3.25.21 \(\int \frac {e^{e^{\frac {8 x}{-3+3 x}} (9-e^4)+\frac {8 x}{-3+3 x}} (-72+8 e^4)}{3-6 x+3 x^2} \, dx\)

Optimal. Leaf size=24 \[ e^{e^{-\frac {8 x}{3 (1-x)}} \left (9-e^4\right )} \]

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Rubi [F]  time = 0.30, 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 {\exp \left (e^{\frac {8 x}{-3+3 x}} \left (9-e^4\right )+\frac {8 x}{-3+3 x}\right ) \left (-72+8 e^4\right )}{3-6 x+3 x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((8*x)/(-3 + 3*x))*(9 - E^4) + (8*x)/(-3 + 3*x))*(-72 + 8*E^4))/(3 - 6*x + 3*x^2),x]

[Out]

(-8*(9 - E^4)*Defer[Int][E^(E^((8*x)/(-3 + 3*x))*(9 - E^4) + (8*x)/(-3 + 3*x))/(-1 + x)^2, x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (8 \left (9-e^4\right )\right ) \int \frac {\exp \left (e^{\frac {8 x}{-3+3 x}} \left (9-e^4\right )+\frac {8 x}{-3+3 x}\right )}{3-6 x+3 x^2} \, dx\right )\\ &=-\left (\left (8 \left (9-e^4\right )\right ) \int \frac {\exp \left (e^{\frac {8 x}{-3+3 x}} \left (9-e^4\right )+\frac {8 x}{-3+3 x}\right )}{3 (-1+x)^2} \, dx\right )\\ &=-\left (\frac {1}{3} \left (8 \left (9-e^4\right )\right ) \int \frac {\exp \left (e^{\frac {8 x}{-3+3 x}} \left (9-e^4\right )+\frac {8 x}{-3+3 x}\right )}{(-1+x)^2} \, dx\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.28, size = 21, normalized size = 0.88 \begin {gather*} e^{-e^{\frac {8 x}{3 (-1+x)}} \left (-9+e^4\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((8*x)/(-3 + 3*x))*(9 - E^4) + (8*x)/(-3 + 3*x))*(-72 + 8*E^4))/(3 - 6*x + 3*x^2),x]

[Out]

E^(-(E^((8*x)/(3*(-1 + x)))*(-9 + E^4)))

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fricas [B]  time = 0.63, size = 43, normalized size = 1.79 \begin {gather*} e^{\left (-\frac {3 \, {\left ({\left (x - 1\right )} e^{4} - 9 \, x + 9\right )} e^{\left (\frac {8 \, x}{3 \, {\left (x - 1\right )}}\right )} - 8 \, x}{3 \, {\left (x - 1\right )}} - \frac {8 \, x}{3 \, {\left (x - 1\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(2)^2-72)*exp((-exp(2)^2+9)/exp(-4*x/(3*x-3))^2)/(3*x^2-6*x+3)/exp(-4*x/(3*x-3))^2,x, algorith
m="fricas")

[Out]

e^(-1/3*(3*((x - 1)*e^4 - 9*x + 9)*e^(8/3*x/(x - 1)) - 8*x)/(x - 1) - 8/3*x/(x - 1))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {8 \, {\left (e^{4} - 9\right )} e^{\left (-{\left (e^{4} - 9\right )} e^{\left (\frac {8 \, x}{3 \, {\left (x - 1\right )}}\right )} + \frac {8 \, x}{3 \, {\left (x - 1\right )}}\right )}}{3 \, {\left (x^{2} - 2 \, x + 1\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(2)^2-72)*exp((-exp(2)^2+9)/exp(-4*x/(3*x-3))^2)/(3*x^2-6*x+3)/exp(-4*x/(3*x-3))^2,x, algorith
m="giac")

[Out]

integrate(8/3*(e^4 - 9)*e^(-(e^4 - 9)*e^(8/3*x/(x - 1)) + 8/3*x/(x - 1))/(x^2 - 2*x + 1), x)

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maple [B]  time = 0.39, size = 51, normalized size = 2.12

method	result	size
risch	\(\frac {{\mathrm e}^{-\left ({\mathrm e}^{4}-9\right ) {\mathrm e}^{\frac {8 x}{3 \left (x -1\right )}}} {\mathrm e}^{4}}{{\mathrm e}^{4}-9}-\frac {9 \,{\mathrm e}^{-\left ({\mathrm e}^{4}-9\right ) {\mathrm e}^{\frac {8 x}{3 \left (x -1\right )}}}}{{\mathrm e}^{4}-9}\)	\(51\)
norman	\(\frac {\left (x \,{\mathrm e}^{-\frac {8 x}{3 x -3}} {\mathrm e}^{\left (-{\mathrm e}^{4}+9\right ) {\mathrm e}^{\frac {8 x}{3 x -3}}}-{\mathrm e}^{-\frac {8 x}{3 x -3}} {\mathrm e}^{\left (-{\mathrm e}^{4}+9\right ) {\mathrm e}^{\frac {8 x}{3 x -3}}}\right ) {\mathrm e}^{\frac {8 x}{3 x -3}}}{x -1}\)	\(97\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*exp(2)^2-72)*exp((-exp(2)^2+9)/exp(-4*x/(3*x-3))^2)/(3*x^2-6*x+3)/exp(-4*x/(3*x-3))^2,x,method=_RETURNV
ERBOSE)

[Out]

1/(exp(4)-9)*exp(-(exp(4)-9)*exp(8/3*x/(x-1)))*exp(4)-9/(exp(4)-9)*exp(-(exp(4)-9)*exp(8/3*x/(x-1)))

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maxima [A]  time = 0.38, size = 26, normalized size = 1.08 \begin {gather*} e^{\left (-e^{\left (\frac {8}{3 \, {\left (x - 1\right )}} + \frac {20}{3}\right )} + 9 \, e^{\left (\frac {8}{3 \, {\left (x - 1\right )}} + \frac {8}{3}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(2)^2-72)*exp((-exp(2)^2+9)/exp(-4*x/(3*x-3))^2)/(3*x^2-6*x+3)/exp(-4*x/(3*x-3))^2,x, algorith
m="maxima")

[Out]

e^(-e^(8/3/(x - 1) + 20/3) + 9*e^(8/3/(x - 1) + 8/3))

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mupad [B]  time = 1.67, size = 31, normalized size = 1.29 \begin {gather*} {\mathrm {e}}^{9\,{\mathrm {e}}^{\frac {8\,x}{3\,x-3}}}\,{\mathrm {e}}^{-{\mathrm {e}}^4\,{\mathrm {e}}^{\frac {8\,x}{3\,x-3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-exp((8*x)/(3*x - 3))*(exp(4) - 9))*exp((8*x)/(3*x - 3))*(8*exp(4) - 72))/(3*x^2 - 6*x + 3),x)

[Out]

exp(9*exp((8*x)/(3*x - 3)))*exp(-exp(4)*exp((8*x)/(3*x - 3)))

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sympy [A]  time = 0.45, size = 15, normalized size = 0.62 \begin {gather*} e^{\left (9 - e^{4}\right ) e^{\frac {8 x}{3 x - 3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(2)**2-72)*exp((-exp(2)**2+9)/exp(-4*x/(3*x-3))**2)/(3*x**2-6*x+3)/exp(-4*x/(3*x-3))**2,x)

[Out]

exp((9 - exp(4))*exp(8*x/(3*x - 3)))

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