3.57.92 \(\int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) (-16 x+6 x^2)}{e^2})}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 (-4 x^2+x^3)}{e^8}+\frac {(-4+x)^3 (-16 x^3+4 x^4)}{e^6}+\frac {(-4+x)^2 (-8 x+2 x^2+8 x^3-26 x^4+6 x^5)}{e^4}+\frac {(-4+x) (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6)}{e^2}} \, dx\)

Optimal. Leaf size=33 \[ 1-e^{e^{\frac {x}{-x+\frac {1}{x-\left (\frac {-4+x}{e^2}+x\right )^2}}}} \]

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Rubi [F]  time = 138.81, 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 (\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 +
x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^
2 + (2*(-4 + x)*x^2)/E^2 + x^3))*(8*x - 14*x^2 + 3*x^3 + ((-4 + x)^2*(-4 + 3*x))/E^4 + ((-4 + x)*(-16*x + 6*x^
2))/E^2))/(-4 + x + 8*x^2 - 10*x^3 - 2*x^4 + 9*x^5 - 6*x^6 + x^7 + ((-4 + x)^4*(-4*x^2 + x^3))/E^8 + ((-4 + x)
^3*(-16*x^3 + 4*x^4))/E^6 + ((-4 + x)^2*(-8*x + 2*x^2 + 8*x^3 - 26*x^4 + 6*x^5))/E^4 + ((-4 + x)*(-16*x^2 + 4*
x^3 + 16*x^4 - 20*x^5 + 4*x^6))/E^2),x]

[Out]

16*Defer[Int][E^(4 + E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x
^2 + (2*(-4 + x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^
2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3))/(E^4 + 16*x - (8 + 8*E^2 + E^4)*x^2 + (1 + E^2)^2*x^3)^2, x] - 2
*(8 + 8*E^2 + E^4)*Defer[Int][(E^(4 + E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4
+ x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3
)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3))*x)/(E^4 + 16*x - (8 + 8*E^2 + E^4)*x^2 + (1 + E
^2)^2*x^3)^2, x] + 3*(1 + E^2)^2*Defer[Int][(E^(4 + E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x
^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*
x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3))*x^2)/(E^4 + 16*x - (8 + 8*E^2 + E
^4)*x^2 + (1 + E^2)^2*x^3)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) \left (16 e^4+\left (-16 e^4-16 e^6-2 e^8\right ) x+\left (3 e^4+6 e^6+3 e^8\right ) x^2\right )}{e^8+32 e^4 x+\left (256-16 e^4-16 e^6-2 e^8\right ) x^2+\left (-256-256 e^2-30 e^4+4 e^6+2 e^8\right ) x^3+\left (96+192 e^2+112 e^4+16 e^6+e^8\right ) x^4+\left (-16-48 e^2-50 e^4-20 e^6-2 e^8\right ) x^5+\left (1+4 e^2+6 e^4+4 e^6+e^8\right ) x^6} \, dx\\ &=\int \frac {\exp \left (\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) \left (16 e^4-2 e^4 \left (8+8 e^2+e^4\right ) x+3 e^4 \left (1+e^2\right )^2 x^2\right )}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2} \, dx\\ &=\int \left (\frac {16 \exp \left (4+\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2}+\frac {2 \exp \left (4+\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) \left (-8-8 e^2-e^4\right ) x}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2}+\frac {3 \exp \left (4+\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) \left (1+e^2\right )^2 x^2}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2}\right ) \, dx\\ &=16 \int \frac {\exp \left (4+\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2} \, dx+\left (3 \left (1+e^2\right )^2\right ) \int \frac {\exp \left (4+\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) x^2}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2} \, dx-\left (2 \left (8+8 e^2+e^4\right )\right ) \int \frac {\exp \left (4+\exp \left (\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right )+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}\right ) x}{\left (e^4+16 x-\left (8+8 e^2+e^4\right ) x^2+\left (1+e^2\right )^2 x^3\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.41, size = 47, normalized size = 1.42 \begin {gather*} -e^{e^{-1+\frac {e^4}{(-4+x)^2 x+2 e^2 (-4+x) x^2+e^4 \left (1-x^2+x^3\right )}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2
*(-4 + x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^
4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3))*(8*x - 14*x^2 + 3*x^3 + ((-4 + x)^2*(-4 + 3*x))/E^4 + ((-4 + x)*(-16*x
+ 6*x^2))/E^2))/(-4 + x + 8*x^2 - 10*x^3 - 2*x^4 + 9*x^5 - 6*x^6 + x^7 + ((-4 + x)^4*(-4*x^2 + x^3))/E^8 + ((-
4 + x)^3*(-16*x^3 + 4*x^4))/E^6 + ((-4 + x)^2*(-8*x + 2*x^2 + 8*x^3 - 26*x^4 + 6*x^5))/E^4 + ((-4 + x)*(-16*x^
2 + 4*x^3 + 16*x^4 - 20*x^5 + 4*x^6))/E^2),x]

[Out]

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

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fricas [B]  time = 0.65, size = 281, normalized size = 8.52 \begin {gather*} -e^{\left (-\frac {x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} - {\left (x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x\right )} e^{\left (-\frac {x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}{x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}\right )} + 16 \, x}{x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x} + \frac {x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}{x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x-4)*exp(log(x-4)-2)^2+(6*x^2-16*x)*exp(log(x-4)-2)+3*x^3-14*x^2+8*x)*exp((-x*exp(log(x-4)-2)^2-
2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(log(x-4)
-2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(
log(x-4)-2)^4+(4*x^4-16*x^3)*exp(log(x-4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(log(x-4)-2)^2+(4*x^6-20*x^5+
16*x^4+4*x^3-16*x^2)*exp(log(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4),x, algorithm="fricas")

[Out]

-e^(-(x^3 - 8*x^2 + (x^3 - x^2)*e^4 + 2*(x^3 - 4*x^2)*e^2 - (x^3 - 8*x^2 + (x^3 - x^2 + 1)*e^4 + 2*(x^3 - 4*x^
2)*e^2 + 16*x)*e^(-(x^3 - 8*x^2 + (x^3 - x^2)*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)/(x^3 - 8*x^2 + (x^3 - x^2 + 1)
*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)) + 16*x)/(x^3 - 8*x^2 + (x^3 - x^2 + 1)*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x) +
(x^3 - 8*x^2 + (x^3 - x^2)*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)/(x^3 - 8*x^2 + (x^3 - x^2 + 1)*e^4 + 2*(x^3 - 4*
x^2)*e^2 + 16*x))

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giac [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(((3*x-4)*exp(log(x-4)-2)^2+(6*x^2-16*x)*exp(log(x-4)-2)+3*x^3-14*x^2+8*x)*exp((-x*exp(log(x-4)-2)^2-
2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(log(x-4)
-2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(
log(x-4)-2)^4+(4*x^4-16*x^3)*exp(log(x-4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(log(x-4)-2)^2+(4*x^6-20*x^5+
16*x^4+4*x^3-16*x^2)*exp(log(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 10.24, size = 86, normalized size = 2.61

method	result	size
risch	\(-{\mathrm e}^{{\mathrm e}^{-\frac {x \left ({\mathrm e}^{-4} x^{2}+2 x^{2} {\mathrm e}^{-2}-8 x \,{\mathrm e}^{-4}-8 \,{\mathrm e}^{-2} x +x^{2}+16 \,{\mathrm e}^{-4}-x \right )}{{\mathrm e}^{-4} x^{3}+2 x^{3} {\mathrm e}^{-2}-8 \,{\mathrm e}^{-4} x^{2}-8 x^{2} {\mathrm e}^{-2}+x^{3}+16 x \,{\mathrm e}^{-4}-x^{2}+1}}}\)	\(86\)
norman	\(\frac {\left (\left ({\mathrm e}^{4}+8 \,{\mathrm e}^{2}+8\right ) {\mathrm e}^{4} {\mathrm e}^{-2} x^{2} {\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}-{\mathrm e}^{2} {\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}-16 \,{\mathrm e}^{-2} {\mathrm e}^{4} x \,{\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}-{\mathrm e}^{-2} \left (1+{\mathrm e}^{4}+2 \,{\mathrm e}^{2}\right ) {\mathrm e}^{4} x^{3} {\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}\right ) {\mathrm e}^{-2}}{x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4}+2 x^{3} {\mathrm e}^{2}-8 x^{2} {\mathrm e}^{2}+x^{3}+{\mathrm e}^{4}-8 x^{2}+16 x}\)	\(388\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x-4)*exp(ln(x-4)-2)^2+(6*x^2-16*x)*exp(ln(x-4)-2)+3*x^3-14*x^2+8*x)*exp((-x*exp(ln(x-4)-2)^2-2*x^2*exp
(ln(x-4)-2)-x^3+x^2)/(x*exp(ln(x-4)-2)^2+2*x^2*exp(ln(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(ln(x-4)-2)^2-2*x^2*e
xp(ln(x-4)-2)-x^3+x^2)/(x*exp(ln(x-4)-2)^2+2*x^2*exp(ln(x-4)-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(ln(x-4)-2)^4+(4*
x^4-16*x^3)*exp(ln(x-4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(ln(x-4)-2)^2+(4*x^6-20*x^5+16*x^4+4*x^3-16*x^2
)*exp(ln(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4),x,method=_RETURNVERBOSE)

[Out]

-exp(exp(-x*(exp(-4)*x^2+2*x^2*exp(-2)-8*x*exp(-4)-8*exp(-2)*x+x^2+16*exp(-4)-x)/(exp(-4)*x^3+2*x^3*exp(-2)-8*
exp(-4)*x^2-8*x^2*exp(-2)+x^3+16*x*exp(-4)-x^2+1)))

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maxima [B]  time = 6.83, size = 947, normalized size = 28.70 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x-4)*exp(log(x-4)-2)^2+(6*x^2-16*x)*exp(log(x-4)-2)+3*x^3-14*x^2+8*x)*exp((-x*exp(log(x-4)-2)^2-
2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(log(x-4)
-2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(
log(x-4)-2)^4+(4*x^4-16*x^3)*exp(log(x-4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(log(x-4)-2)^2+(4*x^6-20*x^5+
16*x^4+4*x^3-16*x^2)*exp(log(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4),x, algorithm="maxima")

[Out]

-e^(e^(-x^2*e^8/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4
+ 2*e^2 + 1) + e^8 + 2*e^6 + e^4) - 10*x^2*e^6/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25
*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) - 25*x^2*e^4/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^
2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + x^2*e^4/(x^3
*(e^4 + 2*e^2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) - 24*x^2*e^2/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) -
x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 8*x^2*e^2/(x^3*(e^4
+ 2*e^2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) - 8*x^2/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 +
10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 8*x^2/(x^3*(e^4 + 2*e^2 + 1) -
x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) + 16*x*e^4/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25
*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 32*x*e^2/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2
+ 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 16*x/(x^3*(e^8
+ 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^
6 + e^4) - 16*x/(x^3*(e^4 + 2*e^2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) + e^8/(x^3*(e^8 + 4*e^6 + 6*e^4 +
4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 2*e^6/(
x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^
8 + 2*e^6 + e^4) + e^4/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*
x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) - e^4/(e^4 + 2*e^2 + 1) - 2*e^2/(e^4 + 2*e^2 + 1) - 1/(e^4 + 2*e^2 +
1)))

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mupad [B]  time = 5.87, size = 361, normalized size = 10.94 \begin {gather*} -{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^2}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {x^3}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {16\,x\,{\mathrm {e}}^{-4}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{-2}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {x^3\,{\mathrm {e}}^{-4}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{-2}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{-4}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(-(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^3)/(x*exp(2*log(x - 4) - 4) + 2*x
^2*exp(log(x - 4) - 2) - x^2 + x^3 + 1)))*exp(-(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^
3)/(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^3 + 1))*(8*x - exp(log(x - 4) - 2)*(16*x - 6
*x^2) - 14*x^2 + 3*x^3 + exp(2*log(x - 4) - 4)*(3*x - 4)))/(x - exp(4*log(x - 4) - 8)*(4*x^2 - x^3) - exp(3*lo
g(x - 4) - 6)*(16*x^3 - 4*x^4) + 8*x^2 - 10*x^3 - 2*x^4 + 9*x^5 - 6*x^6 + x^7 + exp(2*log(x - 4) - 4)*(2*x^2 -
8*x + 8*x^3 - 26*x^4 + 6*x^5) + exp(log(x - 4) - 2)*(4*x^3 - 16*x^2 + 16*x^4 - 20*x^5 + 4*x^6) - 4),x)

[Out]

-exp(exp(x^2/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*exp
(-x^3/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*exp(-(16*x
*exp(-4))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*exp(-(
2*x^3*exp(-2))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*e
xp(-(x^3*exp(-4))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1)
)*exp((8*x^2*exp(-2))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3
+ 1))*exp((8*x^2*exp(-4))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 +
x^3 + 1)))

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sympy [B]  time = 8.22, size = 63, normalized size = 1.91 \begin {gather*} - e^{e^{\frac {- x^{3} - \frac {2 x^{2} \left (x - 4\right )}{e^{2}} + x^{2} - \frac {x \left (x - 4\right )^{2}}{e^{4}}}{x^{3} + \frac {2 x^{2} \left (x - 4\right )}{e^{2}} - x^{2} + \frac {x \left (x - 4\right )^{2}}{e^{4}} + 1}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x-4)*exp(ln(x-4)-2)**2+(6*x**2-16*x)*exp(ln(x-4)-2)+3*x**3-14*x**2+8*x)*exp((-x*exp(ln(x-4)-2)**
2-2*x**2*exp(ln(x-4)-2)-x**3+x**2)/(x*exp(ln(x-4)-2)**2+2*x**2*exp(ln(x-4)-2)+x**3-x**2+1))*exp(exp((-x*exp(ln
(x-4)-2)**2-2*x**2*exp(ln(x-4)-2)-x**3+x**2)/(x*exp(ln(x-4)-2)**2+2*x**2*exp(ln(x-4)-2)+x**3-x**2+1)))/((x**3-
4*x**2)*exp(ln(x-4)-2)**4+(4*x**4-16*x**3)*exp(ln(x-4)-2)**3+(6*x**5-26*x**4+8*x**3+2*x**2-8*x)*exp(ln(x-4)-2)
**2+(4*x**6-20*x**5+16*x**4+4*x**3-16*x**2)*exp(ln(x-4)-2)+x**7-6*x**6+9*x**5-2*x**4-10*x**3+8*x**2+x-4),x)

[Out]

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

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