3.64.55 \(\int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x (-78-87 x-30 x^2-3 x^3+(36+24 x+3 x^2) \log ^2(2))+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} (9-12 x-11 x^2-2 x^3+(-6+10 x+4 x^2) \log ^2(2)+(1-2 x) \log ^4(2)))}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx\)

Optimal. Leaf size=33 \[ x-x^2+3 e^{-\frac {e^x (5+x)}{3+x-\log ^2(2)}} (2+x) \]

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Rubi [F]  time = 127.96, 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 {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(27 + 18*x + 3*x^2 + (-18 - 6*x)*Log[2]^2 + 3*Log[2]^4 + E^x*(-78 - 87*x - 30*x^2 - 3*x^3 + (36 + 24*x + 3
*x^2)*Log[2]^2) + E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 - 12*x - 11*x^2 - 2*x^3 + (-6 + 10*x + 4*x^2)*Log[
2]^2 + (1 - 2*x)*Log[2]^4))/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 + 6*x + x^2 + (-6 - 2*x)*Log[2]^2 + Log
[2]^4)),x]

[Out]

-1/4*(1 - 2*x)^2 + 3*Defer[Int][E^(-((E^x*(-5 - x))/(-3 - x + Log[2]^2))), x] - 3*(4 + Log[2]^2)*Defer[Int][E^
(x - (E^x*(-5 - x))/(-3 - x + Log[2]^2)), x] - 3*Defer[Int][E^(x - (E^x*(-5 - x))/(-3 - x + Log[2]^2))*x, x] -
18*(3 - Log[2]^2)*Defer[Int][1/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(3 + x - Log[2]^2)^2), x] + 3*(3 - Log
[2]^2)^2*Defer[Int][1/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(3 + x - Log[2]^2)^2), x] + 3*(9 + Log[2]^4)*Def
er[Int][1/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(3 + x - Log[2]^2)^2), x] - 3*(2 - Log[2]^2 - Log[2]^4)*Defe
r[Int][E^(x - (E^x*(-5 - x))/(-3 - x + Log[2]^2))/(3 + x - Log[2]^2)^2, x] + 18*Defer[Int][1/(E^((E^x*(-5 - x)
)/(-3 - x + Log[2]^2))*(3 + x - Log[2]^2)), x] - 6*Log[2]^2*Defer[Int][1/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2
))*(3 + x - Log[2]^2)), x] - 6*(3 - Log[2]^2)*Defer[Int][1/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(3 + x - Lo
g[2]^2)), x] + 3*(4 - Log[2]^4)*Defer[Int][E^(x - (E^x*(-5 - x))/(-3 - x + Log[2]^2))/(3 + x - Log[2]^2), x] -
6*Log[2]^4*Defer[Int][1/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(-3 - x + Log[2]^2)^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (18 x+3 x^2+(-18-6 x) \log ^2(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+27 \left (1+\frac {\log ^4(2)}{9}\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{x^2+2 x \left (3-\log ^2(2)\right )+\left (-3+\log ^2(2)\right )^2} \, dx\\ &=\int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (18 x+3 x^2+(-18-6 x) \log ^2(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+27 \left (1+\frac {\log ^4(2)}{9}\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{\left (3+x-\log ^2(2)\right )^2} \, dx\\ &=\int \left (-\exp \left (\frac {e^x (5+x)}{3+x-\log ^2(2)}-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}\right ) (-1+2 x)+\frac {18 e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} x}{\left (3+x-\log ^2(2)\right )^2}+\frac {3 e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} x^2}{\left (3+x-\log ^2(2)\right )^2}-\frac {6 e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} (3+x) \log ^2(2)}{\left (3+x-\log ^2(2)\right )^2}+\frac {3 e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9+\log ^4(2)\right )}{\left (3+x-\log ^2(2)\right )^2}+\frac {3 e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} (2+x) \left (-13-x^2+6 \log ^2(2)-x \left (8-\log ^2(2)\right )\right )}{\left (3+x-\log ^2(2)\right )^2}\right ) \, dx\\ &=3 \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} x^2}{\left (3+x-\log ^2(2)\right )^2} \, dx+3 \int \frac {e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} (2+x) \left (-13-x^2+6 \log ^2(2)-x \left (8-\log ^2(2)\right )\right )}{\left (3+x-\log ^2(2)\right )^2} \, dx+18 \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} x}{\left (3+x-\log ^2(2)\right )^2} \, dx-\left (6 \log ^2(2)\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} (3+x)}{\left (3+x-\log ^2(2)\right )^2} \, dx+\left (3 \left (9+\log ^4(2)\right )\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (3+x-\log ^2(2)\right )^2} \, dx-\int \exp \left (\frac {e^x (5+x)}{3+x-\log ^2(2)}-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}\right ) (-1+2 x) \, dx\\ &=-\frac {1}{4} (1-2 x)^2+3 \int \left (e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}+\frac {2 e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (-3+\log ^2(2)\right )}{3+x-\log ^2(2)}+\frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (-3+\log ^2(2)\right )^2}{\left (3+x-\log ^2(2)\right )^2}\right ) \, dx+3 \int \left (-e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} x+e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (-4-\log ^2(2)\right )+\frac {e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (4-\log ^4(2)\right )}{3+x-\log ^2(2)}+\frac {e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (-2+\log ^2(2)+\log ^4(2)\right )}{\left (3+x-\log ^2(2)\right )^2}\right ) \, dx+18 \int \left (\frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{3+x-\log ^2(2)}+\frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (-3+\log ^2(2)\right )}{\left (3+x-\log ^2(2)\right )^2}\right ) \, dx-\left (6 \log ^2(2)\right ) \int \left (\frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{3+x-\log ^2(2)}+\frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \log ^2(2)}{\left (-3-x+\log ^2(2)\right )^2}\right ) \, dx+\left (3 \left (9+\log ^4(2)\right )\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (3+x-\log ^2(2)\right )^2} \, dx\\ &=-\frac {1}{4} (1-2 x)^2+3 \int e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \, dx-3 \int e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} x \, dx+18 \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{3+x-\log ^2(2)} \, dx-\left (6 \log ^2(2)\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{3+x-\log ^2(2)} \, dx-\left (6 \log ^4(2)\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (-3-x+\log ^2(2)\right )^2} \, dx-\left (6 \left (3-\log ^2(2)\right )\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{3+x-\log ^2(2)} \, dx-\left (18 \left (3-\log ^2(2)\right )\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (3+x-\log ^2(2)\right )^2} \, dx+\left (3 \left (3-\log ^2(2)\right )^2\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (3+x-\log ^2(2)\right )^2} \, dx-\left (3 \left (4+\log ^2(2)\right )\right ) \int e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \, dx+\left (3 \left (4-\log ^4(2)\right )\right ) \int \frac {e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{3+x-\log ^2(2)} \, dx-\left (3 \left (2-\log ^2(2)-\log ^4(2)\right )\right ) \int \frac {e^{x-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (3+x-\log ^2(2)\right )^2} \, dx+\left (3 \left (9+\log ^4(2)\right )\right ) \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}}}{\left (3+x-\log ^2(2)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.26, size = 34, normalized size = 1.03 \begin {gather*} x-x^2+e^{-\frac {e^x (5+x)}{3+x-\log ^2(2)}} (6+3 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(27 + 18*x + 3*x^2 + (-18 - 6*x)*Log[2]^2 + 3*Log[2]^4 + E^x*(-78 - 87*x - 30*x^2 - 3*x^3 + (36 + 24
*x + 3*x^2)*Log[2]^2) + E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 - 12*x - 11*x^2 - 2*x^3 + (-6 + 10*x + 4*x^2
)*Log[2]^2 + (1 - 2*x)*Log[2]^4))/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 + 6*x + x^2 + (-6 - 2*x)*Log[2]^2
+ Log[2]^4)),x]

[Out]

x - x^2 + (6 + 3*x)/E^((E^x*(5 + x))/(3 + x - Log[2]^2))

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fricas [A]  time = 0.71, size = 30, normalized size = 0.91 \begin {gather*} -x^{2} + 3 \, {\left (x + 2\right )} e^{\left (\frac {{\left (x + 5\right )} e^{x}}{\log \relax (2)^{2} - x - 3}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)*exp((-x-5)*exp(x)/(log(2)^2-3-x))+((
3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-87*x-78)*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-
2*x-6)*log(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x, algorithm="fricas")

[Out]

-x^2 + 3*(x + 2)*e^((x + 5)*e^x/(log(2)^2 - x - 3)) + x

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (3 \, \log \relax (2)^{4} - 6 \, {\left (x + 3\right )} \log \relax (2)^{2} + 3 \, x^{2} - 3 \, {\left (x^{3} - {\left (x^{2} + 8 \, x + 12\right )} \log \relax (2)^{2} + 10 \, x^{2} + 29 \, x + 26\right )} e^{x} - {\left ({\left (2 \, x - 1\right )} \log \relax (2)^{4} + 2 \, x^{3} - 2 \, {\left (2 \, x^{2} + 5 \, x - 3\right )} \log \relax (2)^{2} + 11 \, x^{2} + 12 \, x - 9\right )} e^{\left (-\frac {{\left (x + 5\right )} e^{x}}{\log \relax (2)^{2} - x - 3}\right )} + 18 \, x + 27\right )} e^{\left (\frac {{\left (x + 5\right )} e^{x}}{\log \relax (2)^{2} - x - 3}\right )}}{\log \relax (2)^{4} - 2 \, {\left (x + 3\right )} \log \relax (2)^{2} + x^{2} + 6 \, x + 9}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)*exp((-x-5)*exp(x)/(log(2)^2-3-x))+((
3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-87*x-78)*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-
2*x-6)*log(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x, algorithm="giac")

[Out]

integrate((3*log(2)^4 - 6*(x + 3)*log(2)^2 + 3*x^2 - 3*(x^3 - (x^2 + 8*x + 12)*log(2)^2 + 10*x^2 + 29*x + 26)*
e^x - ((2*x - 1)*log(2)^4 + 2*x^3 - 2*(2*x^2 + 5*x - 3)*log(2)^2 + 11*x^2 + 12*x - 9)*e^(-(x + 5)*e^x/(log(2)^
2 - x - 3)) + 18*x + 27)*e^((x + 5)*e^x/(log(2)^2 - x - 3))/(log(2)^4 - 2*(x + 3)*log(2)^2 + x^2 + 6*x + 9), x
)

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maple [A]  time = 0.68, size = 32, normalized size = 0.97

method	result	size
risch	\(-x^{2}+x +\left (6+3 x \right ) {\mathrm e}^{\frac {\left (5+x \right ) {\mathrm e}^{x}}{\ln \relax (2)^{2}-3-x}}\)	\(32\)
norman	\(\frac {\left (x^{3} {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \relax (2)^{2}-3-x}}+\left (-15+3 \ln \relax (2)^{2}\right ) x +\left (\ln \relax (2)^{4}-6 \ln \relax (2)^{2}+9\right ) {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \relax (2)^{2}-3-x}}+\left (2-\ln \relax (2)^{2}\right ) x^{2} {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \relax (2)^{2}-3-x}}-3 x^{2}+6 \ln \relax (2)^{2}-18\right ) {\mathrm e}^{-\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \relax (2)^{2}-3-x}}}{\ln \relax (2)^{2}-3-x}\)	\(147\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((1-2*x)*ln(2)^4+(4*x^2+10*x-6)*ln(2)^2-2*x^3-11*x^2-12*x+9)*exp((-x-5)*exp(x)/(ln(2)^2-3-x))+((3*x^2+24*
x+36)*ln(2)^2-3*x^3-30*x^2-87*x-78)*exp(x)+3*ln(2)^4+(-6*x-18)*ln(2)^2+3*x^2+18*x+27)/(ln(2)^4+(-2*x-6)*ln(2)^
2+x^2+6*x+9)/exp((-x-5)*exp(x)/(ln(2)^2-3-x)),x,method=_RETURNVERBOSE)

[Out]

-x^2+x+(6+3*x)*exp((5+x)*exp(x)/(ln(2)^2-3-x))

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maxima [B]  time = 0.63, size = 357, normalized size = 10.82 \begin {gather*} -2 \, {\left (\frac {\log \relax (2)^{2} - 3}{\log \relax (2)^{2} - x - 3} + \log \left (-\log \relax (2)^{2} + x + 3\right )\right )} \log \relax (2)^{4} + 4 \, {\left (2 \, {\left (\log \relax (2)^{2} - 3\right )} \log \left (-\log \relax (2)^{2} + x + 3\right ) + x + \frac {\log \relax (2)^{4} - 6 \, \log \relax (2)^{2} + 9}{\log \relax (2)^{2} - x - 3}\right )} \log \relax (2)^{2} + 10 \, {\left (\frac {\log \relax (2)^{2} - 3}{\log \relax (2)^{2} - x - 3} + \log \left (-\log \relax (2)^{2} + x + 3\right )\right )} \log \relax (2)^{2} + \frac {\log \relax (2)^{4}}{\log \relax (2)^{2} - x - 3} - 4 \, {\left (\log \relax (2)^{2} - 3\right )} x - x^{2} + 3 \, {\left (x + 2\right )} e^{\left (\frac {e^{x} \log \relax (2)^{2}}{\log \relax (2)^{2} - x - 3} + \frac {2 \, e^{x}}{\log \relax (2)^{2} - x - 3} - e^{x}\right )} - 6 \, {\left (\log \relax (2)^{4} - 6 \, \log \relax (2)^{2} + 9\right )} \log \left (-\log \relax (2)^{2} + x + 3\right ) - 22 \, {\left (\log \relax (2)^{2} - 3\right )} \log \left (-\log \relax (2)^{2} + x + 3\right ) - 11 \, x - \frac {6 \, \log \relax (2)^{2}}{\log \relax (2)^{2} - x - 3} - \frac {2 \, {\left (\log \relax (2)^{6} - 9 \, \log \relax (2)^{4} + 27 \, \log \relax (2)^{2} - 27\right )}}{\log \relax (2)^{2} - x - 3} - \frac {11 \, {\left (\log \relax (2)^{4} - 6 \, \log \relax (2)^{2} + 9\right )}}{\log \relax (2)^{2} - x - 3} - \frac {12 \, {\left (\log \relax (2)^{2} - 3\right )}}{\log \relax (2)^{2} - x - 3} + \frac {9}{\log \relax (2)^{2} - x - 3} - 12 \, \log \left (-\log \relax (2)^{2} + x + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)*exp((-x-5)*exp(x)/(log(2)^2-3-x))+((
3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-87*x-78)*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-
2*x-6)*log(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x, algorithm="maxima")

[Out]

-2*((log(2)^2 - 3)/(log(2)^2 - x - 3) + log(-log(2)^2 + x + 3))*log(2)^4 + 4*(2*(log(2)^2 - 3)*log(-log(2)^2 +
x + 3) + x + (log(2)^4 - 6*log(2)^2 + 9)/(log(2)^2 - x - 3))*log(2)^2 + 10*((log(2)^2 - 3)/(log(2)^2 - x - 3)
+ log(-log(2)^2 + x + 3))*log(2)^2 + log(2)^4/(log(2)^2 - x - 3) - 4*(log(2)^2 - 3)*x - x^2 + 3*(x + 2)*e^(e^
x*log(2)^2/(log(2)^2 - x - 3) + 2*e^x/(log(2)^2 - x - 3) - e^x) - 6*(log(2)^4 - 6*log(2)^2 + 9)*log(-log(2)^2
+ x + 3) - 22*(log(2)^2 - 3)*log(-log(2)^2 + x + 3) - 11*x - 6*log(2)^2/(log(2)^2 - x - 3) - 2*(log(2)^6 - 9*l
og(2)^4 + 27*log(2)^2 - 27)/(log(2)^2 - x - 3) - 11*(log(2)^4 - 6*log(2)^2 + 9)/(log(2)^2 - x - 3) - 12*(log(2
)^2 - 3)/(log(2)^2 - x - 3) + 9/(log(2)^2 - x - 3) - 12*log(-log(2)^2 + x + 3)

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mupad [B]  time = 4.75, size = 46, normalized size = 1.39 \begin {gather*} x+{\mathrm {e}}^{-\frac {5\,{\mathrm {e}}^x}{x-{\ln \relax (2)}^2+3}-\frac {x\,{\mathrm {e}}^x}{x-{\ln \relax (2)}^2+3}}\,\left (3\,x+6\right )-x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(exp(x)*(x + 5))/(x - log(2)^2 + 3))*(18*x - log(2)^2*(6*x + 18) - exp(x)*(87*x - log(2)^2*(24*x + 3
*x^2 + 36) + 30*x^2 + 3*x^3 + 78) + 3*log(2)^4 + 3*x^2 - exp((exp(x)*(x + 5))/(x - log(2)^2 + 3))*(12*x + log(
2)^4*(2*x - 1) - log(2)^2*(10*x + 4*x^2 - 6) + 11*x^2 + 2*x^3 - 9) + 27))/(6*x - log(2)^2*(2*x + 6) + log(2)^4
+ x^2 + 9),x)

[Out]

x + exp(- (5*exp(x))/(x - log(2)^2 + 3) - (x*exp(x))/(x - log(2)^2 + 3))*(3*x + 6) - x^2

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sympy [A]  time = 31.35, size = 27, normalized size = 0.82 \begin {gather*} - x^{2} + x + \left (3 x + 6\right ) e^{- \frac {\left (- x - 5\right ) e^{x}}{- x - 3 + \log {\relax (2 )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-2*x)*ln(2)**4+(4*x**2+10*x-6)*ln(2)**2-2*x**3-11*x**2-12*x+9)*exp((-x-5)*exp(x)/(ln(2)**2-3-x))
+((3*x**2+24*x+36)*ln(2)**2-3*x**3-30*x**2-87*x-78)*exp(x)+3*ln(2)**4+(-6*x-18)*ln(2)**2+3*x**2+18*x+27)/(ln(2
)**4+(-2*x-6)*ln(2)**2+x**2+6*x+9)/exp((-x-5)*exp(x)/(ln(2)**2-3-x)),x)

[Out]

-x**2 + x + (3*x + 6)*exp(-(-x - 5)*exp(x)/(-x - 3 + log(2)**2))

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