3.37.9 \(\int \frac {e^x (80 x^2+85 x^3+30 x^4+e^4 (75+75 x+25 x^2)+e^2 (15-165 x-165 x^2-55 x^3))}{9 x^2+6 x^3+x^4+e^4 (9+6 x+x^2)+e^2 (-18 x-12 x^2-2 x^3)} \, dx\)

Optimal. Leaf size=27 \[ \frac {5 e^x \left (5-\frac {-1+x}{e^2-x}\right ) x}{3+x} \]

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Rubi [B]  time = 1.19, antiderivative size = 60, normalized size of antiderivative = 2.22, number of steps used = 12, number of rules used = 7, integrand size = 99, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6741, 6688, 12, 6742, 2194, 2177, 2178} \begin {gather*} 30 e^x-\frac {15 \left (19+5 e^2\right ) e^x}{\left (3+e^2\right ) (x+3)}+\frac {5 \left (1-e^2\right ) e^{x+2}}{\left (3+e^2\right ) \left (e^2-x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^x*(80*x^2 + 85*x^3 + 30*x^4 + E^4*(75 + 75*x + 25*x^2) + E^2*(15 - 165*x - 165*x^2 - 55*x^3)))/(9*x^2 +
6*x^3 + x^4 + E^4*(9 + 6*x + x^2) + E^2*(-18*x - 12*x^2 - 2*x^3)),x]

[Out]

30*E^x + (5*E^(2 + x)*(1 - E^2))/((3 + E^2)*(E^2 - x)) - (15*E^x*(19 + 5*E^2))/((3 + E^2)*(3 + x))

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2177

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

Rule 2178

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

Rule 2194

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 6688

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

Rule 6741

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

Rule 6742

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (15 e^2 \left (1+5 e^2\right )-15 e^2 \left (11-5 e^2\right ) x+5 \left (16-33 e^2+5 e^4\right ) x^2+5 \left (17-11 e^2\right ) x^3+30 x^4\right )}{9 e^4-6 e^2 \left (3-e^2\right ) x+\left (9-12 e^2+e^4\right ) x^2+2 \left (3-e^2\right ) x^3+x^4} \, dx\\ &=\int \frac {5 e^x \left (3 e^2 \left (1+5 e^2\right )-3 e^2 \left (11-5 e^2\right ) x+\left (16-33 e^2+5 e^4\right ) x^2+\left (17-11 e^2\right ) x^3+6 x^4\right )}{\left (e^2-x\right )^2 (3+x)^2} \, dx\\ &=5 \int \frac {e^x \left (3 e^2 \left (1+5 e^2\right )-3 e^2 \left (11-5 e^2\right ) x+\left (16-33 e^2+5 e^4\right ) x^2+\left (17-11 e^2\right ) x^3+6 x^4\right )}{\left (e^2-x\right )^2 (3+x)^2} \, dx\\ &=5 \int \left (6 e^x+\frac {e^x \left (e^2-e^4\right )}{\left (3+e^2\right ) \left (e^2-x\right )^2}+\frac {e^x \left (e^2-e^4\right )}{\left (3+e^2\right ) \left (e^2-x\right )}+\frac {3 e^x \left (19+5 e^2\right )}{\left (3+e^2\right ) (3+x)^2}-\frac {3 e^x \left (19+5 e^2\right )}{\left (3+e^2\right ) (3+x)}\right ) \, dx\\ &=30 \int e^x \, dx+\frac {\left (5 e^2 \left (1-e^2\right )\right ) \int \frac {e^x}{\left (e^2-x\right )^2} \, dx}{3+e^2}+\frac {\left (5 e^2 \left (1-e^2\right )\right ) \int \frac {e^x}{e^2-x} \, dx}{3+e^2}+\frac {\left (15 \left (19+5 e^2\right )\right ) \int \frac {e^x}{(3+x)^2} \, dx}{3+e^2}-\frac {\left (15 \left (19+5 e^2\right )\right ) \int \frac {e^x}{3+x} \, dx}{3+e^2}\\ &=30 e^x+\frac {5 e^{2+x} \left (1-e^2\right )}{\left (3+e^2\right ) \left (e^2-x\right )}-\frac {15 e^x \left (19+5 e^2\right )}{\left (3+e^2\right ) (3+x)}-\frac {15 \left (19+5 e^2\right ) \text {Ei}(3+x)}{e^3 \left (3+e^2\right )}-\frac {5 e^{2+e^2} \left (1-e^2\right ) \text {Ei}\left (-e^2+x\right )}{3+e^2}-\frac {\left (5 e^2 \left (1-e^2\right )\right ) \int \frac {e^x}{e^2-x} \, dx}{3+e^2}+\frac {\left (15 \left (19+5 e^2\right )\right ) \int \frac {e^x}{3+x} \, dx}{3+e^2}\\ &=30 e^x+\frac {5 e^{2+x} \left (1-e^2\right )}{\left (3+e^2\right ) \left (e^2-x\right )}-\frac {15 e^x \left (19+5 e^2\right )}{\left (3+e^2\right ) (3+x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.30, size = 30, normalized size = 1.11 \begin {gather*} \frac {5 e^x \left (1+5 e^2-6 x\right ) x}{\left (e^2-x\right ) (3+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(80*x^2 + 85*x^3 + 30*x^4 + E^4*(75 + 75*x + 25*x^2) + E^2*(15 - 165*x - 165*x^2 - 55*x^3)))/(9
*x^2 + 6*x^3 + x^4 + E^4*(9 + 6*x + x^2) + E^2*(-18*x - 12*x^2 - 2*x^3)),x]

[Out]

(5*E^x*(1 + 5*E^2 - 6*x)*x)/((E^2 - x)*(3 + x))

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fricas [A]  time = 0.69, size = 34, normalized size = 1.26 \begin {gather*} \frac {5 \, {\left (6 \, x^{2} - 5 \, x e^{2} - x\right )} e^{x}}{x^{2} - {\left (x + 3\right )} e^{2} + 3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((25*x^2+75*x+75)*exp(2)^2+(-55*x^3-165*x^2-165*x+15)*exp(2)+30*x^4+85*x^3+80*x^2)*exp(x)/((x^2+6*x+
9)*exp(2)^2+(-2*x^3-12*x^2-18*x)*exp(2)+x^4+6*x^3+9*x^2),x, algorithm="fricas")

[Out]

5*(6*x^2 - 5*x*e^2 - x)*e^x/(x^2 - (x + 3)*e^2 + 3*x)

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giac [A]  time = 0.14, size = 40, normalized size = 1.48 \begin {gather*} \frac {5 \, {\left (6 \, x^{2} e^{x} - 5 \, x e^{\left (x + 2\right )} - x e^{x}\right )}}{x^{2} - x e^{2} + 3 \, x - 3 \, e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((25*x^2+75*x+75)*exp(2)^2+(-55*x^3-165*x^2-165*x+15)*exp(2)+30*x^4+85*x^3+80*x^2)*exp(x)/((x^2+6*x+
9)*exp(2)^2+(-2*x^3-12*x^2-18*x)*exp(2)+x^4+6*x^3+9*x^2),x, algorithm="giac")

[Out]

5*(6*x^2*e^x - 5*x*e^(x + 2) - x*e^x)/(x^2 - x*e^2 + 3*x - 3*e^2)

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maple [A]  time = 0.17, size = 33, normalized size = 1.22

method	result	size
norman	\(\frac {\left (5+25 \,{\mathrm e}^{2}\right ) x \,{\mathrm e}^{x}-30 \,{\mathrm e}^{x} x^{2}}{\left (3+x \right ) \left ({\mathrm e}^{2}-x \right )}\)	\(33\)
gosper	\(\frac {5 x \left (-6 x +5 \,{\mathrm e}^{2}+1\right ) {\mathrm e}^{x}}{{\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x}\)	\(34\)
default	\(\frac {80 \,{\mathrm e}^{x} \left (x \,{\mathrm e}^{4}+3 \,{\mathrm e}^{4}-9 \,{\mathrm e}^{2}+9 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {80 \,{\mathrm e}^{2} \left (3 \,{\mathrm e}^{2}+{\mathrm e}^{4}+6\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {240 \left (-{\mathrm e}^{2}-9\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {85 \,{\mathrm e}^{x} \left (x \,{\mathrm e}^{6}+3 \,{\mathrm e}^{6}+27 \,{\mathrm e}^{2}-27 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {85 \,{\mathrm e}^{2} \left ({\mathrm e}^{6}+9 \,{\mathrm e}^{2}+4 \,{\mathrm e}^{4}\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}-\frac {255 \left (-{\mathrm e}^{2} {\mathrm e}^{4}+{\mathrm e}^{6}-18\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+30 \,{\mathrm e}^{x}+\frac {30 \,{\mathrm e}^{x} \left (x \,{\mathrm e}^{8}+3 \,{\mathrm e}^{8}-81 \,{\mathrm e}^{2}+81 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {30 \,{\mathrm e}^{2} \left (5 \,{\mathrm e}^{6}+12 \,{\mathrm e}^{4}+{\mathrm e}^{8}\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {90 \left ({\mathrm e}^{2} {\mathrm e}^{6}+2 \,{\mathrm e}^{2} {\mathrm e}^{4}-2 \,{\mathrm e}^{6}+9 \,{\mathrm e}^{2}-{\mathrm e}^{8}-27\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+15 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{x} \left ({\mathrm e}^{2}-2 x -3\right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {\left ({\mathrm e}^{2}+1\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}-\frac {\left ({\mathrm e}^{2}+5\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )+75 \,{\mathrm e}^{4} \left (-\frac {{\mathrm e}^{x} \left ({\mathrm e}^{2}-2 x -3\right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {\left ({\mathrm e}^{2}+1\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}-\frac {\left ({\mathrm e}^{2}+5\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )+75 \,{\mathrm e}^{4} \left (\frac {{\mathrm e}^{x} \left ({\mathrm e}^{2} x +6 \,{\mathrm e}^{2}-3 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {\left ({\mathrm e}^{4}+2 \,{\mathrm e}^{2}+3\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {2 \left ({\mathrm e}^{2}+6\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )-165 \,{\mathrm e}^{2} \left (\frac {{\mathrm e}^{x} \left (x \,{\mathrm e}^{4}+3 \,{\mathrm e}^{4}-9 \,{\mathrm e}^{2}+9 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {{\mathrm e}^{2} \left (3 \,{\mathrm e}^{2}+{\mathrm e}^{4}+6\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {3 \left (-{\mathrm e}^{2}-9\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )+25 \,{\mathrm e}^{4} \left (\frac {{\mathrm e}^{x} \left (x \,{\mathrm e}^{4}+3 \,{\mathrm e}^{4}-9 \,{\mathrm e}^{2}+9 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {{\mathrm e}^{2} \left (3 \,{\mathrm e}^{2}+{\mathrm e}^{4}+6\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {3 \left (-{\mathrm e}^{2}-9\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )-55 \,{\mathrm e}^{2} \left (\frac {{\mathrm e}^{x} \left (x \,{\mathrm e}^{6}+3 \,{\mathrm e}^{6}+27 \,{\mathrm e}^{2}-27 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {{\mathrm e}^{2} \left ({\mathrm e}^{6}+9 \,{\mathrm e}^{2}+4 \,{\mathrm e}^{4}\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}-\frac {3 \left (-{\mathrm e}^{2} {\mathrm e}^{4}+{\mathrm e}^{6}-18\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )-165 \,{\mathrm e}^{2} \left (\frac {{\mathrm e}^{x} \left ({\mathrm e}^{2} x +6 \,{\mathrm e}^{2}-3 x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2} x -x^{2}+3 \,{\mathrm e}^{2}-3 x \right )}-\frac {\left ({\mathrm e}^{4}+2 \,{\mathrm e}^{2}+3\right ) {\mathrm e}^{{\mathrm e}^{2}} \expIntegralEi \left (1, {\mathrm e}^{2}-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}+\frac {2 \left ({\mathrm e}^{2}+6\right ) {\mathrm e}^{-3} \expIntegralEi \left (1, -3-x \right )}{\left (6 \,{\mathrm e}^{2}+9+{\mathrm e}^{4}\right ) \left ({\mathrm e}^{2}+3\right )}\right )\)	\(1336\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((25*x^2+75*x+75)*exp(2)^2+(-55*x^3-165*x^2-165*x+15)*exp(2)+30*x^4+85*x^3+80*x^2)*exp(x)/((x^2+6*x+9)*exp
(2)^2+(-2*x^3-12*x^2-18*x)*exp(2)+x^4+6*x^3+9*x^2),x,method=_RETURNVERBOSE)

[Out]

((5+25*exp(2))*x*exp(x)-30*exp(x)*x^2)/(3+x)/(exp(2)-x)

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maxima [A]  time = 0.84, size = 36, normalized size = 1.33 \begin {gather*} \frac {5 \, {\left (6 \, x^{2} - x {\left (5 \, e^{2} + 1\right )}\right )} e^{x}}{x^{2} - x {\left (e^{2} - 3\right )} - 3 \, e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((25*x^2+75*x+75)*exp(2)^2+(-55*x^3-165*x^2-165*x+15)*exp(2)+30*x^4+85*x^3+80*x^2)*exp(x)/((x^2+6*x+
9)*exp(2)^2+(-2*x^3-12*x^2-18*x)*exp(2)+x^4+6*x^3+9*x^2),x, algorithm="maxima")

[Out]

5*(6*x^2 - x*(5*e^2 + 1))*e^x/(x^2 - x*(e^2 - 3) - 3*e^2)

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mupad [B]  time = 2.63, size = 37, normalized size = 1.37 \begin {gather*} -\frac {{\mathrm {e}}^x\,\left (30\,x^2-x\,\left (25\,{\mathrm {e}}^2+5\right )\right )}{-x^2+\left ({\mathrm {e}}^2-3\right )\,x+3\,{\mathrm {e}}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(exp(4)*(75*x + 25*x^2 + 75) - exp(2)*(165*x + 165*x^2 + 55*x^3 - 15) + 80*x^2 + 85*x^3 + 30*x^4))
/(exp(4)*(6*x + x^2 + 9) - exp(2)*(18*x + 12*x^2 + 2*x^3) + 9*x^2 + 6*x^3 + x^4),x)

[Out]

-(exp(x)*(30*x^2 - x*(25*exp(2) + 5)))/(3*exp(2) + x*(exp(2) - 3) - x^2)

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sympy [A]  time = 0.22, size = 34, normalized size = 1.26 \begin {gather*} \frac {\left (30 x^{2} - 25 x e^{2} - 5 x\right ) e^{x}}{x^{2} - x e^{2} + 3 x - 3 e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((25*x**2+75*x+75)*exp(2)**2+(-55*x**3-165*x**2-165*x+15)*exp(2)+30*x**4+85*x**3+80*x**2)*exp(x)/((x
**2+6*x+9)*exp(2)**2+(-2*x**3-12*x**2-18*x)*exp(2)+x**4+6*x**3+9*x**2),x)

[Out]

(30*x**2 - 25*x*exp(2) - 5*x)*exp(x)/(x**2 - x*exp(2) + 3*x - 3*exp(2))

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