3.12.24 \(\int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 (-2 e^3+2 x) \log (-2+x^2+\log (2-e^x))+2 \log ^2(-2+x^2+\log (2-e^x))} (16 x-16 x^2-8 x^3+e^3 (-16+16 x+8 x^2)+e^x (-4 x+8 x^2+4 x^3+e^3 (4-8 x-4 x^2))+(8 e^3-8 x+e^x (-4 e^3+4 x)) \log (2-e^x)+(16-16 x-8 x^2+e^x (-4+8 x+4 x^2)+(-8+4 e^x) \log (2-e^x)) \log (-2+x^2+\log (2-e^x)))}{4-2 x^2+e^x (-2+x^2)+(-2+e^x) \log (2-e^x)} \, dx\) [1124]

Optimal. Leaf size=27 \[ e^{2 \left (-e^3+x+\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )^2} \]

[Out]

exp((x-exp(3)+ln(ln(-exp(x)+2)+x^2-2))^2)^2

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Rubi [F]
time = 62.70, 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 (2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right ) \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2*E^6 - 4*E^3*x + 2*x^2 + 2*(-2*E^3 + 2*x)*Log[-2 + x^2 + Log[2 - E^x]] + 2*Log[-2 + x^2 + Log[2 - E^x
]]^2)*(16*x - 16*x^2 - 8*x^3 + E^3*(-16 + 16*x + 8*x^2) + E^x*(-4*x + 8*x^2 + 4*x^3 + E^3*(4 - 8*x - 4*x^2)) +
(8*E^3 - 8*x + E^x*(-4*E^3 + 4*x))*Log[2 - E^x] + (16 - 16*x - 8*x^2 + E^x*(-4 + 8*x + 4*x^2) + (-8 + 4*E^x)*
Log[2 - E^x])*Log[-2 + x^2 + Log[2 - E^x]]))/(4 - 2*x^2 + E^x*(-2 + x^2) + (-2 + E^x)*Log[2 - E^x]),x]

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (2 \left (-2+2 x+x^2\right )-e^x \left (-1+2 x+x^2\right )-\left (-2+e^x\right ) \log \left (2-e^x\right )\right ) \left (-e^3+x+\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{2-e^x} \, dx\\ &=4 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (2 \left (-2+2 x+x^2\right )-e^x \left (-1+2 x+x^2\right )-\left (-2+e^x\right ) \log \left (2-e^x\right )\right ) \left (-e^3+x+\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{2-e^x} \, dx\\ &=4 \int \left (-\frac {2 \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (e^3-x-\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{-2+e^x}+\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (-1+2 x+x^2+\log \left (2-e^x\right )\right ) \left (-e^3+x+\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \, dx\\ &=4 \int \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (-1+2 x+x^2+\log \left (2-e^x\right )\right ) \left (-e^3+x+\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right ) \, dx-8 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (e^3-x-\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{-2+e^x} \, dx\\ &=4 \int \left (-\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (e^3-x\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (-1+2 x+x^2+\log \left (2-e^x\right )\right )+\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (-1+2 x+x^2+\log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right ) \, dx-8 \int \left (\frac {\exp \left (3+2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}}{-2+e^x}-\frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) x \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}}{-2+e^x}-\frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )}{-2+e^x}\right ) \, dx\\ &=-\left (4 \int \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (e^3-x\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (-1+2 x+x^2+\log \left (2-e^x\right )\right ) \, dx\right )+4 \int \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \left (-1+2 x+x^2+\log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right ) \, dx-8 \int \frac {\exp \left (3+2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}}{-2+e^x} \, dx+8 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) x \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}}{-2+e^x} \, dx+8 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )}{-2+e^x} \, dx\\ &=-\left (4 \int \left (\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (e^3-x\right ) \left (-1+2 x+x^2\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}+\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (e^3-x\right ) \log \left (2-e^x\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}\right ) \, dx\right )+4 \int \left (-\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) x \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )+\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) x^2 \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )+\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \log \left (2-e^x\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right ) \, dx-8 \int \frac {\exp \left (3+2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}}{-2+e^x} \, dx+8 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) x \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x}}{-2+e^x} \, dx+8 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )\right ) \left (-2+x^2+\log \left (2-e^x\right )\right )^{-1-4 e^3+4 x} \log \left (-2+x^2+\log \left (2-e^x\right )\right )}{-2+e^x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.21, size = 54, normalized size = 2.00 \begin {gather*} e^{2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )} \left (-2+x^2+\log \left (2-e^x\right )\right )^{-4 e^3+4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2*E^6 - 4*E^3*x + 2*x^2 + 2*(-2*E^3 + 2*x)*Log[-2 + x^2 + Log[2 - E^x]] + 2*Log[-2 + x^2 + Log[2
- E^x]]^2)*(16*x - 16*x^2 - 8*x^3 + E^3*(-16 + 16*x + 8*x^2) + E^x*(-4*x + 8*x^2 + 4*x^3 + E^3*(4 - 8*x - 4*x
^2)) + (8*E^3 - 8*x + E^x*(-4*E^3 + 4*x))*Log[2 - E^x] + (16 - 16*x - 8*x^2 + E^x*(-4 + 8*x + 4*x^2) + (-8 + 4
*E^x)*Log[2 - E^x])*Log[-2 + x^2 + Log[2 - E^x]]))/(4 - 2*x^2 + E^x*(-2 + x^2) + (-2 + E^x)*Log[2 - E^x]),x]

[Out]

E^(2*((E^3 - x)^2 + Log[-2 + x^2 + Log[2 - E^x]]^2))*(-2 + x^2 + Log[2 - E^x])^(-4*E^3 + 4*x)

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(24)=48\).
time = 0.07, size = 58, normalized size = 2.15

method	result	size
risch	\(\left (\ln \left (-{\mathrm e}^{x}+2\right )+x^{2}-2\right )^{4 x -4 \,{\mathrm e}^{3}} {\mathrm e}^{2 \ln \left (\ln \left (-{\mathrm e}^{x}+2\right )+x^{2}-2\right )^{2}+2 \,{\mathrm e}^{6}-4 x \,{\mathrm e}^{3}+2 x^{2}}\)	\(58\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*exp(x)-8)*ln(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16)*ln(ln(-exp(x)+2)+x^2-2)+((4*x-4*exp(3))*e
xp(x)+8*exp(3)-8*x)*ln(-exp(x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp(3)-8*x^3-
16*x^2+16*x)*exp(ln(ln(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*ln(ln(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*exp(3)+x^2)^2/
((exp(x)-2)*ln(-exp(x)+2)+(x^2-2)*exp(x)-2*x^2+4),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (24) = 48\).
time = 0.50, size = 66, normalized size = 2.44 \begin {gather*} e^{\left (2 \, x^{2} - 4 \, x e^{3} + 4 \, x \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) - 4 \, e^{3} \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) + 2 \, \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right )^{2} + 2 \, e^{6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*exp(x)-8)*log(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16)*log(log(-exp(x)+2)+x^2-2)+((4*x-4*
exp(3))*exp(x)+8*exp(3)-8*x)*log(-exp(x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp
(3)-8*x^3-16*x^2+16*x)*exp(log(log(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*log(log(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*
exp(3)+x^2)^2/((exp(x)-2)*log(-exp(x)+2)+(x^2-2)*exp(x)-2*x^2+4),x, algorithm="maxima")

[Out]

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

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (24) = 48\).
time = 0.38, size = 54, normalized size = 2.00 \begin {gather*} e^{\left (2 \, x^{2} - 4 \, x e^{3} + 4 \, {\left (x - e^{3}\right )} \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) + 2 \, \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right )^{2} + 2 \, e^{6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*exp(x)-8)*log(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16)*log(log(-exp(x)+2)+x^2-2)+((4*x-4*
exp(3))*exp(x)+8*exp(3)-8*x)*log(-exp(x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp
(3)-8*x^3-16*x^2+16*x)*exp(log(log(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*log(log(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*
exp(3)+x^2)^2/((exp(x)-2)*log(-exp(x)+2)+(x^2-2)*exp(x)-2*x^2+4),x, algorithm="fricas")

[Out]

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

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Sympy [F(-1)] Timed out
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*exp(x)-8)*ln(-exp(x)+2)+(4*x**2+8*x-4)*exp(x)-8*x**2-16*x+16)*ln(ln(-exp(x)+2)+x**2-2)+((4*x-4*
exp(3))*exp(x)+8*exp(3)-8*x)*ln(-exp(x)+2)+((-4*x**2-8*x+4)*exp(3)+4*x**3+8*x**2-4*x)*exp(x)+(8*x**2+16*x-16)*
exp(3)-8*x**3-16*x**2+16*x)*exp(ln(ln(-exp(x)+2)+x**2-2)**2+(-2*exp(3)+2*x)*ln(ln(-exp(x)+2)+x**2-2)+exp(3)**2
-2*x*exp(3)+x**2)**2/((exp(x)-2)*ln(-exp(x)+2)+(x**2-2)*exp(x)-2*x**2+4),x)

[Out]

Timed out

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*exp(x)-8)*log(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16)*log(log(-exp(x)+2)+x^2-2)+((4*x-4*
exp(3))*exp(x)+8*exp(3)-8*x)*log(-exp(x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp
(3)-8*x^3-16*x^2+16*x)*exp(log(log(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*log(log(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*
exp(3)+x^2)^2/((exp(x)-2)*log(-exp(x)+2)+(x^2-2)*exp(x)-2*x^2+4),x, algorithm="giac")

[Out]

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

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Mupad [B]
time = 1.24, size = 57, normalized size = 2.11 \begin {gather*} {\mathrm {e}}^{2\,{\mathrm {e}}^6}\,{\mathrm {e}}^{2\,x^2}\,{\mathrm {e}}^{-4\,x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{2\,{\ln \left (\ln \left (2-{\mathrm {e}}^x\right )+x^2-2\right )}^2}\,{\left (\ln \left (2-{\mathrm {e}}^x\right )+x^2-2\right )}^{4\,x-4\,{\mathrm {e}}^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*exp(6) + 2*log(log(2 - exp(x)) + x^2 - 2)*(2*x - 2*exp(3)) + 2*log(log(2 - exp(x)) + x^2 - 2)^2 - 4
*x*exp(3) + 2*x^2)*(16*x - exp(x)*(4*x + exp(3)*(8*x + 4*x^2 - 4) - 8*x^2 - 4*x^3) + log(log(2 - exp(x)) + x^2
- 2)*(log(2 - exp(x))*(4*exp(x) - 8) - 16*x + exp(x)*(8*x + 4*x^2 - 4) - 8*x^2 + 16) + exp(3)*(16*x + 8*x^2 -
16) + log(2 - exp(x))*(8*exp(3) - 8*x + exp(x)*(4*x - 4*exp(3))) - 16*x^2 - 8*x^3))/(exp(x)*(x^2 - 2) + log(2
- exp(x))*(exp(x) - 2) - 2*x^2 + 4),x)

[Out]

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

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