3.82.69 \(\int \frac {e^{-e^{\frac {-4-x+6 x^2-5 x^3}{x}}} (-x+e^{e^{\frac {-4-x+6 x^2-5 x^3}{x}}} x+e^{\frac {-4-x+6 x^2-5 x^3}{x}} (4+6 x^2-10 x^3))}{x} \, dx\)

Optimal. Leaf size=32 \[ x-e^{-e^{\frac {-4-x+x^2+(5-5 x) x^2}{x}}} x \]

________________________________________________________________________________________

Rubi [F]  time = 2.61, 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 {e^{-e^{\frac {-4-x+6 x^2-5 x^3}{x}}} \left (-x+e^{e^{\frac {-4-x+6 x^2-5 x^3}{x}}} x+e^{\frac {-4-x+6 x^2-5 x^3}{x}} \left (4+6 x^2-10 x^3\right )\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-x + E^E^((-4 - x + 6*x^2 - 5*x^3)/x)*x + E^((-4 - x + 6*x^2 - 5*x^3)/x)*(4 + 6*x^2 - 10*x^3))/(E^E^((-4
- x + 6*x^2 - 5*x^3)/x)*x),x]

[Out]

x - Defer[Int][E^(-E^(-1 - 4/x + 6*x - 5*x^2)), x] + 4*Defer[Int][E^(-1 - E^(-1 - 4/x + 6*x - 5*x^2) - 4/x + 6
*x - 5*x^2)/x, x] + 6*Defer[Int][E^(-1 - E^(-1 - 4/x + 6*x - 5*x^2) - 4/x + 6*x - 5*x^2)*x, x] - 10*Defer[Int]
[E^(-1 - E^(-1 - 4/x + 6*x - 5*x^2) - 4/x + 6*x - 5*x^2)*x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-e^{-1-\frac {4}{x}+6 x-5 x^2}} \left (-x+e^{e^{\frac {-4-x+6 x^2-5 x^3}{x}}} x+e^{\frac {-4-x+6 x^2-5 x^3}{x}} \left (4+6 x^2-10 x^3\right )\right )}{x} \, dx\\ &=\int \left (1-e^{-e^{-1-\frac {4}{x}+6 x-5 x^2}}-\frac {2 \exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right ) \left (-2-3 x^2+5 x^3\right )}{x}\right ) \, dx\\ &=x-2 \int \frac {\exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right ) \left (-2-3 x^2+5 x^3\right )}{x} \, dx-\int e^{-e^{-1-\frac {4}{x}+6 x-5 x^2}} \, dx\\ &=x-2 \int \left (-\frac {2 \exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right )}{x}-3 \exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right ) x+5 \exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right ) x^2\right ) \, dx-\int e^{-e^{-1-\frac {4}{x}+6 x-5 x^2}} \, dx\\ &=x+4 \int \frac {\exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right )}{x} \, dx+6 \int \exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right ) x \, dx-10 \int \exp \left (-1-e^{-1-\frac {4}{x}+6 x-5 x^2}-\frac {4}{x}+6 x-5 x^2\right ) x^2 \, dx-\int e^{-e^{-1-\frac {4}{x}+6 x-5 x^2}} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [F]  time = 0.52, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{-e^{\frac {-4-x+6 x^2-5 x^3}{x}}} \left (-x+e^{e^{\frac {-4-x+6 x^2-5 x^3}{x}}} x+e^{\frac {-4-x+6 x^2-5 x^3}{x}} \left (4+6 x^2-10 x^3\right )\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-x + E^E^((-4 - x + 6*x^2 - 5*x^3)/x)*x + E^((-4 - x + 6*x^2 - 5*x^3)/x)*(4 + 6*x^2 - 10*x^3))/(E^E
^((-4 - x + 6*x^2 - 5*x^3)/x)*x),x]

[Out]

Integrate[(-x + E^E^((-4 - x + 6*x^2 - 5*x^3)/x)*x + E^((-4 - x + 6*x^2 - 5*x^3)/x)*(4 + 6*x^2 - 10*x^3))/(E^E
^((-4 - x + 6*x^2 - 5*x^3)/x)*x), x]

________________________________________________________________________________________

fricas [A]  time = 0.72, size = 49, normalized size = 1.53 \begin {gather*} {\left (x e^{\left (e^{\left (-\frac {5 \, x^{3} - 6 \, x^{2} + x + 4}{x}\right )}\right )} - x\right )} e^{\left (-e^{\left (-\frac {5 \, x^{3} - 6 \, x^{2} + x + 4}{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(exp((-5*x^3+6*x^2-x-4)/x))+(-10*x^3+6*x^2+4)*exp((-5*x^3+6*x^2-x-4)/x)-x)/x/exp(exp((-5*x^3+6
*x^2-x-4)/x)),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (2 \, {\left (5 \, x^{3} - 3 \, x^{2} - 2\right )} e^{\left (-\frac {5 \, x^{3} - 6 \, x^{2} + x + 4}{x}\right )} - x e^{\left (e^{\left (-\frac {5 \, x^{3} - 6 \, x^{2} + x + 4}{x}\right )}\right )} + x\right )} e^{\left (-e^{\left (-\frac {5 \, x^{3} - 6 \, x^{2} + x + 4}{x}\right )}\right )}}{x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(exp((-5*x^3+6*x^2-x-4)/x))+(-10*x^3+6*x^2+4)*exp((-5*x^3+6*x^2-x-4)/x)-x)/x/exp(exp((-5*x^3+6
*x^2-x-4)/x)),x, algorithm="giac")

[Out]

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

________________________________________________________________________________________

maple [A]  time = 0.22, size = 28, normalized size = 0.88

method	result	size
risch	\(x -x \,{\mathrm e}^{-{\mathrm e}^{-\frac {5 x^{3}-6 x^{2}+x +4}{x}}}\)	\(28\)
norman	\(\left (x \,{\mathrm e}^{{\mathrm e}^{\frac {-5 x^{3}+6 x^{2}-x -4}{x}}}-x \right ) {\mathrm e}^{-{\mathrm e}^{\frac {-5 x^{3}+6 x^{2}-x -4}{x}}}\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*exp(exp((-5*x^3+6*x^2-x-4)/x))+(-10*x^3+6*x^2+4)*exp((-5*x^3+6*x^2-x-4)/x)-x)/x/exp(exp((-5*x^3+6*x^2-x
-4)/x)),x,method=_RETURNVERBOSE)

[Out]

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

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x - \int \frac {{\left (x e^{\left (5 \, x^{2} + \frac {4}{x} + 1\right )} + 2 \, {\left (5 \, x^{3} - 3 \, x^{2} - 2\right )} e^{\left (6 \, x\right )}\right )} e^{\left (-5 \, x^{2} - \frac {4}{x} - e^{\left (-5 \, x^{2} + 6 \, x - \frac {4}{x} - 1\right )} - 1\right )}}{x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(exp((-5*x^3+6*x^2-x-4)/x))+(-10*x^3+6*x^2+4)*exp((-5*x^3+6*x^2-x-4)/x)-x)/x/exp(exp((-5*x^3+6
*x^2-x-4)/x)),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 5.34, size = 26, normalized size = 0.81 \begin {gather*} -x\,\left ({\mathrm {e}}^{-{\mathrm {e}}^{6\,x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-\frac {4}{x}}\,{\mathrm {e}}^{-5\,x^2}}-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-exp(-(x - 6*x^2 + 5*x^3 + 4)/x))*(exp(-(x - 6*x^2 + 5*x^3 + 4)/x)*(6*x^2 - 10*x^3 + 4) - x + x*exp(e
xp(-(x - 6*x^2 + 5*x^3 + 4)/x))))/x,x)

[Out]

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

________________________________________________________________________________________

sympy [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((x*exp(exp((-5*x**3+6*x**2-x-4)/x))+(-10*x**3+6*x**2+4)*exp((-5*x**3+6*x**2-x-4)/x)-x)/x/exp(exp((-5
*x**3+6*x**2-x-4)/x)),x)

[Out]

Timed out

________________________________________________________________________________________