3.73.58 \(\int \frac {2^{\frac {1}{-2+x}} (e^{e^{e^{3+e^{6+x}}}})^{\frac {1}{-2+x}} (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log (2 e^{e^{e^{3+e^{6+x}}}}))}{4-4 x+x^2} \, dx\)

Optimal. Leaf size=30 \[ -2-2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \]

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Rubi [F]  time = 1.87, 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 {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)*(E^(9 + E^(3 + E^(6 + x)) + E^(6 + x) + x)*(2 - x)
+ Log[2*E^E^E^(3 + E^(6 + x))]))/(4 - 4*x + x^2),x]

[Out]

Log[2*E^E^E^(3 + E^(6 + x))]*Defer[Int][(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1))/(-2 + x)^2, x]
- Defer[Int][(2^(-2 + x)^(-1)*E^(9 + E^(3 + E^(6 + x)) + E^(6 + x) + x)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)
)/(-2 + x), x] - Defer[Int][E^(9 + E^(3 + E^(6 + x)) + E^(6 + x) + x)*Defer[Int][(2^(-2 + x)^(-1)*(E^E^E^(3 +
E^(6 + x)))^(-2 + x)^(-1))/(-2 + x)^2, x], x]

Rubi steps

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

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Mathematica [F]  time = 8.45, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)*(E^(9 + E^(3 + E^(6 + x)) + E^(6 + x) + x)*(2
- x) + Log[2*E^E^E^(3 + E^(6 + x))]))/(4 - 4*x + x^2),x]

[Out]

Integrate[(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)*(E^(9 + E^(3 + E^(6 + x)) + E^(6 + x) + x)*(2
- x) + Log[2*E^E^E^(3 + E^(6 + x))]))/(4 - 4*x + x^2), x]

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fricas [B]  time = 0.85, size = 48, normalized size = 1.60 \begin {gather*} -e^{\left (\frac {{\left (e^{\left (x + e^{\left (x + 6\right )} + 9\right )} \log \relax (2) + e^{\left (x + e^{\left (x + 6\right )} + e^{\left (e^{\left (x + 6\right )} + 3\right )} + 9\right )}\right )} e^{\left (-x - e^{\left (x + 6\right )} - 9\right )}}{x - 2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^((e^(x + e^(x + 6) + 9)*log(2) + e^(x + e^(x + 6) + e^(e^(x + 6) + 3) + 9))*e^(-x - e^(x + 6) - 9)/(x - 2))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(-((x - 2)*e^(x + e^(x + 6) + e^(e^(x + 6) + 3) + 9) - log(2*e^(e^(e^(e^(x + 6) + 3)))))*(2*e^(e^(e^(
e^(x + 6) + 3))))^(1/(x - 2))/(x^2 - 4*x + 4), x)

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maple [A]  time = 0.40, size = 25, normalized size = 0.83

method	result	size
risch	\(-2^{\frac {1}{x -2}} \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+{\mathrm e}^{x +6}}}}\right )^{\frac {1}{x -2}}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(2*exp(exp(exp(3)*exp(exp(x+6)))))+(2-x)*exp(3)*exp(x+6)*exp(exp(x+6))*exp(exp(3)*exp(exp(x+6))))*exp(l
n(2*exp(exp(exp(3)*exp(exp(x+6)))))/(x-2))/(x^2-4*x+4),x,method=_RETURNVERBOSE)

[Out]

-2^(1/(x-2))*exp(exp(exp(3+exp(x+6))))^(1/(x-2))

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maxima [A]  time = 0.62, size = 26, normalized size = 0.87 \begin {gather*} -e^{\left (\frac {e^{\left (e^{\left (e^{\left (x + 6\right )} + 3\right )}\right )}}{x - 2} + \frac {\log \relax (2)}{x - 2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^(e^(e^(e^(x + 6) + 3))/(x - 2) + log(2)/(x - 2))

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mupad [B]  time = 4.80, size = 26, normalized size = 0.87 \begin {gather*} -2^{\frac {1}{x-2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^6\,{\mathrm {e}}^x}\,{\mathrm {e}}^3}}{x-2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(log(2*exp(exp(exp(3)*exp(exp(x + 6)))))/(x - 2))*(log(2*exp(exp(exp(3)*exp(exp(x + 6))))) - exp(x + 6
)*exp(3)*exp(exp(x + 6))*exp(exp(3)*exp(exp(x + 6)))*(x - 2)))/(x^2 - 4*x + 4),x)

[Out]

-2^(1/(x - 2))*exp(exp(exp(exp(6)*exp(x))*exp(3))/(x - 2))

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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((ln(2*exp(exp(exp(3)*exp(exp(x+6)))))+(2-x)*exp(3)*exp(x+6)*exp(exp(x+6))*exp(exp(3)*exp(exp(x+6))))
*exp(ln(2*exp(exp(exp(3)*exp(exp(x+6)))))/(x-2))/(x**2-4*x+4),x)

[Out]

Timed out

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