3.15.2 \(\int e^{1-2 x+162 e^{2 x} x^2+e^{-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)} (4 x^3-2 x^4+e^{2 x} (360 x^5+324 x^6)+e^{2 x} (76 x^5+72 x^6) \log (x)+e^{2 x} (4 x^5+4 x^6) \log ^2(x)) \, dx\)

Optimal. Leaf size=30 \[ e^{1+e^{-2 x+2 e^{2 x} x^2 (9+\log (x))^2} x^4} \]

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Rubi [F]  time = 27.34, 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 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(1 - 2*x + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)
*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*(4*x^3 - 2*x^4 + E^(2*x)*(360*x^5 + 324*x^6) + E^(2*x)*
(76*x^5 + 72*x^6)*Log[x] + E^(2*x)*(4*x^5 + 4*x^6)*Log[x]^2),x]

[Out]

4*Defer[Int][E^(1 - 2*x + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*
Log[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^3, x] - 2*Defer[Int][E^(1 - 2*x + 162*E^(2*x
)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x
] + 2*E^(2*x)*x^2*Log[x]^2)*x^4, x] + 360*Defer[Int][E^(1 + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E
^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^5, x] + 32
4*Defer[Int][E^(1 + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]
^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^6, x] + 76*Defer[Int][E^(1 + 162*E^(2*x)*x^2 + E^(
-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*
x)*x^2*Log[x]^2)*x^5*Log[x], x] + 72*Defer[Int][E^(1 + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x
)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^6*Log[x], x] +
4*Defer[Int][E^(1 + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]
^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^5*Log[x]^2, x] + 4*Defer[Int][E^(1 + 162*E^(2*x)*x
^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x] +
2*E^(2*x)*x^2*Log[x]^2)*x^6*Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3-2 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (10+9 x)+4 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (19+18 x) \log (x)+4 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (1+x) \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (19+18 x) \log (x) \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (1+x) \log ^2(x) \, dx+36 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (10+9 x) \, dx\\ &=-\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \left (19 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log (x)+18 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log (x)\right ) \, dx+4 \int \left (\exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log ^2(x)+\exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log ^2(x)\right ) \, dx+36 \int \left (10 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5+9 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6\right ) \, dx\\ &=-\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log ^2(x) \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log ^2(x) \, dx+72 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log (x) \, dx+76 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log (x) \, dx+324 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \, dx+360 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 39, normalized size = 1.30 \begin {gather*} e^{1+e^{2 x \left (-1+e^{2 x} x \left (81+\log ^2(x)\right )\right )} x^{4+36 e^{2 x} x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(1 - 2*x + 162*E^(2*x)*x^2 + E^(-2*x + 162*E^(2*x)*x^2 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log
[x]^2)*x^4 + 36*E^(2*x)*x^2*Log[x] + 2*E^(2*x)*x^2*Log[x]^2)*(4*x^3 - 2*x^4 + E^(2*x)*(360*x^5 + 324*x^6) + E^
(2*x)*(76*x^5 + 72*x^6)*Log[x] + E^(2*x)*(4*x^5 + 4*x^6)*Log[x]^2),x]

[Out]

E^(1 + E^(2*x*(-1 + E^(2*x)*x*(81 + Log[x]^2)))*x^(4 + 36*E^(2*x)*x^2))

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fricas [A]  time = 1.23, size = 45, normalized size = 1.50 \begin {gather*} e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x)^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6+4*x^5)*exp(x)^2*log(x)^2+(72*x^6+76*x^5)*exp(x)^2*log(x)+(324*x^6+360*x^5)*exp(x)^2-2*x^4+4*
x^3)*exp(x^2*exp(x)^2*log(x)^2+18*x^2*exp(x)^2*log(x)+81*exp(x)^2*x^2-x)^2*exp(x^4*exp(x^2*exp(x)^2*log(x)^2+1
8*x^2*exp(x)^2*log(x)+81*exp(x)^2*x^2-x)^2+1),x, algorithm="fricas")

[Out]

e^(x^4*e^(2*x^2*e^(2*x)*log(x)^2 + 36*x^2*e^(2*x)*log(x) + 162*x^2*e^(2*x) - 2*x) + 1)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -2 \, {\left (x^{4} - 2 \, {\left (x^{6} + x^{5}\right )} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 2 \, x^{3} - 2 \, {\left (18 \, x^{6} + 19 \, x^{5}\right )} e^{\left (2 \, x\right )} \log \relax (x) - 18 \, {\left (9 \, x^{6} + 10 \, x^{5}\right )} e^{\left (2 \, x\right )}\right )} e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x)^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 2 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x)^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x + 1\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6+4*x^5)*exp(x)^2*log(x)^2+(72*x^6+76*x^5)*exp(x)^2*log(x)+(324*x^6+360*x^5)*exp(x)^2-2*x^4+4*
x^3)*exp(x^2*exp(x)^2*log(x)^2+18*x^2*exp(x)^2*log(x)+81*exp(x)^2*x^2-x)^2*exp(x^4*exp(x^2*exp(x)^2*log(x)^2+1
8*x^2*exp(x)^2*log(x)+81*exp(x)^2*x^2-x)^2+1),x, algorithm="giac")

[Out]

integrate(-2*(x^4 - 2*(x^6 + x^5)*e^(2*x)*log(x)^2 - 2*x^3 - 2*(18*x^6 + 19*x^5)*e^(2*x)*log(x) - 18*(9*x^6 +
10*x^5)*e^(2*x))*e^(x^4*e^(2*x^2*e^(2*x)*log(x)^2 + 36*x^2*e^(2*x)*log(x) + 162*x^2*e^(2*x) - 2*x) + 2*x^2*e^(
2*x)*log(x)^2 + 36*x^2*e^(2*x)*log(x) + 162*x^2*e^(2*x) - 2*x + 1), x)

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maple [A]  time = 0.13, size = 44, normalized size = 1.47

method	result	size
risch	\({\mathrm e}^{x^{4} x^{36 \,{\mathrm e}^{2 x} x^{2}} {\mathrm e}^{2 x \left (\ln \relax (x )^{2} {\mathrm e}^{2 x} x +81 x \,{\mathrm e}^{2 x}-1\right )}+1}\)	\(44\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6+4*x^5)*exp(x)^2*ln(x)^2+(72*x^6+76*x^5)*exp(x)^2*ln(x)+(324*x^6+360*x^5)*exp(x)^2-2*x^4+4*x^3)*exp
(x^2*exp(x)^2*ln(x)^2+18*x^2*exp(x)^2*ln(x)+81*exp(x)^2*x^2-x)^2*exp(x^4*exp(x^2*exp(x)^2*ln(x)^2+18*x^2*exp(x
)^2*ln(x)+81*exp(x)^2*x^2-x)^2+1),x,method=_RETURNVERBOSE)

[Out]

exp(x^4*(x^(18*exp(2*x)*x^2))^2*exp(2*x*(ln(x)^2*exp(2*x)*x+81*x*exp(2*x)-1))+1)

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maxima [A]  time = 1.31, size = 45, normalized size = 1.50 \begin {gather*} e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x)^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6+4*x^5)*exp(x)^2*log(x)^2+(72*x^6+76*x^5)*exp(x)^2*log(x)+(324*x^6+360*x^5)*exp(x)^2-2*x^4+4*
x^3)*exp(x^2*exp(x)^2*log(x)^2+18*x^2*exp(x)^2*log(x)+81*exp(x)^2*x^2-x)^2*exp(x^4*exp(x^2*exp(x)^2*log(x)^2+1
8*x^2*exp(x)^2*log(x)+81*exp(x)^2*x^2-x)^2+1),x, algorithm="maxima")

[Out]

e^(x^4*e^(2*x^2*e^(2*x)*log(x)^2 + 36*x^2*e^(2*x)*log(x) + 162*x^2*e^(2*x) - 2*x) + 1)

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mupad [B]  time = 1.19, size = 46, normalized size = 1.53 \begin {gather*} \mathrm {e}\,{\mathrm {e}}^{x^{36\,x^2\,{\mathrm {e}}^{2\,x}+4}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{162\,x^2\,{\mathrm {e}}^{2\,x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x^4*exp(162*x^2*exp(2*x) - 2*x + 36*x^2*exp(2*x)*log(x) + 2*x^2*exp(2*x)*log(x)^2) + 1)*exp(162*x^2*ex
p(2*x) - 2*x + 36*x^2*exp(2*x)*log(x) + 2*x^2*exp(2*x)*log(x)^2)*(exp(2*x)*(360*x^5 + 324*x^6) + 4*x^3 - 2*x^4
+ exp(2*x)*log(x)*(76*x^5 + 72*x^6) + exp(2*x)*log(x)^2*(4*x^5 + 4*x^6)),x)

[Out]

exp(1)*exp(x^(36*x^2*exp(2*x) + 4)*exp(2*x^2*exp(2*x)*log(x)^2)*exp(-2*x)*exp(162*x^2*exp(2*x)))

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sympy [A]  time = 34.70, size = 49, normalized size = 1.63 \begin {gather*} e^{x^{4} e^{2 x^{2} e^{2 x} \log {\relax (x )}^{2} + 36 x^{2} e^{2 x} \log {\relax (x )} + 162 x^{2} e^{2 x} - 2 x} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**6+4*x**5)*exp(x)**2*ln(x)**2+(72*x**6+76*x**5)*exp(x)**2*ln(x)+(324*x**6+360*x**5)*exp(x)**2-
2*x**4+4*x**3)*exp(x**2*exp(x)**2*ln(x)**2+18*x**2*exp(x)**2*ln(x)+81*exp(x)**2*x**2-x)**2*exp(x**4*exp(x**2*e
xp(x)**2*ln(x)**2+18*x**2*exp(x)**2*ln(x)+81*exp(x)**2*x**2-x)**2+1),x)

[Out]

exp(x**4*exp(2*x**2*exp(2*x)*log(x)**2 + 36*x**2*exp(2*x)*log(x) + 162*x**2*exp(2*x) - 2*x) + 1)

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