\(\int \frac {3 e^{x+x^2}+e^{x+x^2} (-3+15 x-6 x^2) \log (x)+e^x (-1+5 x) \log ^2(x)+(-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)) \log (\frac {e^{-1/e} (3 e^{x^2} x+x \log (x))}{\log (x)})}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx\) [6293]

Optimal result

Integrand size = 113, antiderivative size = 31 \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=e^x \left (5-\log \left (e^{-1/e} \left (x+\frac {3 e^{x^2} x}{\log (x)}\right )\right )\right ) \]

[Out]

exp(x)*(5-ln((3*exp(x^2)*x/ln(x)+x)/exp(exp(-1))))

Rubi [A] (verified)

Time = 3.41 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.10, number of steps used = 27, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6873, 6874, 2230, 2225, 2209, 2207, 2635} \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=(1+5 e) e^{x-1}-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right ) \]

[In]

Int[(3*E^(x + x^2) + E^(x + x^2)*(-3 + 15*x - 6*x^2)*Log[x] + E^x*(-1 + 5*x)*Log[x]^2 + (-3*E^(x + x^2)*x*Log[
x] - E^x*x*Log[x]^2)*Log[(3*E^x^2*x + x*Log[x])/(E^E^(-1)*Log[x])])/(3*E^x^2*x*Log[x] + x*Log[x]^2),x]

[Out]

E^(-1 + x)*(1 + 5*E) - E^x*Log[(x*(3*E^x^2 + Log[x]))/Log[x]]

Rule 2207

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[(c + d*x)^m*
((b*F^(g*(e + f*x)))^n/(f*g*n*Log[F])), x] - Dist[d*(m/(f*g*n*Log[F])), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !TrueQ[$UseGamma]

Rule 2209

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - c*(f/d)))/d)*ExpInteg
ralEi[f*g*(c + d*x)*(Log[F]/d)], x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !TrueQ[$UseGamma]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2230

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), w*NormalizePo
werOfLinear[u, x]^m, x], x] /; FreeQ[{F, c}, x] && PolynomialQ[w, x] && LinearQ[v, x] && PowerOfLinearQ[u, x]
&& IntegerQ[m] &&  !TrueQ[$UseGamma]

Rule 2635

Int[Log[u_]*(v_), x_Symbol] :> With[{w = IntHide[v, x]}, Dist[Log[u], w, x] - Int[SimplifyIntegrand[w*Simplify
[D[u, x]/u], x], x] /; InverseFunctionFreeQ[w, x]] /; ProductQ[u]

Rule 6873

Int[u_, x_Symbol] :> With[{v = NormalizeIntegrand[u, x]}, Int[v, x] /; v =!= u]

Rule 6874

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps \begin{align*} \text {integral}& = \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{x \log (x) \left (3 e^{x^2}+\log (x)\right )} \, dx \\ & = \int \left (\frac {e^x \left (-1+2 x^2 \log (x)\right )}{x \left (3 e^{x^2}+\log (x)\right )}+\frac {e^{-1+x} \left (e-e \log (x)+(1+5 e) x \log (x)-2 e x^2 \log (x)-e x \log (x) \log \left (x+\frac {3 e^{x^2} x}{\log (x)}\right )\right )}{x \log (x)}\right ) \, dx \\ & = \int \frac {e^x \left (-1+2 x^2 \log (x)\right )}{x \left (3 e^{x^2}+\log (x)\right )} \, dx+\int \frac {e^{-1+x} \left (e-e \log (x)+(1+5 e) x \log (x)-2 e x^2 \log (x)-e x \log (x) \log \left (x+\frac {3 e^{x^2} x}{\log (x)}\right )\right )}{x \log (x)} \, dx \\ & = \int \left (-\frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )}+\frac {2 e^x x \log (x)}{3 e^{x^2}+\log (x)}\right ) \, dx+\int \left (\frac {e^{-1+x} \left (e-e \log (x)+(1+5 e) x \log (x)-2 e x^2 \log (x)\right )}{x \log (x)}-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )\right ) \, dx \\ & = 2 \int \frac {e^x x \log (x)}{3 e^{x^2}+\log (x)} \, dx-\int \frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )} \, dx+\int \frac {e^{-1+x} \left (e-e \log (x)+(1+5 e) x \log (x)-2 e x^2 \log (x)\right )}{x \log (x)} \, dx-\int e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right ) \, dx \\ & = -e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )+2 \int \frac {e^x x \log (x)}{3 e^{x^2}+\log (x)} \, dx+\int \left (\frac {e^{-1+x} \left (-e+(1+5 e) x-2 e x^2\right )}{x}+\frac {e^x}{x \log (x)}\right ) \, dx-\int \frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )} \, dx+\int \frac {e^x \left (-3 e^{x^2}+3 e^{x^2} \left (1+2 x^2\right ) \log (x)+\log ^2(x)\right )}{x \log (x) \left (3 e^{x^2}+\log (x)\right )} \, dx \\ & = -e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )+2 \int \frac {e^x x \log (x)}{3 e^{x^2}+\log (x)} \, dx+\int \frac {e^{-1+x} \left (-e+(1+5 e) x-2 e x^2\right )}{x} \, dx+\int \frac {e^x}{x \log (x)} \, dx-\int \frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )} \, dx+\int \left (-\frac {e^x \left (-1+2 x^2 \log (x)\right )}{x \left (3 e^{x^2}+\log (x)\right )}+\frac {e^x \left (-1+\log (x)+2 x^2 \log (x)\right )}{x \log (x)}\right ) \, dx \\ & = -e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )+2 \int \frac {e^x x \log (x)}{3 e^{x^2}+\log (x)} \, dx+\int \left (e^{-1+x} (1+5 e)-\frac {e^x}{x}-2 e^x x\right ) \, dx+\int \frac {e^x}{x \log (x)} \, dx-\int \frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )} \, dx-\int \frac {e^x \left (-1+2 x^2 \log (x)\right )}{x \left (3 e^{x^2}+\log (x)\right )} \, dx+\int \frac {e^x \left (-1+\log (x)+2 x^2 \log (x)\right )}{x \log (x)} \, dx \\ & = -e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )-2 \int e^x x \, dx+2 \int \frac {e^x x \log (x)}{3 e^{x^2}+\log (x)} \, dx+(1+5 e) \int e^{-1+x} \, dx-\int \frac {e^x}{x} \, dx+\int \left (\frac {e^x \left (1+2 x^2\right )}{x}-\frac {e^x}{x \log (x)}\right ) \, dx+\int \frac {e^x}{x \log (x)} \, dx-\int \frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )} \, dx-\int \left (-\frac {e^x}{x \left (3 e^{x^2}+\log (x)\right )}+\frac {2 e^x x \log (x)}{3 e^{x^2}+\log (x)}\right ) \, dx \\ & = e^{-1+x} (1+5 e)-2 e^x x-\text {Ei}(x)-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )+2 \int e^x \, dx+\int \frac {e^x \left (1+2 x^2\right )}{x} \, dx \\ & = 2 e^x+e^{-1+x} (1+5 e)-2 e^x x-\text {Ei}(x)-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )+\int \left (\frac {e^x}{x}+2 e^x x\right ) \, dx \\ & = 2 e^x+e^{-1+x} (1+5 e)-2 e^x x-\text {Ei}(x)-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )+2 \int e^x x \, dx+\int \frac {e^x}{x} \, dx \\ & = 2 e^x+e^{-1+x} (1+5 e)-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right )-2 \int e^x \, dx \\ & = e^{-1+x} (1+5 e)-e^x \log \left (\frac {x \left (3 e^{x^2}+\log (x)\right )}{\log (x)}\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.21 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=e^{-1+x} \left (1+5 e-e \log \left (x+\frac {3 e^{x^2} x}{\log (x)}\right )\right ) \]

[In]

Integrate[(3*E^(x + x^2) + E^(x + x^2)*(-3 + 15*x - 6*x^2)*Log[x] + E^x*(-1 + 5*x)*Log[x]^2 + (-3*E^(x + x^2)*
x*Log[x] - E^x*x*Log[x]^2)*Log[(3*E^x^2*x + x*Log[x])/(E^E^(-1)*Log[x])])/(3*E^x^2*x*Log[x] + x*Log[x]^2),x]

[Out]

E^(-1 + x)*(1 + 5*E - E*Log[x + (3*E^x^2*x)/Log[x]])

Maple [A] (verified)

Time = 6.43 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06

method	result	size
parallelrisch	\(-{\mathrm e}^{x} \ln \left (\frac {x \left (3 \,{\mathrm e}^{x^{2}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{-1}}}{\ln \left (x \right )}\right )+5 \,{\mathrm e}^{x}\)	\(33\)
risch	\(-{\mathrm e}^{x} \ln \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )+\frac {\left (i \pi {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right )}^{3} {\mathrm e}+i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right ) {\mathrm e}+i \pi {\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right )}^{3} {\mathrm e}-i \pi \,\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right ) {\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right )}^{2} {\mathrm e}-i \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right )}^{2} {\mathrm e}+i \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )\right ) \operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right ) {\mathrm e}-i \pi \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right )}^{2} {\mathrm e}-i \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )\right ) {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{x^{2}}+\frac {\ln \left (x \right )}{3}\right )}{\ln \left (x \right )}\right )}^{2} {\mathrm e}+2-2 \ln \left (3\right ) {\mathrm e}-2 \,{\mathrm e} \ln \left (x \right )+2 \ln \left (\ln \left (x \right )\right ) {\mathrm e}+10 \,{\mathrm e}\right ) {\mathrm e}^{-1+x}}{2}\)	\(333\)

[In]

int(((-x*exp(x)*ln(x)^2-3*x*exp(x)*exp(x^2)*ln(x))*ln((x*ln(x)+3*exp(x^2)*x)/exp(1/exp(1))/ln(x))+(5*x-1)*exp(
x)*ln(x)^2+(-6*x^2+15*x-3)*exp(x)*exp(x^2)*ln(x)+3*exp(x)*exp(x^2))/(x*ln(x)^2+3*x*exp(x^2)*ln(x)),x,method=_R
ETURNVERBOSE)

[Out]

-exp(x)*ln(x*(3*exp(x^2)+ln(x))/exp(1/exp(1))/ln(x))+5*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.52 \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=-{\left (e^{\left (x^{2} + x\right )} \log \left (\frac {{\left (3 \, x e^{\left (x^{2}\right )} + x \log \left (x\right )\right )} e^{\left (-e^{\left (-1\right )}\right )}}{\log \left (x\right )}\right ) - 5 \, e^{\left (x^{2} + x\right )}\right )} e^{\left (-x^{2}\right )} \]

[In]

integrate(((-x*exp(x)*log(x)^2-3*x*exp(x)*exp(x^2)*log(x))*log((x*log(x)+3*exp(x^2)*x)/exp(1/exp(1))/log(x))+(
5*x-1)*exp(x)*log(x)^2+(-6*x^2+15*x-3)*exp(x)*exp(x^2)*log(x)+3*exp(x)*exp(x^2))/(x*log(x)^2+3*x*exp(x^2)*log(
x)),x, algorithm="fricas")

[Out]

-(e^(x^2 + x)*log((3*x*e^(x^2) + x*log(x))*e^(-e^(-1))/log(x)) - 5*e^(x^2 + x))*e^(-x^2)

Sympy [F(-1)]

Timed out. \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=\text {Timed out} \]

[In]

integrate(((-x*exp(x)*ln(x)**2-3*x*exp(x)*exp(x**2)*ln(x))*ln((x*ln(x)+3*exp(x**2)*x)/exp(1/exp(1))/ln(x))+(5*
x-1)*exp(x)*ln(x)**2+(-6*x**2+15*x-3)*exp(x)*exp(x**2)*ln(x)+3*exp(x)*exp(x**2))/(x*ln(x)**2+3*x*exp(x**2)*ln(
x)),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39 \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=-{\left ({\left (e \log \left (x\right ) - 5 \, e - 1\right )} e^{x} + e^{\left (x + 1\right )} \log \left (3 \, e^{\left (x^{2}\right )} + \log \left (x\right )\right ) - e^{\left (x + 1\right )} \log \left (\log \left (x\right )\right )\right )} e^{\left (-1\right )} \]

[In]

integrate(((-x*exp(x)*log(x)^2-3*x*exp(x)*exp(x^2)*log(x))*log((x*log(x)+3*exp(x^2)*x)/exp(1/exp(1))/log(x))+(
5*x-1)*exp(x)*log(x)^2+(-6*x^2+15*x-3)*exp(x)*exp(x^2)*log(x)+3*exp(x)*exp(x^2))/(x*log(x)^2+3*x*exp(x^2)*log(
x)),x, algorithm="maxima")

[Out]

-((e*log(x) - 5*e - 1)*e^x + e^(x + 1)*log(3*e^(x^2) + log(x)) - e^(x + 1)*log(log(x)))*e^(-1)

Giac [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=-{\left (e^{\left (x + 1\right )} \log \left (x\right ) + e^{\left (x + 1\right )} \log \left (3 \, e^{\left (x^{2}\right )} + \log \left (x\right )\right ) - e^{\left (x + 1\right )} \log \left (\log \left (x\right )\right ) - 5 \, e^{\left (x + 1\right )} - e^{x}\right )} e^{\left (-1\right )} \]

[In]

integrate(((-x*exp(x)*log(x)^2-3*x*exp(x)*exp(x^2)*log(x))*log((x*log(x)+3*exp(x^2)*x)/exp(1/exp(1))/log(x))+(
5*x-1)*exp(x)*log(x)^2+(-6*x^2+15*x-3)*exp(x)*exp(x^2)*log(x)+3*exp(x)*exp(x^2))/(x*log(x)^2+3*x*exp(x^2)*log(
x)),x, algorithm="giac")

[Out]

-(e^(x + 1)*log(x) + e^(x + 1)*log(3*e^(x^2) + log(x)) - e^(x + 1)*log(log(x)) - 5*e^(x + 1) - e^x)*e^(-1)

Mupad [B] (verification not implemented)

Time = 11.73 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {3 e^{x+x^2}+e^{x+x^2} \left (-3+15 x-6 x^2\right ) \log (x)+e^x (-1+5 x) \log ^2(x)+\left (-3 e^{x+x^2} x \log (x)-e^x x \log ^2(x)\right ) \log \left (\frac {e^{-1/e} \left (3 e^{x^2} x+x \log (x)\right )}{\log (x)}\right )}{3 e^{x^2} x \log (x)+x \log ^2(x)} \, dx=-{\mathrm {e}}^x\,\left (\ln \left (\frac {{\mathrm {e}}^{-{\mathrm {e}}^{-1}}\,\left (3\,x\,{\mathrm {e}}^{x^2}+x\,\ln \left (x\right )\right )}{\ln \left (x\right )}\right )-5\right ) \]

[In]

int((3*exp(x^2)*exp(x) - log((exp(-exp(-1))*(3*x*exp(x^2) + x*log(x)))/log(x))*(x*exp(x)*log(x)^2 + 3*x*exp(x^
2)*exp(x)*log(x)) + exp(x)*log(x)^2*(5*x - 1) - exp(x^2)*exp(x)*log(x)*(6*x^2 - 15*x + 3))/(x*log(x)^2 + 3*x*e
xp(x^2)*log(x)),x)

[Out]

-exp(x)*(log((exp(-exp(-1))*(3*x*exp(x^2) + x*log(x)))/log(x)) - 5)