4*E^3)/(1 - x) + x - 4*E^3*x - 4*E^3*x^2 - x^2/ (1 - x)^2 - 4*E^3*x^3 - 4*E^3*x^4 + 4*E^6*x^7 + 2*x*Log[x] - (2*x*Log[x])/ (1 - x) - 4*E^3*x^4*Log[x] + x*Log[x]^2
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]
Leaf count of result is larger than twice the leaf count of optimal. \(83\) vs. \(2(24)=48\).
Time = 12.55 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.36
method | result | size |
default | \(x \ln \left (x \right )^{2}+2 x \ln \left (x \right )+x +4 \,{\mathrm e}^{6} x^{7}-4 x^{4} {\mathrm e}^{3}-4 x^{3} {\mathrm e}^{3}-4 x^{2} {\mathrm e}^{3}-4 x \,{\mathrm e}^{3}+\frac {1}{\left (-1+x \right )^{2}}-\frac {4 \,{\mathrm e}^{3}-3}{-1+x}-4 \,{\mathrm e}^{3} \ln \left (x \right ) x^{4}+\frac {2 \ln \left (x \right ) x}{-1+x}\) | \(84\) |
parts | \(x \ln \left (x \right )^{2}+2 x \ln \left (x \right )+x +4 \,{\mathrm e}^{6} x^{7}-4 x^{4} {\mathrm e}^{3}-4 x^{3} {\mathrm e}^{3}-4 x^{2} {\mathrm e}^{3}-4 x \,{\mathrm e}^{3}+\frac {1}{\left (-1+x \right )^{2}}-\frac {4 \,{\mathrm e}^{3}-3}{-1+x}-4 \,{\mathrm e}^{3} \ln \left (x \right ) x^{4}+\frac {2 \ln \left (x \right ) x}{-1+x}\) | \(84\) |
parallelrisch | \(\frac {4 \,{\mathrm e}^{6} x^{9}-8 \,{\mathrm e}^{6} x^{8}+4 \,{\mathrm e}^{6} x^{7}-4 \,{\mathrm e}^{3} \ln \left (x \right ) x^{6}-4 x^{6} {\mathrm e}^{3}+8 \,{\mathrm e}^{3} \ln \left (x \right ) x^{5}+4 x^{5} {\mathrm e}^{3}-4 \,{\mathrm e}^{3} \ln \left (x \right ) x^{4}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (x \right )-2 x^{2} \ln \left (x \right )^{2}+x^{3}-2 x^{2} \ln \left (x \right )+x \ln \left (x \right )^{2}}{x^{2}-2 x +1}\) | \(121\) |
risch | \(x \ln \left (x \right )^{2}-\frac {2 \left (2 x^{5} {\mathrm e}^{3}-2 x^{4} {\mathrm e}^{3}-x^{2}+x -1\right ) \ln \left (x \right )}{-1+x}+\frac {4 \,{\mathrm e}^{6} x^{9}-8 \,{\mathrm e}^{6} x^{8}+4 \,{\mathrm e}^{6} x^{7}-4 x^{6} {\mathrm e}^{3}+4 x^{5} {\mathrm e}^{3}+4 x^{2} {\mathrm e}^{3}+2 x^{2} \ln \left (x \right )+x^{3}-8 x \,{\mathrm e}^{3}-4 x \ln \left (x \right )-2 x^{2}+4 \,{\mathrm e}^{3}+2 \ln \left (x \right )+4 x -2}{\left (-1+x \right )^{2}}\) | \(125\) |
Input:
int(((x^3-3*x^2+3*x-1)*ln(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp(3)+4*x^ 3-12*x^2+10*x-2)*ln(x)+(28*x^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20*x^6+48* x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x,method=_RETU RNVERBOSE)
Output:
x*ln(x)^2+2*x*ln(x)+x+4*exp(6)*x^7-4*x^4*exp(3)-4*x^3*exp(3)-4*x^2*exp(3)- 4*x*exp(3)+1/(-1+x)^2-(4*exp(3)-3)/(-1+x)-4*exp(3)*ln(x)*x^4+2*ln(x)*x/(-1 +x)
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (24) = 48\).
Time = 0.08 (sec) , antiderivative size = 106, normalized size of antiderivative = 4.24 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=\frac {x^{3} + {\left (x^{3} - 2 \, x^{2} + x\right )} \log \left (x\right )^{2} - 2 \, x^{2} + 4 \, {\left (x^{9} - 2 \, x^{8} + x^{7}\right )} e^{6} - 4 \, {\left (x^{6} - x^{5} - x^{2} + 2 \, x - 1\right )} e^{3} + 2 \, {\left (x^{3} - x^{2} - 2 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{3}\right )} \log \left (x\right ) + 4 \, x - 2}{x^{2} - 2 \, x + 1} \] Input:
integrate(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp( 3)+4*x^3-12*x^2+10*x-2)*log(x)+(28*x^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20 *x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x, alg orithm="fricas")
Output:
(x^3 + (x^3 - 2*x^2 + x)*log(x)^2 - 2*x^2 + 4*(x^9 - 2*x^8 + x^7)*e^6 - 4* (x^6 - x^5 - x^2 + 2*x - 1)*e^3 + 2*(x^3 - x^2 - 2*(x^6 - 2*x^5 + x^4)*e^3 )*log(x) + 4*x - 2)/(x^2 - 2*x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (19) = 38\).
Time = 0.36 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.40 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=4 x^{7} e^{6} - 4 x^{4} e^{3} - 4 x^{3} e^{3} - 4 x^{2} e^{3} + x \log {\left (x \right )}^{2} + x \left (1 - 4 e^{3}\right ) + 2 \log {\left (x \right )} + \frac {x \left (3 - 4 e^{3}\right ) - 2 + 4 e^{3}}{x^{2} - 2 x + 1} + \frac {\left (- 4 x^{5} e^{3} + 4 x^{4} e^{3} + 2 x^{2} - 2 x + 2\right ) \log {\left (x \right )}}{x - 1} \] Input:
integrate(((x**3-3*x**2+3*x-1)*ln(x)**2+((-16*x**6+48*x**5-48*x**4+16*x**3 )*exp(3)+4*x**3-12*x**2+10*x-2)*ln(x)+(28*x**9-84*x**8+84*x**7-28*x**6)*ex p(3)**2+(-20*x**6+48*x**5-32*x**4+4*x**3)*exp(3)+3*x**3-7*x**2+2*x)/(x**3- 3*x**2+3*x-1),x)
Output:
4*x**7*exp(6) - 4*x**4*exp(3) - 4*x**3*exp(3) - 4*x**2*exp(3) + x*log(x)** 2 + x*(1 - 4*exp(3)) + 2*log(x) + (x*(3 - 4*exp(3)) - 2 + 4*exp(3))/(x**2 - 2*x + 1) + (-4*x**5*exp(3) + 4*x**4*exp(3) + 2*x**2 - 2*x + 2)*log(x)/(x - 1)
Leaf count of result is larger than twice the leaf count of optimal. 557 vs. \(2 (24) = 48\).
Time = 0.10 (sec) , antiderivative size = 557, normalized size of antiderivative = 22.28 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx =\text {Too large to display} \] Input:
integrate(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp( 3)+4*x^3-12*x^2+10*x-2)*log(x)+(28*x^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20 *x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x, alg orithm="maxima")
Output:
2/5*(10*x^7 + 35*x^6 + 84*x^5 + 175*x^4 + 350*x^3 + 735*x^2 + 1960*x - 35* (18*x - 17)/(x^2 - 2*x + 1) + 2520*log(x - 1))*e^6 - 14/5*(5*x^6 + 18*x^5 + 45*x^4 + 100*x^3 + 225*x^2 + 630*x - 15*(16*x - 15)/(x^2 - 2*x + 1) + 84 0*log(x - 1))*e^6 + 21/5*(4*x^5 + 15*x^4 + 40*x^3 + 100*x^2 + 300*x - 10*( 14*x - 13)/(x^2 - 2*x + 1) + 420*log(x - 1))*e^6 - 7*(x^4 + 4*x^3 + 12*x^2 + 40*x - 2*(12*x - 11)/(x^2 - 2*x + 1) + 60*log(x - 1))*e^6 - 5*(x^4 + 4* x^3 + 12*x^2 + 40*x - 2*(12*x - 11)/(x^2 - 2*x + 1) + 60*log(x - 1))*e^3 + 8*(2*x^3 + 9*x^2 + 36*x - 3*(10*x - 9)/(x^2 - 2*x + 1) + 60*log(x - 1))*e ^3 - 16*(x^2 + 6*x - (8*x - 7)/(x^2 - 2*x + 1) + 12*log(x - 1))*e^3 + 2*(2 *x - (6*x - 5)/(x^2 - 2*x + 1) + 6*log(x - 1))*e^3 + 3*x - 5*(2*x - 1)*log (x)/(x^2 - 2*x + 1) + (x^6*e^3 - 2*x^5*e^3 + x^4*e^3 - 2*x^3 + (x^3 - 2*x^ 2 + x)*log(x)^2 + 4*x^2 - 2*(2*x^6*e^3 - 4*x^5*e^3 + 2*x^4*e^3 - x^3 - 2*x ^2 + x)*log(x) + 2*x - 4)/(x^2 - 2*x + 1) - 3/2*(6*x - 5)/(x^2 - 2*x + 1) + 7/2*(4*x - 3)/(x^2 - 2*x + 1) - (2*x - 1)/(x^2 - 2*x + 1) + log(x)/(x^2 - 2*x + 1) - 4/(x - 1) - 6*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (24) = 48\).
Time = 0.12 (sec) , antiderivative size = 139, normalized size of antiderivative = 5.56 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=\frac {4 \, x^{9} e^{6} - 8 \, x^{8} e^{6} + 4 \, x^{7} e^{6} - 4 \, x^{6} e^{3} \log \left (x\right ) - 4 \, x^{6} e^{3} + 8 \, x^{5} e^{3} \log \left (x\right ) + 4 \, x^{5} e^{3} - 4 \, x^{4} e^{3} \log \left (x\right ) + x^{3} \log \left (x\right )^{2} + 2 \, x^{3} \log \left (x\right ) - 2 \, x^{2} \log \left (x\right )^{2} + x^{3} + 4 \, x^{2} e^{3} - 2 \, x^{2} \log \left (x\right ) + x \log \left (x\right )^{2} - 2 \, x^{2} - 8 \, x e^{3} + 4 \, x + 4 \, e^{3} - 2}{x^{2} - 2 \, x + 1} \] Input:
integrate(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp( 3)+4*x^3-12*x^2+10*x-2)*log(x)+(28*x^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20 *x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x, alg orithm="giac")
Output:
(4*x^9*e^6 - 8*x^8*e^6 + 4*x^7*e^6 - 4*x^6*e^3*log(x) - 4*x^6*e^3 + 8*x^5* e^3*log(x) + 4*x^5*e^3 - 4*x^4*e^3*log(x) + x^3*log(x)^2 + 2*x^3*log(x) - 2*x^2*log(x)^2 + x^3 + 4*x^2*e^3 - 2*x^2*log(x) + x*log(x)^2 - 2*x^2 - 8*x *e^3 + 4*x + 4*e^3 - 2)/(x^2 - 2*x + 1)
Time = 7.18 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.32 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=\frac {x\,{\left (x-\ln \left (x\right )+2\,x^3\,{\mathrm {e}}^3-2\,x^4\,{\mathrm {e}}^3+x\,\ln \left (x\right )\right )}^2}{{\left (x-1\right )}^2} \] Input:
int((2*x - 7*x^2 + 3*x^3 + log(x)*(10*x - 12*x^2 + 4*x^3 + exp(3)*(16*x^3 - 48*x^4 + 48*x^5 - 16*x^6) - 2) + log(x)^2*(3*x - 3*x^2 + x^3 - 1) + exp( 3)*(4*x^3 - 32*x^4 + 48*x^5 - 20*x^6) - exp(6)*(28*x^6 - 84*x^7 + 84*x^8 - 28*x^9))/(3*x - 3*x^2 + x^3 - 1),x)
Output:
(x*(x - log(x) + 2*x^3*exp(3) - 2*x^4*exp(3) + x*log(x))^2)/(x - 1)^2
Time = 0.17 (sec) , antiderivative size = 129, normalized size of antiderivative = 5.16 \[ \int \frac {2 x-7 x^2+3 x^3+e^3 \left (4 x^3-32 x^4+48 x^5-20 x^6\right )+e^6 \left (-28 x^6+84 x^7-84 x^8+28 x^9\right )+\left (-2+10 x-12 x^2+4 x^3+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right ) \log (x)+\left (-1+3 x-3 x^2+x^3\right ) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx=\frac {\mathrm {log}\left (x \right )^{2} x^{3}-2 \mathrm {log}\left (x \right )^{2} x^{2}+\mathrm {log}\left (x \right )^{2} x -4 \,\mathrm {log}\left (x \right ) e^{3} x^{6}+8 \,\mathrm {log}\left (x \right ) e^{3} x^{5}-4 \,\mathrm {log}\left (x \right ) e^{3} x^{4}+2 \,\mathrm {log}\left (x \right ) x^{3}-2 \,\mathrm {log}\left (x \right ) x^{2}+4 e^{6} x^{9}-8 e^{6} x^{8}+4 e^{6} x^{7}-4 e^{3} x^{6}+4 e^{3} x^{5}+x^{3}+x^{2}-2 x +1}{x^{2}-2 x +1} \] Input:
int(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp(3)+4*x ^3-12*x^2+10*x-2)*log(x)+(28*x^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20*x^6+4 8*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x)
Output:
(log(x)**2*x**3 - 2*log(x)**2*x**2 + log(x)**2*x - 4*log(x)*e**3*x**6 + 8* log(x)*e**3*x**5 - 4*log(x)*e**3*x**4 + 2*log(x)*x**3 - 2*log(x)*x**2 + 4* e**6*x**9 - 8*e**6*x**8 + 4*e**6*x**7 - 4*e**3*x**6 + 4*e**3*x**5 + x**3 + x**2 - 2*x + 1)/(x**2 - 2*x + 1)