3.34.39 \(\int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} (3 x^4-6 x^5+3 x^6+e^6 (-8 x^3+4 x^4)))}{1-2 x+x^2} \, dx\)

Optimal. Leaf size=30 \[ 2+e^{e^{e^{x^2 \left (-\frac {4 e^6}{1-x}+x\right )}} x^2} \]

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Rubi [F]  time = 50.18, 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 {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*x^2)*(2*x - 4*x^2 + 2*x^
3 + E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*(3*x^4 - 6*x^5 + 3*x^6 + E^6*(-8*x^3 + 4*x^4))))/(1 - 2*x + x^2),x]

[Out]

-4*Defer[Int][E^(6 + E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*x^2 + (4*E^
6*x^2)/(-1 + x) + x^3), x] - 4*Defer[Int][E^(6 + E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3
+ x^4)/(-1 + x))*x^2 + (4*E^6*x^2)/(-1 + x) + x^3)/(-1 + x)^2, x] - 8*Defer[Int][E^(6 + E^((4*E^6*x^2 - x^3 +
x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*x^2 + (4*E^6*x^2)/(-1 + x) + x^3)/(-1 + x), x] + 2*Def
er[Int][E^(E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*x^2)*x, x] + 4*Defer[
Int][E^(6 + E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*x^2 + (4*E^6*x^2)/(-
1 + x) + x^3)*x^2, x] + 3*Defer[Int][E^(E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-
1 + x))*x^2 + (4*E^6*x^2)/(-1 + x) + x^3)*x^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{(-1+x)^2} \, dx\\ &=\int \left (2 \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x+\frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^3 \left (-8 e^6+\left (3+4 e^6\right ) x-6 x^2+3 x^3\right )}{(1-x)^2}\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x \, dx+\int \frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^3 \left (-8 e^6+\left (3+4 e^6\right ) x-6 x^2+3 x^3\right )}{(1-x)^2} \, dx\\ &=2 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x \, dx+\int \left (-4 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )-\frac {4 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{(-1+x)^2}-\frac {8 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{-1+x}+4 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^2+3 \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^4\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x \, dx+3 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^4 \, dx-4 \int \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) \, dx-4 \int \frac {\exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{(-1+x)^2} \, dx+4 \int \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^2 \, dx-8 \int \frac {\exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{-1+x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.40, size = 26, normalized size = 0.87 \begin {gather*} e^{e^{e^{x^2 \left (\frac {4 e^6}{-1+x}+x\right )}} x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x)) + E^E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*x^2)*(2*x - 4*x^2
+ 2*x^3 + E^((4*E^6*x^2 - x^3 + x^4)/(-1 + x))*(3*x^4 - 6*x^5 + 3*x^6 + E^6*(-8*x^3 + 4*x^4))))/(1 - 2*x + x^2
),x]

[Out]

E^(E^E^(x^2*((4*E^6)/(-1 + x) + x))*x^2)

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fricas [A]  time = 0.50, size = 29, normalized size = 0.97 \begin {gather*} e^{\left (x^{2} e^{\left (e^{\left (\frac {x^{4} - x^{3} + 4 \, x^{2} e^{6}}{x - 1}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-8*x^3)*exp(3)^2+3*x^6-6*x^5+3*x^4)*exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))+2*x^3-4*x^2+2*x)*exp
(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1)))*exp(x^2*exp(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))))/(x^2-2*x+1),x, algorit
hm="fricas")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-8*x^3)*exp(3)^2+3*x^6-6*x^5+3*x^4)*exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))+2*x^3-4*x^2+2*x)*exp
(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1)))*exp(x^2*exp(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))))/(x^2-2*x+1),x, algorit
hm="giac")

[Out]

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

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maple [A]  time = 0.49, size = 28, normalized size = 0.93

method	result	size
risch	\({\mathrm e}^{x^{2} {\mathrm e}^{{\mathrm e}^{\frac {x^{2} \left (x^{2}+4 \,{\mathrm e}^{6}-x \right )}{x -1}}}}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^4-8*x^3)*exp(3)^2+3*x^6-6*x^5+3*x^4)*exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))+2*x^3-4*x^2+2*x)*exp(exp((
4*x^2*exp(3)^2+x^4-x^3)/(x-1)))*exp(x^2*exp(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))))/(x^2-2*x+1),x,method=_RETURN
VERBOSE)

[Out]

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

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maxima [A]  time = 1.24, size = 29, normalized size = 0.97 \begin {gather*} e^{\left (x^{2} e^{\left (e^{\left (x^{3} + 4 \, x e^{6} + \frac {4 \, e^{6}}{x - 1} + 4 \, e^{6}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-8*x^3)*exp(3)^2+3*x^6-6*x^5+3*x^4)*exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))+2*x^3-4*x^2+2*x)*exp
(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1)))*exp(x^2*exp(exp((4*x^2*exp(3)^2+x^4-x^3)/(x-1))))/(x^2-2*x+1),x, algorit
hm="maxima")

[Out]

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

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mupad [B]  time = 2.40, size = 41, normalized size = 1.37 \begin {gather*} {\mathrm {e}}^{x^2\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,x^2\,{\mathrm {e}}^6}{x-1}}\,{\mathrm {e}}^{\frac {x^4}{x-1}}\,{\mathrm {e}}^{-\frac {x^3}{x-1}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2*exp(exp((4*x^2*exp(6) - x^3 + x^4)/(x - 1))))*exp(exp((4*x^2*exp(6) - x^3 + x^4)/(x - 1)))*(2*x -
4*x^2 + 2*x^3 - exp((4*x^2*exp(6) - x^3 + x^4)/(x - 1))*(exp(6)*(8*x^3 - 4*x^4) - 3*x^4 + 6*x^5 - 3*x^6)))/(x
^2 - 2*x + 1),x)

[Out]

exp(x^2*exp(exp((4*x^2*exp(6))/(x - 1))*exp(x^4/(x - 1))*exp(-x^3/(x - 1))))

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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((((4*x**4-8*x**3)*exp(3)**2+3*x**6-6*x**5+3*x**4)*exp((4*x**2*exp(3)**2+x**4-x**3)/(x-1))+2*x**3-4*x
**2+2*x)*exp(exp((4*x**2*exp(3)**2+x**4-x**3)/(x-1)))*exp(x**2*exp(exp((4*x**2*exp(3)**2+x**4-x**3)/(x-1))))/(
x**2-2*x+1),x)

[Out]

Timed out

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