3.14.48 \(\int \frac {15 e^{4 e^x}+540 e^{4 x}+15 e^{\frac {2 e^{e^x}}{5}+4 x}+e^{2 e^x} (60 e^{2 x}+120 e^{3 x})+e^{\frac {e^{e^x}}{5}} (-180 e^{4 x}-30 e^{2 e^x+2 x}-12 e^{e^x+5 x})}{5 e^{4 e^x} x^2+5 e^{\frac {2 e^{e^x}}{5}+4 x} x^2+e^{2 e^x+2 x} (-40 x+60 x^2)+e^{4 x} (80-240 x+180 x^2)+e^{\frac {e^{e^x}}{5}} (-10 e^{2 e^x+2 x} x^2+e^{4 x} (40 x-60 x^2))} \, dx\)

Optimal. Leaf size=38 \[ \frac {3}{\frac {4}{6-e^{\frac {e^{e^x}}{5}}+e^{2 e^x-2 x}}-x} \]

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Rubi [F]  time = 83.88, 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 {15 e^{4 e^x}+540 e^{4 x}+15 e^{\frac {2 e^{e^x}}{5}+4 x}+e^{2 e^x} \left (60 e^{2 x}+120 e^{3 x}\right )+e^{\frac {e^{e^x}}{5}} \left (-180 e^{4 x}-30 e^{2 e^x+2 x}-12 e^{e^x+5 x}\right )}{5 e^{4 e^x} x^2+5 e^{\frac {2 e^{e^x}}{5}+4 x} x^2+e^{2 e^x+2 x} \left (-40 x+60 x^2\right )+e^{4 x} \left (80-240 x+180 x^2\right )+e^{\frac {e^{e^x}}{5}} \left (-10 e^{2 e^x+2 x} x^2+e^{4 x} \left (40 x-60 x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(15*E^(4*E^x) + 540*E^(4*x) + 15*E^((2*E^E^x)/5 + 4*x) + E^(2*E^x)*(60*E^(2*x) + 120*E^(3*x)) + E^(E^E^x/5
)*(-180*E^(4*x) - 30*E^(2*E^x + 2*x) - 12*E^(E^x + 5*x)))/(5*E^(4*E^x)*x^2 + 5*E^((2*E^E^x)/5 + 4*x)*x^2 + E^(
2*E^x + 2*x)*(-40*x + 60*x^2) + E^(4*x)*(80 - 240*x + 180*x^2) + E^(E^E^x/5)*(-10*E^(2*E^x + 2*x)*x^2 + E^(4*x
)*(40*x - 60*x^2))),x]

[Out]

-3/x - (12*Defer[Int][E^(E^E^x/5 + E^x + x)/(4 - 6*x + E^(E^E^x/5)*x)^2, x])/5 + 48*Defer[Int][1/(x^2*(4 - 6*x
+ E^(E^E^x/5)*x)^2), x] - 24*Defer[Int][1/(x^2*(4 - 6*x + E^(E^E^x/5)*x)), x] + 48*Defer[Int][E^(4*E^x)/((4 -
6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)^2), x] - 96*Defer[Int][(
E^(4*E^x)*x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)^2), x]
+ 96*Defer[Int][(E^(4*E^x + x)*x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^
E^x/5 + 2*x)*x)^2), x] + 144*Defer[Int][(E^(4*E^x)*x^2)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x
- 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)^2), x] - 24*Defer[Int][(E^((E^E^x + 20*E^x)/5)*x^2)/((4 - 6*x + E^(E^E^x/
5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)^2), x] - 144*Defer[Int][(E^(4*E^x + x)*x
^2)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)^2), x] + 24*Def
er[Int][(E^((E^E^x + 20*E^x + 5*x)/5)*x^2)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x
+ E^(E^E^x/5 + 2*x)*x)^2), x] - (12*Defer[Int][(E^((E^E^x + 25*E^x + 5*x)/5)*x^2)/((4 - 6*x + E^(E^E^x/5)*x)^
2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)^2), x])/5 + 48*Defer[Int][E^(2*E^x)/((4 - 6*x
+ E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)), x] - 24*Defer[Int][E^((E^E^
x + 10*E^x)/5)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)), x]
+ 96*Defer[Int][E^(2*E^x + x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/
5 + 2*x)*x)), x] + 144*Defer[Int][(E^(2*E^x)*x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2
*x)*x + E^(E^E^x/5 + 2*x)*x)), x] - 24*Defer[Int][(E^((E^E^x + 10*E^x)/5)*x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E
^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)), x] - 144*Defer[Int][(E^(2*E^x + x)*x)/((4 - 6*x +
E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)), x] + 24*Defer[Int][(E^((E^E^x
+ 10*E^x + 5*x)/5)*x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)
*x)), x] - (24*Defer[Int][(E^((E^E^x + 15*E^x + 5*x)/5)*x)/((4 - 6*x + E^(E^E^x/5)*x)^2*(4*E^(2*x) - E^(2*E^x)
*x - 6*E^(2*x)*x + E^(E^E^x/5 + 2*x)*x)), x])/5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (5 e^{4 e^x}+180 e^{4 x}+20 e^{2 \left (e^x+x\right )}-10 e^{\frac {e^{e^x}}{5}+2 e^x+2 x}+40 e^{2 e^x+3 x}-60 e^{\frac {e^{e^x}}{5}+4 x}+5 e^{\frac {2 e^{e^x}}{5}+4 x}-4 e^{\frac {e^{e^x}}{5}+e^x+5 x}\right )}{5 \left (e^{2 x} (4-6 x)-e^{2 e^x} x+e^{\frac {e^{e^x}}{5}+2 x} x\right )^2} \, dx\\ &=\frac {3}{5} \int \frac {5 e^{4 e^x}+180 e^{4 x}+20 e^{2 \left (e^x+x\right )}-10 e^{\frac {e^{e^x}}{5}+2 e^x+2 x}+40 e^{2 e^x+3 x}-60 e^{\frac {e^{e^x}}{5}+4 x}+5 e^{\frac {2 e^{e^x}}{5}+4 x}-4 e^{\frac {e^{e^x}}{5}+e^x+5 x}}{\left (e^{2 x} (4-6 x)-e^{2 e^x} x+e^{\frac {e^{e^x}}{5}+2 x} x\right )^2} \, dx\\ &=\frac {3}{5} \int \left (-\frac {4 e^{\frac {e^{e^x}}{5}+e^x+x}}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2}+\frac {5 \left (-6+e^{\frac {e^{e^x}}{5}}\right )^2}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2}+\frac {8 e^{2 e^x} \left (-10+5 e^{\frac {e^{e^x}}{5}}-20 e^x-30 x+5 e^{\frac {e^{e^x}}{5}} x+30 e^x x-5 e^{\frac {e^{e^x}}{5}+x} x+e^{\frac {e^{e^x}}{5}+e^x+x} x\right )}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2 \left (-4 e^{2 x}+e^{2 e^x} x+6 e^{2 x} x-e^{\frac {e^{e^x}}{5}+2 x} x\right )}-\frac {4 e^{4 e^x} \left (-20+40 x-40 e^x x-60 x^2+10 e^{\frac {e^{e^x}}{5}} x^2+60 e^x x^2-10 e^{\frac {e^{e^x}}{5}+x} x^2+e^{\frac {e^{e^x}}{5}+e^x+x} x^2\right )}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2 \left (-4 e^{2 x}+e^{2 e^x} x+6 e^{2 x} x-e^{\frac {e^{e^x}}{5}+2 x} x\right )^2}\right ) \, dx\\ &=-\left (\frac {12}{5} \int \frac {e^{\frac {e^{e^x}}{5}+e^x+x}}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2} \, dx\right )-\frac {12}{5} \int \frac {e^{4 e^x} \left (-20+40 x-40 e^x x-60 x^2+10 e^{\frac {e^{e^x}}{5}} x^2+60 e^x x^2-10 e^{\frac {e^{e^x}}{5}+x} x^2+e^{\frac {e^{e^x}}{5}+e^x+x} x^2\right )}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2 \left (-4 e^{2 x}+e^{2 e^x} x+6 e^{2 x} x-e^{\frac {e^{e^x}}{5}+2 x} x\right )^2} \, dx+3 \int \frac {\left (-6+e^{\frac {e^{e^x}}{5}}\right )^2}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2} \, dx+\frac {24}{5} \int \frac {e^{2 e^x} \left (-10+5 e^{\frac {e^{e^x}}{5}}-20 e^x-30 x+5 e^{\frac {e^{e^x}}{5}} x+30 e^x x-5 e^{\frac {e^{e^x}}{5}+x} x+e^{\frac {e^{e^x}}{5}+e^x+x} x\right )}{\left (4-6 x+e^{\frac {e^{e^x}}{5}} x\right )^2 \left (-4 e^{2 x}+e^{2 e^x} x+6 e^{2 x} x-e^{\frac {e^{e^x}}{5}+2 x} x\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.19, size = 55, normalized size = 1.45 \begin {gather*} -\frac {3 \left (1-\frac {4 e^{2 x}}{e^{2 x} (4-6 x)-e^{2 e^x} x+e^{\frac {e^{e^x}}{5}+2 x} x}\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(15*E^(4*E^x) + 540*E^(4*x) + 15*E^((2*E^E^x)/5 + 4*x) + E^(2*E^x)*(60*E^(2*x) + 120*E^(3*x)) + E^(E
^E^x/5)*(-180*E^(4*x) - 30*E^(2*E^x + 2*x) - 12*E^(E^x + 5*x)))/(5*E^(4*E^x)*x^2 + 5*E^((2*E^E^x)/5 + 4*x)*x^2
+ E^(2*E^x + 2*x)*(-40*x + 60*x^2) + E^(4*x)*(80 - 240*x + 180*x^2) + E^(E^E^x/5)*(-10*E^(2*E^x + 2*x)*x^2 +
E^(4*x)*(40*x - 60*x^2))),x]

[Out]

(-3*(1 - (4*E^(2*x))/(E^(2*x)*(4 - 6*x) - E^(2*E^x)*x + E^(E^E^x/5 + 2*x)*x)))/x

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fricas [B]  time = 0.96, size = 68, normalized size = 1.79 \begin {gather*} -\frac {3 \, {\left (6 \, e^{\left (12 \, x\right )} - e^{\left (12 \, x + \frac {1}{5} \, e^{\left (e^{x}\right )}\right )} + e^{\left (10 \, x + 2 \, e^{x}\right )}\right )}}{2 \, {\left (3 \, x - 2\right )} e^{\left (12 \, x\right )} - x e^{\left (12 \, x + \frac {1}{5} \, e^{\left (e^{x}\right )}\right )} + x e^{\left (10 \, x + 2 \, e^{x}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*exp(x)^4*exp(1/5*exp(exp(x)))^2+(-30*exp(x)^2*exp(exp(x))^2-12*exp(x)^5*exp(exp(x))-180*exp(x)^4
)*exp(1/5*exp(exp(x)))+15*exp(exp(x))^4+(120*exp(x)^3+60*exp(x)^2)*exp(exp(x))^2+540*exp(x)^4)/(5*x^2*exp(x)^4
*exp(1/5*exp(exp(x)))^2+(-10*x^2*exp(x)^2*exp(exp(x))^2+(-60*x^2+40*x)*exp(x)^4)*exp(1/5*exp(exp(x)))+5*x^2*ex
p(exp(x))^4+(60*x^2-40*x)*exp(x)^2*exp(exp(x))^2+(180*x^2-240*x+80)*exp(x)^4),x, algorithm="fricas")

[Out]

-3*(6*e^(12*x) - e^(12*x + 1/5*e^(e^x)) + e^(10*x + 2*e^x))/(2*(3*x - 2)*e^(12*x) - x*e^(12*x + 1/5*e^(e^x)) +
x*e^(10*x + 2*e^x))

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giac [B]  time = 2.26, size = 62, normalized size = 1.63 \begin {gather*} -\frac {3 \, {\left (6 \, e^{\left (2 \, x\right )} - e^{\left (2 \, x + \frac {1}{5} \, e^{\left (e^{x}\right )}\right )} + e^{\left (2 \, e^{x}\right )}\right )}}{6 \, x e^{\left (2 \, x\right )} - x e^{\left (2 \, x + \frac {1}{5} \, e^{\left (e^{x}\right )}\right )} + x e^{\left (2 \, e^{x}\right )} - 4 \, e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*exp(x)^4*exp(1/5*exp(exp(x)))^2+(-30*exp(x)^2*exp(exp(x))^2-12*exp(x)^5*exp(exp(x))-180*exp(x)^4
)*exp(1/5*exp(exp(x)))+15*exp(exp(x))^4+(120*exp(x)^3+60*exp(x)^2)*exp(exp(x))^2+540*exp(x)^4)/(5*x^2*exp(x)^4
*exp(1/5*exp(exp(x)))^2+(-10*x^2*exp(x)^2*exp(exp(x))^2+(-60*x^2+40*x)*exp(x)^4)*exp(1/5*exp(exp(x)))+5*x^2*ex
p(exp(x))^4+(60*x^2-40*x)*exp(x)^2*exp(exp(x))^2+(180*x^2-240*x+80)*exp(x)^4),x, algorithm="giac")

[Out]

-3*(6*e^(2*x) - e^(2*x + 1/5*e^(e^x)) + e^(2*e^x))/(6*x*e^(2*x) - x*e^(2*x + 1/5*e^(e^x)) + x*e^(2*e^x) - 4*e^
(2*x))

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maple [A]  time = 0.08, size = 52, normalized size = 1.37

method	result	size
risch	\(-\frac {3}{x}+\frac {12 \,{\mathrm e}^{2 x}}{x \left (x \,{\mathrm e}^{2 x +\frac {{\mathrm e}^{{\mathrm e}^{x}}}{5}}-6 x \,{\mathrm e}^{2 x}-x \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+4 \,{\mathrm e}^{2 x}\right )}\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((15*exp(x)^4*exp(1/5*exp(exp(x)))^2+(-30*exp(x)^2*exp(exp(x))^2-12*exp(x)^5*exp(exp(x))-180*exp(x)^4)*exp(
1/5*exp(exp(x)))+15*exp(exp(x))^4+(120*exp(x)^3+60*exp(x)^2)*exp(exp(x))^2+540*exp(x)^4)/(5*x^2*exp(x)^4*exp(1
/5*exp(exp(x)))^2+(-10*x^2*exp(x)^2*exp(exp(x))^2+(-60*x^2+40*x)*exp(x)^4)*exp(1/5*exp(exp(x)))+5*x^2*exp(exp(
x))^4+(60*x^2-40*x)*exp(x)^2*exp(exp(x))^2+(180*x^2-240*x+80)*exp(x)^4),x,method=_RETURNVERBOSE)

[Out]

-3/x+12/x*exp(2*x)/(x*exp(2*x+1/5*exp(exp(x)))-6*x*exp(2*x)-x*exp(2*exp(x))+4*exp(2*x))

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maxima [B]  time = 0.85, size = 60, normalized size = 1.58 \begin {gather*} -\frac {3 \, {\left (6 \, e^{\left (2 \, x\right )} - e^{\left (2 \, x + \frac {1}{5} \, e^{\left (e^{x}\right )}\right )} + e^{\left (2 \, e^{x}\right )}\right )}}{2 \, {\left (3 \, x - 2\right )} e^{\left (2 \, x\right )} - x e^{\left (2 \, x + \frac {1}{5} \, e^{\left (e^{x}\right )}\right )} + x e^{\left (2 \, e^{x}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*exp(x)^4*exp(1/5*exp(exp(x)))^2+(-30*exp(x)^2*exp(exp(x))^2-12*exp(x)^5*exp(exp(x))-180*exp(x)^4
)*exp(1/5*exp(exp(x)))+15*exp(exp(x))^4+(120*exp(x)^3+60*exp(x)^2)*exp(exp(x))^2+540*exp(x)^4)/(5*x^2*exp(x)^4
*exp(1/5*exp(exp(x)))^2+(-10*x^2*exp(x)^2*exp(exp(x))^2+(-60*x^2+40*x)*exp(x)^4)*exp(1/5*exp(exp(x)))+5*x^2*ex
p(exp(x))^4+(60*x^2-40*x)*exp(x)^2*exp(exp(x))^2+(180*x^2-240*x+80)*exp(x)^4),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 1.31, size = 191, normalized size = 5.03 \begin {gather*} \frac {12\,\left (20\,{\mathrm {e}}^{6\,x}-10\,x^2\,{\mathrm {e}}^{4\,x+2\,{\mathrm {e}}^x}+10\,x^2\,{\mathrm {e}}^{5\,x+2\,{\mathrm {e}}^x}-x^2\,{\mathrm {e}}^{5\,x+3\,{\mathrm {e}}^x}+4\,x\,{\mathrm {e}}^{7\,x+{\mathrm {e}}^x}-6\,x^2\,{\mathrm {e}}^{7\,x+{\mathrm {e}}^x}\right )}{x\,\left (4\,{\mathrm {e}}^{2\,x}-6\,x\,{\mathrm {e}}^{2\,x}+x\,{\mathrm {e}}^{2\,x+\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{5}}-x\,{\mathrm {e}}^{2\,{\mathrm {e}}^x}\right )\,\left (20\,{\mathrm {e}}^{4\,x}-10\,x^2\,{\mathrm {e}}^{2\,x+2\,{\mathrm {e}}^x}+10\,x^2\,{\mathrm {e}}^{3\,x+2\,{\mathrm {e}}^x}-x^2\,{\mathrm {e}}^{3\,x+3\,{\mathrm {e}}^x}+4\,x\,{\mathrm {e}}^{5\,x+{\mathrm {e}}^x}-6\,x^2\,{\mathrm {e}}^{5\,x+{\mathrm {e}}^x}\right )}-\frac {3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((540*exp(4*x) + 15*exp(4*exp(x)) - exp(exp(exp(x))/5)*(180*exp(4*x) + 30*exp(2*x)*exp(2*exp(x)) + 12*exp(5
*x)*exp(exp(x))) + exp(2*exp(x))*(60*exp(2*x) + 120*exp(3*x)) + 15*exp((2*exp(exp(x)))/5)*exp(4*x))/(exp(4*x)*
(180*x^2 - 240*x + 80) + 5*x^2*exp(4*exp(x)) + exp(exp(exp(x))/5)*(exp(4*x)*(40*x - 60*x^2) - 10*x^2*exp(2*x)*
exp(2*exp(x))) + 5*x^2*exp((2*exp(exp(x)))/5)*exp(4*x) - exp(2*x)*exp(2*exp(x))*(40*x - 60*x^2)),x)

[Out]

(12*(20*exp(6*x) - 10*x^2*exp(4*x + 2*exp(x)) + 10*x^2*exp(5*x + 2*exp(x)) - x^2*exp(5*x + 3*exp(x)) + 4*x*exp
(7*x + exp(x)) - 6*x^2*exp(7*x + exp(x))))/(x*(4*exp(2*x) - 6*x*exp(2*x) + x*exp(2*x + exp(exp(x))/5) - x*exp(
2*exp(x)))*(20*exp(4*x) - 10*x^2*exp(2*x + 2*exp(x)) + 10*x^2*exp(3*x + 2*exp(x)) - x^2*exp(3*x + 3*exp(x)) +
4*x*exp(5*x + exp(x)) - 6*x^2*exp(5*x + exp(x)))) - 3/x

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sympy [B]  time = 0.41, size = 54, normalized size = 1.42 \begin {gather*} \frac {12 e^{2 x}}{x^{2} e^{2 x} e^{\frac {e^{e^{x}}}{5}} - 6 x^{2} e^{2 x} - x^{2} e^{2 e^{x}} + 4 x e^{2 x}} - \frac {3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*exp(x)**4*exp(1/5*exp(exp(x)))**2+(-30*exp(x)**2*exp(exp(x))**2-12*exp(x)**5*exp(exp(x))-180*exp
(x)**4)*exp(1/5*exp(exp(x)))+15*exp(exp(x))**4+(120*exp(x)**3+60*exp(x)**2)*exp(exp(x))**2+540*exp(x)**4)/(5*x
**2*exp(x)**4*exp(1/5*exp(exp(x)))**2+(-10*x**2*exp(x)**2*exp(exp(x))**2+(-60*x**2+40*x)*exp(x)**4)*exp(1/5*ex
p(exp(x)))+5*x**2*exp(exp(x))**4+(60*x**2-40*x)*exp(x)**2*exp(exp(x))**2+(180*x**2-240*x+80)*exp(x)**4),x)

[Out]

12*exp(2*x)/(x**2*exp(2*x)*exp(exp(exp(x))/5) - 6*x**2*exp(2*x) - x**2*exp(2*exp(x)) + 4*x*exp(2*x)) - 3/x

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