3.49.67 \(\int \frac {5 x^3+135 e^{12-3 e^x} x^3+135 e^{8-2 e^x} x^3+45 e^{4-e^x} x^3+e^{\frac {2}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}} (-4+e^{4-e^x} (-12+12 e^x x))+e^{\frac {1}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}} (-8+e^{4-e^x} (-24+24 e^x x))}{5 x^3+135 e^{12-3 e^x} x^3+135 e^{8-2 e^x} x^3+45 e^{4-e^x} x^3} \, dx\)

Optimal. Leaf size=30 \[ \left (2+e^{\frac {1}{5 \left (1+3 e^{4-e^x}\right )^2 x^2}}\right )^2+x \]

________________________________________________________________________________________

Rubi [F]  time = 54.22, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {5 x^3+135 e^{12-3 e^x} x^3+135 e^{8-2 e^x} x^3+45 e^{4-e^x} x^3+\exp \left (\frac {2}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}\right ) \left (-4+e^{4-e^x} \left (-12+12 e^x x\right )\right )+\exp \left (\frac {1}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}\right ) \left (-8+e^{4-e^x} \left (-24+24 e^x x\right )\right )}{5 x^3+135 e^{12-3 e^x} x^3+135 e^{8-2 e^x} x^3+45 e^{4-e^x} x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(5*x^3 + 135*E^(12 - 3*E^x)*x^3 + 135*E^(8 - 2*E^x)*x^3 + 45*E^(4 - E^x)*x^3 + E^(2/(5*x^2 + 45*E^(8 - 2*E
^x)*x^2 + 30*E^(4 - E^x)*x^2))*(-4 + E^(4 - E^x)*(-12 + 12*E^x*x)) + E^(5*x^2 + 45*E^(8 - 2*E^x)*x^2 + 30*E^(4
- E^x)*x^2)^(-1)*(-8 + E^(4 - E^x)*(-24 + 24*E^x*x)))/(5*x^3 + 135*E^(12 - 3*E^x)*x^3 + 135*E^(8 - 2*E^x)*x^3
+ 45*E^(4 - E^x)*x^3),x]

[Out]

(-27*E^(8 - x))/(2*(3*E^4 + E^E^x)^2) + x - (8*Defer[Int][E^(2*E^x + E^(2*E^x)/(5*(3*E^4 + E^E^x)^2*x^2))/((3*
E^4 + E^E^x)^2*x^3), x])/5 - (4*Defer[Int][E^(2*E^x + (2*E^(2*E^x))/(5*(3*E^4 + E^E^x)^2*x^2))/((3*E^4 + E^E^x
)^2*x^3), x])/5 + (24*Defer[Int][E^(4 + 2*E^x + E^(2*E^x)/(5*(3*E^4 + E^E^x)^2*x^2) + x)/((3*E^4 + E^E^x)^3*x^
2), x])/5 + (12*Defer[Int][E^(4 + 2*E^x + (2*E^(2*E^x))/(5*(3*E^4 + E^E^x)^2*x^2) + x)/((3*E^4 + E^E^x)^3*x^2)
, x])/5 - (27*E^8*Defer[Subst][Defer[Int][1/((3*E^4 + E^x)^2*x^2), x], x, E^x])/2 + 9*Defer[Subst][Defer[Int][
E^(4 + 2*x)/((3*E^4 + E^x)^3*x), x], x, E^x] + 27*E^8*Defer[Subst][Defer[Int][1/((3*E^4 + E^x)^2*x), x], x, E^
x] - 9*E^4*Defer[Subst][Defer[Int][1/((3*E^4 + E^x)*x), x], x, E^x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3 e^x} \left (5 x^3+135 e^{12-3 e^x} x^3+135 e^{8-2 e^x} x^3+45 e^{4-e^x} x^3+\exp \left (\frac {2}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}\right ) \left (-4+e^{4-e^x} \left (-12+12 e^x x\right )\right )+\exp \left (\frac {1}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}\right ) \left (-8+e^{4-e^x} \left (-24+24 e^x x\right )\right )\right )}{5 \left (3 e^4+e^{e^x}\right )^3 x^3} \, dx\\ &=\frac {1}{5} \int \frac {e^{3 e^x} \left (5 x^3+135 e^{12-3 e^x} x^3+135 e^{8-2 e^x} x^3+45 e^{4-e^x} x^3+\exp \left (\frac {2}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}\right ) \left (-4+e^{4-e^x} \left (-12+12 e^x x\right )\right )+\exp \left (\frac {1}{5 x^2+45 e^{8-2 e^x} x^2+30 e^{4-e^x} x^2}\right ) \left (-8+e^{4-e^x} \left (-24+24 e^x x\right )\right )\right )}{\left (3 e^4+e^{e^x}\right )^3 x^3} \, dx\\ &=\frac {1}{5} \int \left (\frac {5 e^{3 e^x}}{\left (3 e^4+e^{e^x}\right )^3}+\frac {45 e^{4+2 e^x}}{\left (3 e^4+e^{e^x}\right )^3}+\frac {135 e^{3 e^x-3 \left (-4+e^x\right )}}{\left (3 e^4+e^{e^x}\right )^3}+\frac {135 e^{3 e^x-2 \left (-4+e^x\right )}}{\left (3 e^4+e^{e^x}\right )^3}-\frac {8 e^{2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}} \left (3 e^4+e^{e^x}-3 e^{4+x} x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^3}-\frac {4 \exp \left (2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}\right ) \left (3 e^4+e^{e^x}-3 e^{4+x} x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^3}\right ) \, dx\\ &=-\left (\frac {4}{5} \int \frac {\exp \left (2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}\right ) \left (3 e^4+e^{e^x}-3 e^{4+x} x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^3} \, dx\right )-\frac {8}{5} \int \frac {e^{2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}} \left (3 e^4+e^{e^x}-3 e^{4+x} x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^3} \, dx+9 \int \frac {e^{4+2 e^x}}{\left (3 e^4+e^{e^x}\right )^3} \, dx+27 \int \frac {e^{3 e^x-3 \left (-4+e^x\right )}}{\left (3 e^4+e^{e^x}\right )^3} \, dx+27 \int \frac {e^{3 e^x-2 \left (-4+e^x\right )}}{\left (3 e^4+e^{e^x}\right )^3} \, dx+\int \frac {e^{3 e^x}}{\left (3 e^4+e^{e^x}\right )^3} \, dx\\ &=-\left (\frac {4}{5} \int \left (\frac {\exp \left (2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}\right )}{\left (3 e^4+e^{e^x}\right )^2 x^3}-\frac {3 \exp \left (4+2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}+x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^2}\right ) \, dx\right )-\frac {8}{5} \int \left (\frac {e^{2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}}}{\left (3 e^4+e^{e^x}\right )^2 x^3}-\frac {3 \exp \left (4+2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}+x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^2}\right ) \, dx+9 \operatorname {Subst}\left (\int \frac {e^{4+2 x}}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )+27 \operatorname {Subst}\left (\int \frac {e^{12}}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )+27 \operatorname {Subst}\left (\int \frac {e^{8+x}}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )+\operatorname {Subst}\left (\int \frac {e^{3 x}}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )\\ &=-\left (\frac {4}{5} \int \frac {\exp \left (2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}\right )}{\left (3 e^4+e^{e^x}\right )^2 x^3} \, dx\right )-\frac {8}{5} \int \frac {e^{2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}}}{\left (3 e^4+e^{e^x}\right )^2 x^3} \, dx+\frac {12}{5} \int \frac {\exp \left (4+2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}+x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^2} \, dx+\frac {24}{5} \int \frac {\exp \left (4+2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}+x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^2} \, dx+9 \operatorname {Subst}\left (\int \frac {e^{4+2 x}}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )+\left (27 e^8\right ) \operatorname {Subst}\left (\int \frac {e^x}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )+\left (27 e^{12}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )+\operatorname {Subst}\left (\int \left (\frac {1}{x}-\frac {27 e^{12}}{\left (3 e^4+e^x\right )^3 x}+\frac {27 e^8}{\left (3 e^4+e^x\right )^2 x}-\frac {9 e^4}{\left (3 e^4+e^x\right ) x}\right ) \, dx,x,e^x\right )\\ &=-\frac {27 e^{8-x}}{2 \left (3 e^4+e^{e^x}\right )^2}+x-\frac {4}{5} \int \frac {\exp \left (2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}\right )}{\left (3 e^4+e^{e^x}\right )^2 x^3} \, dx-\frac {8}{5} \int \frac {e^{2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}}}{\left (3 e^4+e^{e^x}\right )^2 x^3} \, dx+\frac {12}{5} \int \frac {\exp \left (4+2 e^x+\frac {2 e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}+x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^2} \, dx+\frac {24}{5} \int \frac {\exp \left (4+2 e^x+\frac {e^{2 e^x}}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}+x\right )}{\left (3 e^4+e^{e^x}\right )^3 x^2} \, dx+9 \operatorname {Subst}\left (\int \frac {e^{4+2 x}}{\left (3 e^4+e^x\right )^3 x} \, dx,x,e^x\right )-\left (9 e^4\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3 e^4+e^x\right ) x} \, dx,x,e^x\right )-\frac {1}{2} \left (27 e^8\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3 e^4+e^x\right )^2 x^2} \, dx,x,e^x\right )+\left (27 e^8\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3 e^4+e^x\right )^2 x} \, dx,x,e^x\right )\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 2.01, size = 124, normalized size = 4.13 \begin {gather*} \frac {1}{5} \left (5 e^{\frac {2}{5 x^2}+\frac {18 e^8}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}-\frac {12 e^4}{5 \left (3 e^4+e^{e^x}\right ) x^2}}+20 e^{\frac {1}{5 x^2}+\frac {9 e^8}{5 \left (3 e^4+e^{e^x}\right )^2 x^2}-\frac {6 e^4}{5 \left (3 e^4+e^{e^x}\right ) x^2}}+5 x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5*x^3 + 135*E^(12 - 3*E^x)*x^3 + 135*E^(8 - 2*E^x)*x^3 + 45*E^(4 - E^x)*x^3 + E^(2/(5*x^2 + 45*E^(8
- 2*E^x)*x^2 + 30*E^(4 - E^x)*x^2))*(-4 + E^(4 - E^x)*(-12 + 12*E^x*x)) + E^(5*x^2 + 45*E^(8 - 2*E^x)*x^2 + 3
0*E^(4 - E^x)*x^2)^(-1)*(-8 + E^(4 - E^x)*(-24 + 24*E^x*x)))/(5*x^3 + 135*E^(12 - 3*E^x)*x^3 + 135*E^(8 - 2*E^
x)*x^3 + 45*E^(4 - E^x)*x^3),x]

[Out]

(5*E^(2/(5*x^2) + (18*E^8)/(5*(3*E^4 + E^E^x)^2*x^2) - (12*E^4)/(5*(3*E^4 + E^E^x)*x^2)) + 20*E^(1/(5*x^2) + (
9*E^8)/(5*(3*E^4 + E^E^x)^2*x^2) - (6*E^4)/(5*(3*E^4 + E^E^x)*x^2)) + 5*x)/5

________________________________________________________________________________________

fricas [B]  time = 0.77, size = 70, normalized size = 2.33 \begin {gather*} x + e^{\left (\frac {2}{5 \, {\left (6 \, x^{2} e^{\left (-e^{x} + 4\right )} + 9 \, x^{2} e^{\left (-2 \, e^{x} + 8\right )} + x^{2}\right )}}\right )} + 4 \, e^{\left (\frac {1}{5 \, {\left (6 \, x^{2} e^{\left (-e^{x} + 4\right )} + 9 \, x^{2} e^{\left (-2 \, e^{x} + 8\right )} + x^{2}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*exp(x)*x-12)*exp(-exp(x)+4)-4)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))^2+
((24*exp(x)*x-24)*exp(-exp(x)+4)-8)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))+135*x^3*exp(-
exp(x)+4)^3+135*x^3*exp(-exp(x)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3)/(135*x^3*exp(-exp(x)+4)^3+135*x^3*exp(-exp(x
)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3),x, algorithm="fricas")

[Out]

x + e^(2/5/(6*x^2*e^(-e^x + 4) + 9*x^2*e^(-2*e^x + 8) + x^2)) + 4*e^(1/5/(6*x^2*e^(-e^x + 4) + 9*x^2*e^(-2*e^x
+ 8) + x^2))

________________________________________________________________________________________

giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*exp(x)*x-12)*exp(-exp(x)+4)-4)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))^2+
((24*exp(x)*x-24)*exp(-exp(x)+4)-8)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))+135*x^3*exp(-
exp(x)+4)^3+135*x^3*exp(-exp(x)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3)/(135*x^3*exp(-exp(x)+4)^3+135*x^3*exp(-exp(x
)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3),x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [B]  time = 0.08, size = 61, normalized size = 2.03

method	result	size
risch	\({\mathrm e}^{\frac {2}{5 x^{2} \left (9 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+8}+6 \,{\mathrm e}^{-{\mathrm e}^{x}+4}+1\right )}}+x +4 \,{\mathrm e}^{\frac {1}{5 x^{2} \left (9 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+8}+6 \,{\mathrm e}^{-{\mathrm e}^{x}+4}+1\right )}}\)	\(61\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((12*exp(x)*x-12)*exp(-exp(x)+4)-4)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))^2+((24*e
xp(x)*x-24)*exp(-exp(x)+4)-8)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))+135*x^3*exp(-exp(x)
+4)^3+135*x^3*exp(-exp(x)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3)/(135*x^3*exp(-exp(x)+4)^3+135*x^3*exp(-exp(x)+4)^2
+45*x^3*exp(-exp(x)+4)+5*x^3),x,method=_RETURNVERBOSE)

[Out]

exp(2/5/x^2/(9*exp(-2*exp(x)+8)+6*exp(-exp(x)+4)+1))+x+4*exp(1/5/x^2/(9*exp(-2*exp(x)+8)+6*exp(-exp(x)+4)+1))

________________________________________________________________________________________

maxima [B]  time = 0.41, size = 78, normalized size = 2.60 \begin {gather*} x + e^{\left (\frac {2 \, e^{\left (2 \, e^{x}\right )}}{5 \, {\left (9 \, x^{2} e^{8} + x^{2} e^{\left (2 \, e^{x}\right )} + 6 \, x^{2} e^{\left (e^{x} + 4\right )}\right )}}\right )} + 4 \, e^{\left (\frac {e^{\left (2 \, e^{x}\right )}}{5 \, {\left (9 \, x^{2} e^{8} + x^{2} e^{\left (2 \, e^{x}\right )} + 6 \, x^{2} e^{\left (e^{x} + 4\right )}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*exp(x)*x-12)*exp(-exp(x)+4)-4)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))^2+
((24*exp(x)*x-24)*exp(-exp(x)+4)-8)*exp(1/(45*x^2*exp(-exp(x)+4)^2+30*x^2*exp(-exp(x)+4)+5*x^2))+135*x^3*exp(-
exp(x)+4)^3+135*x^3*exp(-exp(x)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3)/(135*x^3*exp(-exp(x)+4)^3+135*x^3*exp(-exp(x
)+4)^2+45*x^3*exp(-exp(x)+4)+5*x^3),x, algorithm="maxima")

[Out]

x + e^(2/5*e^(2*e^x)/(9*x^2*e^8 + x^2*e^(2*e^x) + 6*x^2*e^(e^x + 4))) + 4*e^(1/5*e^(2*e^x)/(9*x^2*e^8 + x^2*e^
(2*e^x) + 6*x^2*e^(e^x + 4)))

________________________________________________________________________________________

mupad [B]  time = 3.73, size = 72, normalized size = 2.40 \begin {gather*} x+{\mathrm {e}}^{\frac {2}{5\,x^2+30\,x^2\,{\mathrm {e}}^4\,{\mathrm {e}}^{-{\mathrm {e}}^x}+45\,x^2\,{\mathrm {e}}^8\,{\mathrm {e}}^{-2\,{\mathrm {e}}^x}}}+4\,{\mathrm {e}}^{\frac {1}{5\,x^2+30\,x^2\,{\mathrm {e}}^4\,{\mathrm {e}}^{-{\mathrm {e}}^x}+45\,x^2\,{\mathrm {e}}^8\,{\mathrm {e}}^{-2\,{\mathrm {e}}^x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1/(30*x^2*exp(4 - exp(x)) + 45*x^2*exp(8 - 2*exp(x)) + 5*x^2))*(exp(4 - exp(x))*(24*x*exp(x) - 24) -
8) + 45*x^3*exp(4 - exp(x)) + 135*x^3*exp(8 - 2*exp(x)) + 135*x^3*exp(12 - 3*exp(x)) + exp(2/(30*x^2*exp(4 - e
xp(x)) + 45*x^2*exp(8 - 2*exp(x)) + 5*x^2))*(exp(4 - exp(x))*(12*x*exp(x) - 12) - 4) + 5*x^3)/(45*x^3*exp(4 -
exp(x)) + 135*x^3*exp(8 - 2*exp(x)) + 135*x^3*exp(12 - 3*exp(x)) + 5*x^3),x)

[Out]

x + exp(2/(5*x^2 + 30*x^2*exp(4)*exp(-exp(x)) + 45*x^2*exp(8)*exp(-2*exp(x)))) + 4*exp(1/(5*x^2 + 30*x^2*exp(4
)*exp(-exp(x)) + 45*x^2*exp(8)*exp(-2*exp(x))))

________________________________________________________________________________________

sympy [B]  time = 0.87, size = 70, normalized size = 2.33 \begin {gather*} x + e^{\frac {2}{30 x^{2} e^{4 - e^{x}} + 45 x^{2} e^{8 - 2 e^{x}} + 5 x^{2}}} + 4 e^{\frac {1}{30 x^{2} e^{4 - e^{x}} + 45 x^{2} e^{8 - 2 e^{x}} + 5 x^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*exp(x)*x-12)*exp(-exp(x)+4)-4)*exp(1/(45*x**2*exp(-exp(x)+4)**2+30*x**2*exp(-exp(x)+4)+5*x**2)
)**2+((24*exp(x)*x-24)*exp(-exp(x)+4)-8)*exp(1/(45*x**2*exp(-exp(x)+4)**2+30*x**2*exp(-exp(x)+4)+5*x**2))+135*
x**3*exp(-exp(x)+4)**3+135*x**3*exp(-exp(x)+4)**2+45*x**3*exp(-exp(x)+4)+5*x**3)/(135*x**3*exp(-exp(x)+4)**3+1
35*x**3*exp(-exp(x)+4)**2+45*x**3*exp(-exp(x)+4)+5*x**3),x)

[Out]

x + exp(2/(30*x**2*exp(4 - exp(x)) + 45*x**2*exp(8 - 2*exp(x)) + 5*x**2)) + 4*exp(1/(30*x**2*exp(4 - exp(x)) +
45*x**2*exp(8 - 2*exp(x)) + 5*x**2))

________________________________________________________________________________________