3.102.43 \(\int e^{-4+x-x^2-2 x^2 \log (2) \log (5)-e^{2 x} \log ^2(5)-x^2 \log ^2(2) \log ^2(5)+e^x (2 x \log (5)+2 x \log (2) \log ^2(5))} (3 x-2 x^2+(4 x-4 x^2) \log (2) \log (5)+e^{2 x} (2-2 x) \log ^2(5)+(2 x-2 x^2) \log ^2(2) \log ^2(5)+e^x ((-2+2 x^2) \log (5)+(-2+2 x^2) \log (2) \log ^2(5))) \, dx\)

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

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Rubi [F]  time = 15.92, 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 (-4+x-x^2-2 x^2 \log (2) \log (5)-e^{2 x} \log ^2(5)-x^2 \log ^2(2) \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )\right ) \left (3 x-2 x^2+\left (4 x-4 x^2\right ) \log (2) \log (5)+e^{2 x} (2-2 x) \log ^2(5)+\left (2 x-2 x^2\right ) \log ^2(2) \log ^2(5)+e^x \left (\left (-2+2 x^2\right ) \log (5)+\left (-2+2 x^2\right ) \log (2) \log ^2(5)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-4 + x - x^2 - 2*x^2*Log[2]*Log[5] - E^(2*x)*Log[5]^2 - x^2*Log[2]^2*Log[5]^2 + E^x*(2*x*Log[5] + 2*x*L
og[2]*Log[5]^2))*(3*x - 2*x^2 + (4*x - 4*x^2)*Log[2]*Log[5] + E^(2*x)*(2 - 2*x)*Log[5]^2 + (2*x - 2*x^2)*Log[2
]^2*Log[5]^2 + E^x*((-2 + 2*x^2)*Log[5] + (-2 + 2*x^2)*Log[2]*Log[5]^2)),x]

[Out]

-2*Log[5]*(1 + Log[2]*Log[5])*Defer[Int][E^(-4 + 2*x - E^(2*x)*Log[5]^2 + E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^
2) - x^2*(1 + Log[2]*Log[5]*(2 + Log[2]*Log[5]))), x] + 2*Log[5]^2*Defer[Int][E^(-4 + 3*x - E^(2*x)*Log[5]^2 +
E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^2) - x^2*(1 + Log[2]*Log[5]*(2 + Log[2]*Log[5]))), x] + 3*Defer[Int][E^(-
4 + x - E^(2*x)*Log[5]^2 + E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^2) - x^2*(1 + Log[2]*Log[5]*(2 + Log[2]*Log[5])
))*x, x] + 2*Log[2]*Log[5]*(2 + Log[2]*Log[5])*Defer[Int][E^(-4 + x - E^(2*x)*Log[5]^2 + E^x*(2*x*Log[5] + 2*x
*Log[2]*Log[5]^2) - x^2*(1 + Log[2]*Log[5]*(2 + Log[2]*Log[5])))*x, x] - 2*Log[5]^2*Defer[Int][E^(-4 + 3*x - E
^(2*x)*Log[5]^2 + E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^2) - x^2*(1 + Log[2]*Log[5]*(2 + Log[2]*Log[5])))*x, x]
- 2*Defer[Int][E^(-4 + x - E^(2*x)*Log[5]^2 + E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^2) - x^2*(1 + Log[2]*Log[5]*
(2 + Log[2]*Log[5])))*x^2, x] - 2*Log[2]*Log[5]*(2 + Log[2]*Log[5])*Defer[Int][E^(-4 + x - E^(2*x)*Log[5]^2 +
E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^2) - x^2*(1 + Log[2]*Log[5]*(2 + Log[2]*Log[5])))*x^2, x] + 2*Log[5]*(1 +
Log[2]*Log[5])*Defer[Int][E^(-4 + 2*x - E^(2*x)*Log[5]^2 + E^x*(2*x*Log[5] + 2*x*Log[2]*Log[5]^2) - x^2*(1 + L
og[2]*Log[5]*(2 + Log[2]*Log[5])))*x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) \left (3 x-2 x^2+e^{2 x} (2-2 x) \log ^2(5)+\left (4 x-4 x^2\right ) \log (2) \log (5) \left (1+\frac {1}{2} \log (2) \log (5)\right )+e^x \left (\left (-2+2 x^2\right ) \log (5)+\left (-2+2 x^2\right ) \log (2) \log ^2(5)\right )\right ) \, dx\\ &=\int \left (3 \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x-2 \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2-2 \exp \left (-4+3 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) (-1+x) \log ^2(5)+2 \exp \left (-4+2 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) \left (-1+x^2\right ) \log (5) (1+\log (2) \log (5))-2 \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) (-1+x) x \log (2) \log (5) (2+\log (2) \log (5))\right ) \, dx\\ &=-\left (2 \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2 \, dx\right )+3 \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x \, dx-\left (2 \log ^2(5)\right ) \int \exp \left (-4+3 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) (-1+x) \, dx+(2 \log (5) (1+\log (2) \log (5))) \int \exp \left (-4+2 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) \left (-1+x^2\right ) \, dx-(2 \log (2) \log (5) (2+\log (2) \log (5))) \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) (-1+x) x \, dx\\ &=-\left (2 \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2 \, dx\right )+3 \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x \, dx-\left (2 \log ^2(5)\right ) \int \left (-\exp \left (-4+3 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right )+\exp \left (-4+3 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x\right ) \, dx+(2 \log (5) (1+\log (2) \log (5))) \int \left (-\exp \left (-4+2 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right )+\exp \left (-4+2 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2\right ) \, dx-(2 \log (2) \log (5) (2+\log (2) \log (5))) \int \left (-\exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x+\exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2\right ) \, dx\\ &=-\left (2 \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2 \, dx\right )+3 \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x \, dx+\left (2 \log ^2(5)\right ) \int \exp \left (-4+3 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) \, dx-\left (2 \log ^2(5)\right ) \int \exp \left (-4+3 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x \, dx-(2 \log (5) (1+\log (2) \log (5))) \int \exp \left (-4+2 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) \, dx+(2 \log (5) (1+\log (2) \log (5))) \int \exp \left (-4+2 x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2 \, dx+(2 \log (2) \log (5) (2+\log (2) \log (5))) \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x \, dx-(2 \log (2) \log (5) (2+\log (2) \log (5))) \int \exp \left (-4+x-e^{2 x} \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )-x^2 (1+\log (2) \log (5) (2+\log (2) \log (5)))\right ) x^2 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 15.04, size = 0, normalized size = 0.00 \begin {gather*} \int e^{-4+x-x^2-2 x^2 \log (2) \log (5)-e^{2 x} \log ^2(5)-x^2 \log ^2(2) \log ^2(5)+e^x \left (2 x \log (5)+2 x \log (2) \log ^2(5)\right )} \left (3 x-2 x^2+\left (4 x-4 x^2\right ) \log (2) \log (5)+e^{2 x} (2-2 x) \log ^2(5)+\left (2 x-2 x^2\right ) \log ^2(2) \log ^2(5)+e^x \left (\left (-2+2 x^2\right ) \log (5)+\left (-2+2 x^2\right ) \log (2) \log ^2(5)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[E^(-4 + x - x^2 - 2*x^2*Log[2]*Log[5] - E^(2*x)*Log[5]^2 - x^2*Log[2]^2*Log[5]^2 + E^x*(2*x*Log[5] +
2*x*Log[2]*Log[5]^2))*(3*x - 2*x^2 + (4*x - 4*x^2)*Log[2]*Log[5] + E^(2*x)*(2 - 2*x)*Log[5]^2 + (2*x - 2*x^2)
*Log[2]^2*Log[5]^2 + E^x*((-2 + 2*x^2)*Log[5] + (-2 + 2*x^2)*Log[2]*Log[5]^2)),x]

[Out]

Integrate[E^(-4 + x - x^2 - 2*x^2*Log[2]*Log[5] - E^(2*x)*Log[5]^2 - x^2*Log[2]^2*Log[5]^2 + E^x*(2*x*Log[5] +
2*x*Log[2]*Log[5]^2))*(3*x - 2*x^2 + (4*x - 4*x^2)*Log[2]*Log[5] + E^(2*x)*(2 - 2*x)*Log[5]^2 + (2*x - 2*x^2)
*Log[2]^2*Log[5]^2 + E^x*((-2 + 2*x^2)*Log[5] + (-2 + 2*x^2)*Log[2]*Log[5]^2)), x]

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fricas [A]  time = 0.69, size = 62, normalized size = 2.07 \begin {gather*} {\left (x - 1\right )} e^{\left (-x^{2} \log \relax (5)^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (5) \log \relax (2) - e^{\left (2 \, x\right )} \log \relax (5)^{2} - x^{2} + 2 \, {\left (x \log \relax (5)^{2} \log \relax (2) + x \log \relax (5)\right )} e^{x} + x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x+2)*log(5)^2*exp(x)^2+((2*x^2-2)*log(2)*log(5)^2+(2*x^2-2)*log(5))*exp(x)+(-2*x^2+2*x)*log(2)^
2*log(5)^2+(-4*x^2+4*x)*log(2)*log(5)-2*x^2+3*x)*exp(-log(5)^2*exp(x)^2+(2*x*log(2)*log(5)^2+2*x*log(5))*exp(x
)-x^2*log(2)^2*log(5)^2-2*x^2*log(2)*log(5)-x^2+x-4),x, algorithm="fricas")

[Out]

(x - 1)*e^(-x^2*log(5)^2*log(2)^2 - 2*x^2*log(5)*log(2) - e^(2*x)*log(5)^2 - x^2 + 2*(x*log(5)^2*log(2) + x*lo
g(5))*e^x + x - 4)

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giac [B]  time = 0.57, size = 124, normalized size = 4.13 \begin {gather*} {\left (x e^{\left (-x^{2} \log \relax (5)^{2} \log \relax (2)^{2} + 2 \, x e^{x} \log \relax (5)^{2} \log \relax (2) - 2 \, x^{2} \log \relax (5) \log \relax (2) + 2 \, x e^{x} \log \relax (5) - e^{\left (2 \, x\right )} \log \relax (5)^{2} - x^{2} + x\right )} - e^{\left (-x^{2} \log \relax (5)^{2} \log \relax (2)^{2} + 2 \, x e^{x} \log \relax (5)^{2} \log \relax (2) - 2 \, x^{2} \log \relax (5) \log \relax (2) + 2 \, x e^{x} \log \relax (5) - e^{\left (2 \, x\right )} \log \relax (5)^{2} - x^{2} + x\right )}\right )} e^{\left (-4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x+2)*log(5)^2*exp(x)^2+((2*x^2-2)*log(2)*log(5)^2+(2*x^2-2)*log(5))*exp(x)+(-2*x^2+2*x)*log(2)^
2*log(5)^2+(-4*x^2+4*x)*log(2)*log(5)-2*x^2+3*x)*exp(-log(5)^2*exp(x)^2+(2*x*log(2)*log(5)^2+2*x*log(5))*exp(x
)-x^2*log(2)^2*log(5)^2-2*x^2*log(2)*log(5)-x^2+x-4),x, algorithm="giac")

[Out]

(x*e^(-x^2*log(5)^2*log(2)^2 + 2*x*e^x*log(5)^2*log(2) - 2*x^2*log(5)*log(2) + 2*x*e^x*log(5) - e^(2*x)*log(5)
^2 - x^2 + x) - e^(-x^2*log(5)^2*log(2)^2 + 2*x*e^x*log(5)^2*log(2) - 2*x^2*log(5)*log(2) + 2*x*e^x*log(5) - e
^(2*x)*log(5)^2 - x^2 + x))*e^(-4)

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maple [B]  time = 0.19, size = 61, normalized size = 2.03

method	result	size
risch	\(\left (x -1\right ) \left (\frac {1}{4}\right )^{x^{2} \ln \relax (5)} 4^{x \ln \relax (5)^{2} {\mathrm e}^{x}} 25^{{\mathrm e}^{x} x} {\mathrm e}^{-x^{2} \ln \relax (2)^{2} \ln \relax (5)^{2}-4-\ln \relax (5)^{2} {\mathrm e}^{2 x}-x^{2}+x}\)	\(61\)
norman	\(x \,{\mathrm e}^{-\ln \relax (5)^{2} {\mathrm e}^{2 x}+\left (2 x \ln \relax (2) \ln \relax (5)^{2}+2 x \ln \relax (5)\right ) {\mathrm e}^{x}-x^{2} \ln \relax (2)^{2} \ln \relax (5)^{2}-2 x^{2} \ln \relax (2) \ln \relax (5)-x^{2}+x -4}-{\mathrm e}^{-\ln \relax (5)^{2} {\mathrm e}^{2 x}+\left (2 x \ln \relax (2) \ln \relax (5)^{2}+2 x \ln \relax (5)\right ) {\mathrm e}^{x}-x^{2} \ln \relax (2)^{2} \ln \relax (5)^{2}-2 x^{2} \ln \relax (2) \ln \relax (5)-x^{2}+x -4}\)	\(124\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x+2)*ln(5)^2*exp(x)^2+((2*x^2-2)*ln(2)*ln(5)^2+(2*x^2-2)*ln(5))*exp(x)+(-2*x^2+2*x)*ln(2)^2*ln(5)^2+(
-4*x^2+4*x)*ln(2)*ln(5)-2*x^2+3*x)*exp(-ln(5)^2*exp(x)^2+(2*x*ln(2)*ln(5)^2+2*x*ln(5))*exp(x)-x^2*ln(2)^2*ln(5
)^2-2*x^2*ln(2)*ln(5)-x^2+x-4),x,method=_RETURNVERBOSE)

[Out]

(x-1)*(1/4)^(x^2*ln(5))*4^(x*ln(5)^2*exp(x))*25^(exp(x)*x)*exp(-x^2*ln(2)^2*ln(5)^2-4-ln(5)^2*exp(2*x)-x^2+x)

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maxima [B]  time = 0.60, size = 63, normalized size = 2.10 \begin {gather*} {\left (x - 1\right )} e^{\left (-x^{2} \log \relax (5)^{2} \log \relax (2)^{2} + 2 \, x e^{x} \log \relax (5)^{2} \log \relax (2) - 2 \, x^{2} \log \relax (5) \log \relax (2) + 2 \, x e^{x} \log \relax (5) - e^{\left (2 \, x\right )} \log \relax (5)^{2} - x^{2} + x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x+2)*log(5)^2*exp(x)^2+((2*x^2-2)*log(2)*log(5)^2+(2*x^2-2)*log(5))*exp(x)+(-2*x^2+2*x)*log(2)^
2*log(5)^2+(-4*x^2+4*x)*log(2)*log(5)-2*x^2+3*x)*exp(-log(5)^2*exp(x)^2+(2*x*log(2)*log(5)^2+2*x*log(5))*exp(x
)-x^2*log(2)^2*log(5)^2-2*x^2*log(2)*log(5)-x^2+x-4),x, algorithm="maxima")

[Out]

(x - 1)*e^(-x^2*log(5)^2*log(2)^2 + 2*x*e^x*log(5)^2*log(2) - 2*x^2*log(5)*log(2) + 2*x*e^x*log(5) - e^(2*x)*l
og(5)^2 - x^2 + x - 4)

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mupad [B]  time = 7.03, size = 65, normalized size = 2.17 \begin {gather*} \frac {2^{2\,x\,{\mathrm {e}}^x\,{\ln \relax (5)}^2}\,5^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x-{\mathrm {e}}^{2\,x}\,{\ln \relax (5)}^2-x^2-x^2\,{\ln \relax (2)}^2\,{\ln \relax (5)}^2-4}\,\left (x-1\right )}{2^{2\,x^2\,\ln \relax (5)}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x - exp(2*x)*log(5)^2 - x^2 + exp(x)*(2*x*log(5) + 2*x*log(2)*log(5)^2) - 2*x^2*log(2)*log(5) - x^2*lo
g(2)^2*log(5)^2 - 4)*(3*x + exp(x)*(log(5)*(2*x^2 - 2) + log(2)*log(5)^2*(2*x^2 - 2)) - 2*x^2 + log(2)^2*log(5
)^2*(2*x - 2*x^2) - exp(2*x)*log(5)^2*(2*x - 2) + log(2)*log(5)*(4*x - 4*x^2)),x)

[Out]

(2^(2*x*exp(x)*log(5)^2)*5^(2*x*exp(x))*exp(x - exp(2*x)*log(5)^2 - x^2 - x^2*log(2)^2*log(5)^2 - 4)*(x - 1))/
2^(2*x^2*log(5))

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sympy [B]  time = 0.44, size = 68, normalized size = 2.27 \begin {gather*} \left (x - 1\right ) e^{- 2 x^{2} \log {\relax (2 )} \log {\relax (5 )} - x^{2} \log {\relax (2 )}^{2} \log {\relax (5 )}^{2} - x^{2} + x + \left (2 x \log {\relax (5 )} + 2 x \log {\relax (2 )} \log {\relax (5 )}^{2}\right ) e^{x} - e^{2 x} \log {\relax (5 )}^{2} - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x+2)*ln(5)**2*exp(x)**2+((2*x**2-2)*ln(2)*ln(5)**2+(2*x**2-2)*ln(5))*exp(x)+(-2*x**2+2*x)*ln(2)
**2*ln(5)**2+(-4*x**2+4*x)*ln(2)*ln(5)-2*x**2+3*x)*exp(-ln(5)**2*exp(x)**2+(2*x*ln(2)*ln(5)**2+2*x*ln(5))*exp(
x)-x**2*ln(2)**2*ln(5)**2-2*x**2*ln(2)*ln(5)-x**2+x-4),x)

[Out]

(x - 1)*exp(-2*x**2*log(2)*log(5) - x**2*log(2)**2*log(5)**2 - x**2 + x + (2*x*log(5) + 2*x*log(2)*log(5)**2)*
exp(x) - exp(2*x)*log(5)**2 - 4)

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