Integrand size = 117, antiderivative size = 30 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=e^{\frac {x}{3-e-e^4}-(\log (3)-\log (-5+x))^2} \] Output:
exp(x/(-exp(4)+3-exp(1))-(ln(3)-ln(-5+x))^2)
\[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=\int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx \] Input:
Integrate[(E^((-x + (3 - E - E^4)*Log[3]^2 + (-6 + 2*E + 2*E^4)*Log[3]*Log [-5 + x] + (3 - E - E^4)*Log[-5 + x]^2)/(-3 + E + E^4))*(5 - x + (-6 + 2*E + 2*E^4)*Log[3] + (6 - 2*E - 2*E^4)*Log[-5 + x]))/(15 + E*(-5 + x) + E^4* (-5 + x) - 3*x),x]
Output:
Integrate[(E^((-x + (3 - E - E^4)*Log[3]^2 + (-6 + 2*E + 2*E^4)*Log[3]*Log [-5 + x] + (3 - E - E^4)*Log[-5 + x]^2)/(-3 + E + E^4))*(5 - x + (-6 + 2*E + 2*E^4)*Log[3] + (6 - 2*E - 2*E^4)*Log[-5 + x]))/(15 + E*(-5 + x) + E^4* (-5 + x) - 3*x), x]
Leaf count is larger than twice the leaf count of optimal. \(109\) vs. \(2(30)=60\).
Time = 1.39 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.63, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6, 2704, 2019, 27, 2726}
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.
| \(\displaystyle \int \frac {\left (-x+\left (6-2 e-2 e^4\right ) \log (x-5)+5+\left (-6+2 e+2 e^4\right ) \log (3)\right ) \exp \left (\frac {-x+\left (3-e-e^4\right ) \log ^2(x-5)+\left (-6+2 e+2 e^4\right ) \log (3) \log (x-5)+\left (3-e-e^4\right ) \log ^2(3)}{-3+e+e^4}\right )}{e^4 (x-5)+e (x-5)-3 x+15} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (-x+\left (6-2 e-2 e^4\right ) \log (x-5)+5+\left (-6+2 e+2 e^4\right ) \log (3)\right ) \exp \left (\frac {-x+\left (3-e-e^4\right ) \log ^2(x-5)+\left (-6+2 e+2 e^4\right ) \log (3) \log (x-5)+\left (3-e-e^4\right ) \log ^2(3)}{-3+e+e^4}\right )}{\left (e+e^4\right ) (x-5)-3 x+15}dx\) |
| \(\Big \downarrow \) 2704 |
| \(\displaystyle \int \frac {(x-5)^{\frac {\left (-6+2 e+2 e^4\right ) \log (3)}{-3+e+e^4}} \left (-x+\left (6-2 e-2 e^4\right ) \log (x-5)+5+\left (-6+2 e+2 e^4\right ) \log (3)\right ) \exp \left (\frac {-x+\left (3-e-e^4\right ) \log ^2(x-5)+\left (3-e-e^4\right ) \log ^2(3)}{-3+e+e^4}\right )}{\left (e+e^4\right ) (x-5)-3 x+15}dx\) |
| \(\Big \downarrow \) 2019 |
| \(\displaystyle \int \frac {(x-5)^{\frac {\left (-6+2 e+2 e^4\right ) \log (3)}{-3+e+e^4}-1} \left (-x+\left (6-2 e-2 e^4\right ) \log (x-5)+5+\left (-6+2 e+2 e^4\right ) \log (3)\right ) \exp \left (\frac {-x+\left (3-e-e^4\right ) \log ^2(x-5)+\left (3-e-e^4\right ) \log ^2(3)}{-3+e+e^4}\right )}{-3+e+e^4}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {\int \exp \left (\frac {-\left (\left (3-e-e^4\right ) \log ^2(x-5)\right )+x-\left (3-e-e^4\right ) \log ^2(3)}{3-e-e^4}\right ) (x-5)^{-1+\log (9)} \left (-x+2 \left (3-e-e^4\right ) \log (x-5)-2 \left (3-e-e^4\right ) \log (3)+5\right )dx}{3-e-e^4}\) |
| \(\Big \downarrow \) 2726 |
| \(\displaystyle -\frac {(x-5)^{\log (9)-1} \left (-x+2 \left (3-e-e^4\right ) \log (x-5)+5\right ) \exp \left (\frac {x-\left (\left (3-e-e^4\right ) \log ^2(x-5)\right )-\left (3-e-e^4\right ) \log ^2(3)}{3-e-e^4}\right )}{\frac {2 \left (3-e-e^4\right ) \log (x-5)}{5-x}+1}\) |
Input:
Int[(E^((-x + (3 - E - E^4)*Log[3]^2 + (-6 + 2*E + 2*E^4)*Log[3]*Log[-5 + x] + (3 - E - E^4)*Log[-5 + x]^2)/(-3 + E + E^4))*(5 - x + (-6 + 2*E + 2*E ^4)*Log[3] + (6 - 2*E - 2*E^4)*Log[-5 + x]))/(15 + E*(-5 + x) + E^4*(-5 + x) - 3*x),x]
Output:
-((E^((x - (3 - E - E^4)*Log[3]^2 - (3 - E - E^4)*Log[-5 + x]^2)/(3 - E - E^4))*(-5 + x)^(-1 + Log[9])*(5 - x + 2*(3 - E - E^4)*Log[-5 + x]))/(1 + ( 2*(3 - E - E^4)*Log[-5 + x])/(5 - x)))
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_.)*(Qx_)^(q_.), x_Symbol] :> Int[u*PolynomialQuotient[Px , Qx, x]^p*Qx^(p + q), x] /; FreeQ[q, x] && PolyQ[Px, x] && PolyQ[Qx, x] && EqQ[PolynomialRemainder[Px, Qx, x], 0] && IntegerQ[p] && LtQ[p*q, 0]
Int[(u_.)*(F_)^((a_.)*(Log[z_]*(b_.) + (v_.))), x_Symbol] :> Int[u*F^(a*v)* z^(a*b*Log[F]), x] /; FreeQ[{F, a, b}, x]
Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z, x], w*y]] /; FreeQ[F, x]
Leaf count of result is larger than twice the leaf count of optimal. \(63\) vs. \(2(29)=58\).
Time = 0.38 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.13
| method | result | size |
| norman | \({\mathrm e}^{\frac {\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (-5+x \right )^{2}+\left (2 \,{\mathrm e}^{4}+2 \,{\mathrm e}-6\right ) \ln \left (3\right ) \ln \left (-5+x \right )+\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (3\right )^{2}-x}{{\mathrm e}^{4}+{\mathrm e}-3}}\) | \(64\) |
| risch | \({\mathrm e}^{-\frac {{\mathrm e}^{4} \ln \left (3\right )^{2}+\ln \left (3\right )^{2} {\mathrm e}-2 \ln \left (3\right ) \ln \left (-5+x \right ) {\mathrm e}^{4}-2 \ln \left (3\right ) \ln \left (-5+x \right ) {\mathrm e}+\ln \left (-5+x \right )^{2} {\mathrm e}^{4}+\ln \left (-5+x \right )^{2} {\mathrm e}-3 \ln \left (3\right )^{2}+6 \ln \left (3\right ) \ln \left (-5+x \right )-3 \ln \left (-5+x \right )^{2}+x}{{\mathrm e}^{4}+{\mathrm e}-3}}\) | \(88\) |
| parallelrisch | \(\frac {{\mathrm e}^{4} {\mathrm e}^{\frac {\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (-5+x \right )^{2}+\left (2 \,{\mathrm e}^{4}+2 \,{\mathrm e}-6\right ) \ln \left (3\right ) \ln \left (-5+x \right )+\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (3\right )^{2}-x}{{\mathrm e}^{4}+{\mathrm e}-3}}+{\mathrm e} \,{\mathrm e}^{\frac {\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (-5+x \right )^{2}+\left (2 \,{\mathrm e}^{4}+2 \,{\mathrm e}-6\right ) \ln \left (3\right ) \ln \left (-5+x \right )+\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (3\right )^{2}-x}{{\mathrm e}^{4}+{\mathrm e}-3}}-3 \,{\mathrm e}^{\frac {\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (-5+x \right )^{2}+\left (2 \,{\mathrm e}^{4}+2 \,{\mathrm e}-6\right ) \ln \left (3\right ) \ln \left (-5+x \right )+\left (-{\mathrm e}^{4}+3-{\mathrm e}\right ) \ln \left (3\right )^{2}-x}{{\mathrm e}^{4}+{\mathrm e}-3}}}{{\mathrm e}^{4}+{\mathrm e}-3}\) | \(208\) |
Input:
int(((-2*exp(4)-2*exp(1)+6)*ln(-5+x)+(2*exp(4)+2*exp(1)-6)*ln(3)+5-x)*exp( ((-exp(4)+3-exp(1))*ln(-5+x)^2+(2*exp(4)+2*exp(1)-6)*ln(3)*ln(-5+x)+(-exp( 4)+3-exp(1))*ln(3)^2-x)/(exp(4)+exp(1)-3))/((-5+x)*exp(4)+(-5+x)*exp(1)+15 -3*x),x,method=_RETURNVERBOSE)
Output:
exp(((-exp(4)+3-exp(1))*ln(-5+x)^2+(2*exp(4)+2*exp(1)-6)*ln(3)*ln(-5+x)+(- exp(4)+3-exp(1))*ln(3)^2-x)/(exp(4)+exp(1)-3))
Time = 0.12 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.70 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=e^{\left (-\frac {{\left (e^{4} + e - 3\right )} \log \left (3\right )^{2} - 2 \, {\left (e^{4} + e - 3\right )} \log \left (3\right ) \log \left (x - 5\right ) + {\left (e^{4} + e - 3\right )} \log \left (x - 5\right )^{2} + x}{e^{4} + e - 3}\right )} \] Input:
integrate(((-2*exp(4)-2*exp(1)+6)*log(-5+x)+(2*exp(4)+2*exp(1)-6)*log(3)+5 -x)*exp(((-exp(4)+3-exp(1))*log(-5+x)^2+(2*exp(4)+2*exp(1)-6)*log(3)*log(- 5+x)+(-exp(4)+3-exp(1))*log(3)^2-x)/(exp(4)+exp(1)-3))/((-5+x)*exp(4)+(-5+ x)*exp(1)+15-3*x),x, algorithm="fricas")
Output:
e^(-((e^4 + e - 3)*log(3)^2 - 2*(e^4 + e - 3)*log(3)*log(x - 5) + (e^4 + e - 3)*log(x - 5)^2 + x)/(e^4 + e - 3))
Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (20) = 40\).
Time = 0.40 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.00 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=e^{\frac {- x + \left (- e^{4} - e + 3\right ) \log {\left (x - 5 \right )}^{2} + \left (-6 + 2 e + 2 e^{4}\right ) \log {\left (3 \right )} \log {\left (x - 5 \right )} + \left (- e^{4} - e + 3\right ) \log {\left (3 \right )}^{2}}{-3 + e + e^{4}}} \] Input:
integrate(((-2*exp(4)-2*exp(1)+6)*ln(-5+x)+(2*exp(4)+2*exp(1)-6)*ln(3)+5-x )*exp(((-exp(4)+3-exp(1))*ln(-5+x)**2+(2*exp(4)+2*exp(1)-6)*ln(3)*ln(-5+x) +(-exp(4)+3-exp(1))*ln(3)**2-x)/(exp(4)+exp(1)-3))/((-5+x)*exp(4)+(-5+x)*e xp(1)+15-3*x),x)
Output:
exp((-x + (-exp(4) - E + 3)*log(x - 5)**2 + (-6 + 2*E + 2*exp(4))*log(3)*l og(x - 5) + (-exp(4) - E + 3)*log(3)**2)/(-3 + E + exp(4)))
Leaf count of result is larger than twice the leaf count of optimal. 163 vs. \(2 (26) = 52\).
Time = 0.37 (sec) , antiderivative size = 163, normalized size of antiderivative = 5.43 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=e^{\left (-\frac {e^{4} \log \left (3\right )^{2}}{e^{4} + e - 3} - \frac {e \log \left (3\right )^{2}}{e^{4} + e - 3} + \frac {2 \, e^{4} \log \left (3\right ) \log \left (x - 5\right )}{e^{4} + e - 3} + \frac {2 \, e \log \left (3\right ) \log \left (x - 5\right )}{e^{4} + e - 3} - \frac {e^{4} \log \left (x - 5\right )^{2}}{e^{4} + e - 3} - \frac {e \log \left (x - 5\right )^{2}}{e^{4} + e - 3} + \frac {3 \, \log \left (3\right )^{2}}{e^{4} + e - 3} - \frac {6 \, \log \left (3\right ) \log \left (x - 5\right )}{e^{4} + e - 3} + \frac {3 \, \log \left (x - 5\right )^{2}}{e^{4} + e - 3} - \frac {x}{e^{4} + e - 3}\right )} \] Input:
integrate(((-2*exp(4)-2*exp(1)+6)*log(-5+x)+(2*exp(4)+2*exp(1)-6)*log(3)+5 -x)*exp(((-exp(4)+3-exp(1))*log(-5+x)^2+(2*exp(4)+2*exp(1)-6)*log(3)*log(- 5+x)+(-exp(4)+3-exp(1))*log(3)^2-x)/(exp(4)+exp(1)-3))/((-5+x)*exp(4)+(-5+ x)*exp(1)+15-3*x),x, algorithm="maxima")
Output:
e^(-e^4*log(3)^2/(e^4 + e - 3) - e*log(3)^2/(e^4 + e - 3) + 2*e^4*log(3)*l og(x - 5)/(e^4 + e - 3) + 2*e*log(3)*log(x - 5)/(e^4 + e - 3) - e^4*log(x - 5)^2/(e^4 + e - 3) - e*log(x - 5)^2/(e^4 + e - 3) + 3*log(3)^2/(e^4 + e - 3) - 6*log(3)*log(x - 5)/(e^4 + e - 3) + 3*log(x - 5)^2/(e^4 + e - 3) - x/(e^4 + e - 3))
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (26) = 52\).
Time = 0.42 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.57 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=e^{\left (-\log \left (3\right )^{2} + \frac {2 \, e^{4} \log \left (3\right ) \log \left (x - 5\right ) + 2 \, e \log \left (3\right ) \log \left (x - 5\right ) - e^{4} \log \left (x - 5\right )^{2} - e \log \left (x - 5\right )^{2} - 6 \, \log \left (3\right ) \log \left (x - 5\right ) + 3 \, \log \left (x - 5\right )^{2} - x}{e^{4} + e - 3}\right )} \] Input:
integrate(((-2*exp(4)-2*exp(1)+6)*log(-5+x)+(2*exp(4)+2*exp(1)-6)*log(3)+5 -x)*exp(((-exp(4)+3-exp(1))*log(-5+x)^2+(2*exp(4)+2*exp(1)-6)*log(3)*log(- 5+x)+(-exp(4)+3-exp(1))*log(3)^2-x)/(exp(4)+exp(1)-3))/((-5+x)*exp(4)+(-5+ x)*exp(1)+15-3*x),x, algorithm="giac")
Output:
e^(-log(3)^2 + (2*e^4*log(3)*log(x - 5) + 2*e*log(3)*log(x - 5) - e^4*log( x - 5)^2 - e*log(x - 5)^2 - 6*log(3)*log(x - 5) + 3*log(x - 5)^2 - x)/(e^4 + e - 3))
Time = 1.01 (sec) , antiderivative size = 125, normalized size of antiderivative = 4.17 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx={\mathrm {e}}^{\frac {3\,{\ln \left (3\right )}^2}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\mathrm {e}}^{-\frac {{\ln \left (x-5\right )}^2\,\mathrm {e}}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\mathrm {e}}^{-\frac {{\ln \left (x-5\right )}^2\,{\mathrm {e}}^4}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\mathrm {e}}^{-\frac {\mathrm {e}\,{\ln \left (3\right )}^2}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^4\,{\ln \left (3\right )}^2}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\mathrm {e}}^{-\frac {x}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\mathrm {e}}^{\frac {3\,{\ln \left (x-5\right )}^2}{\mathrm {e}+{\mathrm {e}}^4-3}}\,{\left (x-5\right )}^{2\,\ln \left (3\right )} \] Input:
int(-(exp(-(x + log(x - 5)^2*(exp(1) + exp(4) - 3) + log(3)^2*(exp(1) + ex p(4) - 3) - log(x - 5)*log(3)*(2*exp(1) + 2*exp(4) - 6))/(exp(1) + exp(4) - 3))*(x + log(x - 5)*(2*exp(1) + 2*exp(4) - 6) - log(3)*(2*exp(1) + 2*exp (4) - 6) - 5))/(exp(1)*(x - 5) - 3*x + exp(4)*(x - 5) + 15),x)
Output:
exp((3*log(3)^2)/(exp(1) + exp(4) - 3))*exp(-(log(x - 5)^2*exp(1))/(exp(1) + exp(4) - 3))*exp(-(log(x - 5)^2*exp(4))/(exp(1) + exp(4) - 3))*exp(-(ex p(1)*log(3)^2)/(exp(1) + exp(4) - 3))*exp(-(exp(4)*log(3)^2)/(exp(1) + exp (4) - 3))*exp(-x/(exp(1) + exp(4) - 3))*exp((3*log(x - 5)^2)/(exp(1) + exp (4) - 3))*(x - 5)^(2*log(3))
Time = 0.48 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.33 \[ \int \frac {e^{\frac {-x+\left (3-e-e^4\right ) \log ^2(3)+\left (-6+2 e+2 e^4\right ) \log (3) \log (-5+x)+\left (3-e-e^4\right ) \log ^2(-5+x)}{-3+e+e^4}} \left (5-x+\left (-6+2 e+2 e^4\right ) \log (3)+\left (6-2 e-2 e^4\right ) \log (-5+x)\right )}{15+e (-5+x)+e^4 (-5+x)-3 x} \, dx=\frac {\left (-5+x \right )^{2 \,\mathrm {log}\left (3\right )}}{e^{\frac {\mathrm {log}\left (-5+x \right )^{2} e^{4}+\mathrm {log}\left (-5+x \right )^{2} e -3 \mathrm {log}\left (-5+x \right )^{2}+\mathrm {log}\left (3\right )^{2} e^{4}+\mathrm {log}\left (3\right )^{2} e -3 \mathrm {log}\left (3\right )^{2}+x}{e^{4}+e -3}}} \] Input:
int(((-2*exp(4)-2*exp(1)+6)*log(-5+x)+(2*exp(4)+2*exp(1)-6)*log(3)+5-x)*ex p(((-exp(4)+3-exp(1))*log(-5+x)^2+(2*exp(4)+2*exp(1)-6)*log(3)*log(-5+x)+( -exp(4)+3-exp(1))*log(3)^2-x)/(exp(4)+exp(1)-3))/((-5+x)*exp(4)+(-5+x)*exp (1)+15-3*x),x)
Output:
(x - 5)**(2*log(3))/e**((log(x - 5)**2*e**4 + log(x - 5)**2*e - 3*log(x - 5)**2 + log(3)**2*e**4 + log(3)**2*e - 3*log(3)**2 + x)/(e**4 + e - 3))