3.17.93 \(\int e^{e^{-\frac {2+x+2 x^2-\log (4)}{x}} x-\frac {2+x+2 x^2-\log (4)}{x}} (2+3 x-x^2-2 x^3+e^{\frac {2+x+2 x^2-\log (4)}{x}} (1+2 x)+e^{e^4} (2+e^{\frac {2+x+2 x^2-\log (4)}{x}}+x-2 x^2-\log (4))+(-1-x) \log (4)) \, dx\)

Optimal. Leaf size=32 \[ e^{e^{-2 x-\frac {2+x-\log (4)}{x}} x} x \left (1+e^{e^4}+x\right ) \]

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Rubi [F]  time = 26.23, 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 (e^{-\frac {2+x+2 x^2-\log (4)}{x}} x-\frac {2+x+2 x^2-\log (4)}{x}\right ) \left (2+3 x-x^2-2 x^3+e^{\frac {2+x+2 x^2-\log (4)}{x}} (1+2 x)+e^{e^4} \left (2+e^{\frac {2+x+2 x^2-\log (4)}{x}}+x-2 x^2-\log (4)\right )+(-1-x) \log (4)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(x/E^((2 + x + 2*x^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x)*(2 + 3*x - x^2 - 2*x^3 + E^((2 + x + 2*x
^2 - Log[4])/x)*(1 + 2*x) + E^E^4*(2 + E^((2 + x + 2*x^2 - Log[4])/x) + x - 2*x^2 - Log[4]) + (-1 - x)*Log[4])
,x]

[Out]

Defer[Int][E^(4^x^(-1)*E^(-1 - 2/x - 2*x)*x), x] + Defer[Int][E^(E^4 + 4^x^(-1)*E^(-1 - 2/x - 2*x)*x), x] + (1
- Log[2])*Defer[Int][2^(1 + 2/x)*E^(-1 + E^4 - 2/x - 2*x + 4^x^(-1)*E^(-1 - 2/x - 2*x)*x), x] + 2*Defer[Int][
E^(x/E^((2 + x + 2*x^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x), x] - Log[4]*Defer[Int][E^(x/E^((2 + x + 2*x
^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x), x] + 2*Defer[Int][E^(4^x^(-1)*E^(-1 - 2/x - 2*x)*x)*x, x] + Def
er[Int][4^x^(-1)*E^(-1 + E^4 - 2/x - 2*x + 4^x^(-1)*E^(-1 - 2/x - 2*x)*x)*x, x] + 3*Defer[Int][E^(x/E^((2 + x
+ 2*x^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x)*x, x] - Log[4]*Defer[Int][E^(x/E^((2 + x + 2*x^2 - Log[4])/
x) - (2 + x + 2*x^2 - Log[4])/x)*x, x] - Defer[Int][2^(1 + 2/x)*E^(-1 + E^4 - 2/x - 2*x + 4^x^(-1)*E^(-1 - 2/x
- 2*x)*x)*x^2, x] - Defer[Int][E^(x/E^((2 + x + 2*x^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x)*x^2, x] - 2*
Defer[Int][E^(x/E^((2 + x + 2*x^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x)*x^3, x]

Rubi steps

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

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Mathematica [A]  time = 0.19, size = 31, normalized size = 0.97 \begin {gather*} e^{4^{\frac {1}{x}} e^{-1-\frac {2}{x}-2 x} x} x \left (1+e^{e^4}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(x/E^((2 + x + 2*x^2 - Log[4])/x) - (2 + x + 2*x^2 - Log[4])/x)*(2 + 3*x - x^2 - 2*x^3 + E^((2 + x
+ 2*x^2 - Log[4])/x)*(1 + 2*x) + E^E^4*(2 + E^((2 + x + 2*x^2 - Log[4])/x) + x - 2*x^2 - Log[4]) + (-1 - x)*L
og[4]),x]

[Out]

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

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fricas [B]  time = 0.96, size = 69, normalized size = 2.16 \begin {gather*} {\left (x^{2} + x e^{\left (e^{4}\right )} + x\right )} e^{\left (\frac {x^{2} e^{\left (-\frac {2 \, x^{2} + x - 2 \, \log \relax (2) + 2}{x}\right )} - 2 \, x^{2} - x + 2 \, \log \relax (2) - 2}{x} + \frac {2 \, x^{2} + x - 2 \, \log \relax (2) + 2}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp((-2*log(2)+2*x^2+x+2)/x)-2*log(2)-2*x^2+x+2)*exp(exp(4))+(2*x+1)*exp((-2*log(2)+2*x^2+x+2)/x)+
2*(-x-1)*log(2)-2*x^3-x^2+3*x+2)*exp(x/exp((-2*log(2)+2*x^2+x+2)/x))/exp((-2*log(2)+2*x^2+x+2)/x),x, algorithm
="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -{\left (2 \, x^{3} + x^{2} - {\left (2 \, x + 1\right )} e^{\left (\frac {2 \, x^{2} + x - 2 \, \log \relax (2) + 2}{x}\right )} + {\left (2 \, x^{2} - x - e^{\left (\frac {2 \, x^{2} + x - 2 \, \log \relax (2) + 2}{x}\right )} + 2 \, \log \relax (2) - 2\right )} e^{\left (e^{4}\right )} + 2 \, {\left (x + 1\right )} \log \relax (2) - 3 \, x - 2\right )} e^{\left (x e^{\left (-\frac {2 \, x^{2} + x - 2 \, \log \relax (2) + 2}{x}\right )} - \frac {2 \, x^{2} + x - 2 \, \log \relax (2) + 2}{x}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp((-2*log(2)+2*x^2+x+2)/x)-2*log(2)-2*x^2+x+2)*exp(exp(4))+(2*x+1)*exp((-2*log(2)+2*x^2+x+2)/x)+
2*(-x-1)*log(2)-2*x^3-x^2+3*x+2)*exp(x/exp((-2*log(2)+2*x^2+x+2)/x))/exp((-2*log(2)+2*x^2+x+2)/x),x, algorithm
="giac")

[Out]

integrate(-(2*x^3 + x^2 - (2*x + 1)*e^((2*x^2 + x - 2*log(2) + 2)/x) + (2*x^2 - x - e^((2*x^2 + x - 2*log(2) +
2)/x) + 2*log(2) - 2)*e^(e^4) + 2*(x + 1)*log(2) - 3*x - 2)*e^(x*e^(-(2*x^2 + x - 2*log(2) + 2)/x) - (2*x^2 +
x - 2*log(2) + 2)/x), x)

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maple [A]  time = 0.28, size = 31, normalized size = 0.97

method	result	size
risch	\(x \left ({\mathrm e}^{{\mathrm e}^{4}}+x +1\right ) {\mathrm e}^{x \,{\mathrm e}^{\frac {-2 x^{2}+2 \ln \relax (2)-x -2}{x}}}\)	\(31\)
norman	\(\left (x^{2} {\mathrm e}^{\frac {-2 \ln \relax (2)+2 x^{2}+x +2}{x}} {\mathrm e}^{x \,{\mathrm e}^{-\frac {-2 \ln \relax (2)+2 x^{2}+x +2}{x}}}+\left ({\mathrm e}^{{\mathrm e}^{4}}+1\right ) x \,{\mathrm e}^{\frac {-2 \ln \relax (2)+2 x^{2}+x +2}{x}} {\mathrm e}^{x \,{\mathrm e}^{-\frac {-2 \ln \relax (2)+2 x^{2}+x +2}{x}}}\right ) {\mathrm e}^{-\frac {-2 \ln \relax (2)+2 x^{2}+x +2}{x}}\)	\(111\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((exp((-2*ln(2)+2*x^2+x+2)/x)-2*ln(2)-2*x^2+x+2)*exp(exp(4))+(2*x+1)*exp((-2*ln(2)+2*x^2+x+2)/x)+2*(-x-1)*
ln(2)-2*x^3-x^2+3*x+2)*exp(x/exp((-2*ln(2)+2*x^2+x+2)/x))/exp((-2*ln(2)+2*x^2+x+2)/x),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.55, size = 33, normalized size = 1.03 \begin {gather*} {\left (x^{2} + x {\left (e^{\left (e^{4}\right )} + 1\right )}\right )} e^{\left (x e^{\left (-2 \, x + \frac {2 \, \log \relax (2)}{x} - \frac {2}{x} - 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp((-2*log(2)+2*x^2+x+2)/x)-2*log(2)-2*x^2+x+2)*exp(exp(4))+(2*x+1)*exp((-2*log(2)+2*x^2+x+2)/x)+
2*(-x-1)*log(2)-2*x^3-x^2+3*x+2)*exp(x/exp((-2*log(2)+2*x^2+x+2)/x))/exp((-2*log(2)+2*x^2+x+2)/x),x, algorithm
="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int {\mathrm {e}}^{-\frac {2\,x^2+x-2\,\ln \relax (2)+2}{x}}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {2\,x^2+x-2\,\ln \relax (2)+2}{x}}}\,\left (3\,x+{\mathrm {e}}^{\frac {2\,x^2+x-2\,\ln \relax (2)+2}{x}}\,\left (2\,x+1\right )+{\mathrm {e}}^{{\mathrm {e}}^4}\,\left (x-2\,\ln \relax (2)+{\mathrm {e}}^{\frac {2\,x^2+x-2\,\ln \relax (2)+2}{x}}-2\,x^2+2\right )-2\,\ln \relax (2)\,\left (x+1\right )-x^2-2\,x^3+2\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-(x - 2*log(2) + 2*x^2 + 2)/x)*exp(x*exp(-(x - 2*log(2) + 2*x^2 + 2)/x))*(3*x + exp((x - 2*log(2) + 2*
x^2 + 2)/x)*(2*x + 1) + exp(exp(4))*(x - 2*log(2) + exp((x - 2*log(2) + 2*x^2 + 2)/x) - 2*x^2 + 2) - 2*log(2)*
(x + 1) - x^2 - 2*x^3 + 2),x)

[Out]

int(exp(-(x - 2*log(2) + 2*x^2 + 2)/x)*exp(x*exp(-(x - 2*log(2) + 2*x^2 + 2)/x))*(3*x + exp((x - 2*log(2) + 2*
x^2 + 2)/x)*(2*x + 1) + exp(exp(4))*(x - 2*log(2) + exp((x - 2*log(2) + 2*x^2 + 2)/x) - 2*x^2 + 2) - 2*log(2)*
(x + 1) - x^2 - 2*x^3 + 2), x)

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sympy [A]  time = 3.07, size = 31, normalized size = 0.97 \begin {gather*} \left (x^{2} + x + x e^{e^{4}}\right ) e^{x e^{- \frac {2 x^{2} + x - 2 \log {\relax (2 )} + 2}{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp((-2*ln(2)+2*x**2+x+2)/x)-2*ln(2)-2*x**2+x+2)*exp(exp(4))+(2*x+1)*exp((-2*ln(2)+2*x**2+x+2)/x)+
2*(-x-1)*ln(2)-2*x**3-x**2+3*x+2)*exp(x/exp((-2*ln(2)+2*x**2+x+2)/x))/exp((-2*ln(2)+2*x**2+x+2)/x),x)

[Out]

(x**2 + x + x*exp(exp(4)))*exp(x*exp(-(2*x**2 + x - 2*log(2) + 2)/x))

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