3.85.27 \(\int \frac {(2 e^{e^x+x} x^4+12 x^5+(-12 x^5+6 x^6+e^{e^x} (-4 x^3+2 x^4)) \log (\frac {1}{3} (e^{e^x}+3 x^2)) \log (\log (\frac {1}{3} (e^{e^x}+3 x^2)))) \log (\frac {e^{-x} (x^2-5 e^x \log (\log (\frac {1}{3} (e^{e^x}+3 x^2))))}{\log (\log (\frac {1}{3} (e^{e^x}+3 x^2)))})+((-2 e^{e^x} x^3-6 x^5) \log (\frac {1}{3} (e^{e^x}+3 x^2)) \log (\log (\frac {1}{3} (e^{e^x}+3 x^2)))+(10 e^{e^x+x} x+30 e^x x^3) \log (\frac {1}{3} (e^{e^x}+3 x^2)) \log ^2(\log (\frac {1}{3} (e^{e^x}+3 x^2)))) \log ^2(\frac {e^{-x} (x^2-5 e^x \log (\log (\frac {1}{3} (e^{e^x}+3 x^2))))}{\log (\log (\frac {1}{3} (e^{e^x}+3 x^2)))})}{(-e^{e^x} x^2-3 x^4) \log (\frac {1}{3} (e^{e^x}+3 x^2)) \log (\log (\frac {1}{3} (e^{e^x}+3 x^2)))+(5 e^{e^x+x}+15 e^x x^2) \log (\frac {1}{3} (e^{e^x}+3 x^2)) \log ^2(\log (\frac {1}{3} (e^{e^x}+3 x^2)))} \, dx\)

Optimal. Leaf size=35 \[ x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \]

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Rubi [F]  time = 31.30, 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 {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((2*E^(E^x + x)*x^4 + 12*x^5 + (-12*x^5 + 6*x^6 + E^E^x*(-4*x^3 + 2*x^4))*Log[(E^E^x + 3*x^2)/3]*Log[Log[(
E^E^x + 3*x^2)/3]])*Log[(x^2 - 5*E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^E^x + 3*x^2)/3]])] + ((-2*E^
E^x*x^3 - 6*x^5)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]] + (10*E^(E^x + x)*x + 30*E^x*x^3)*Log[(E^E
^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]]^2)*Log[(x^2 - 5*E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^E^
x + 3*x^2)/3]])]^2)/((-(E^E^x*x^2) - 3*x^4)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]] + (5*E^(E^x + x
) + 15*E^x*x^2)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]]^2),x]

[Out]

4*Defer[Int][(E^E^x*x^3*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])])/((E^E^x + 3*x^2)*(x^2 - 5*E^x*Log[Log[E^E
^x/3 + x^2]])), x] - 2*Defer[Int][(E^E^x*x^4*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])])/((E^E^x + 3*x^2)*(x^
2 - 5*E^x*Log[Log[E^E^x/3 + x^2]])), x] + 12*Defer[Int][(x^5*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])])/((E^
E^x + 3*x^2)*(x^2 - 5*E^x*Log[Log[E^E^x/3 + x^2]])), x] - 6*Defer[Int][(x^6*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3
+ x^2]])])/((E^E^x + 3*x^2)*(x^2 - 5*E^x*Log[Log[E^E^x/3 + x^2]])), x] + (2*Defer[Int][(x^4*Log[-5 + x^2/(E^x*
Log[Log[E^E^x/3 + x^2]])])/(Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]]^2), x])/5 + (6*Defer[Int][(x^6*
Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])])/((-E^E^x - 3*x^2)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/
3]]^2), x])/5 + (2*Defer[Int][(E^E^x*x^6*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])])/((-E^E^x - 3*x^2)*Log[(E
^E^x + 3*x^2)/3]*(x^2 - 5*E^x*Log[Log[E^E^x/3 + x^2]])*Log[Log[(E^E^x + 3*x^2)/3]]^2), x])/5 + 12*Defer[Int][(
x^5*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])])/((-E^E^x - 3*x^2)*Log[(E^E^x + 3*x^2)/3]*(x^2 - 5*E^x*Log[Log
[E^E^x/3 + x^2]])*Log[Log[(E^E^x + 3*x^2)/3]]), x] + 2*Defer[Int][x*Log[-5 + x^2/(E^x*Log[Log[E^E^x/3 + x^2]])
]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (-x^3 \left (e^{e^x+x}+6 x\right )-\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \left ((-2+x) x^2-\left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx\\ &=2 \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (-x^3 \left (e^{e^x+x}+6 x\right )-\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \left ((-2+x) x^2-\left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx\\ &=2 \int \left (\frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+10 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 e^{e^x} x \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+30 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-15 x^3 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{5 \left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}+\frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (e^{e^x} x^3+5 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )+15 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{5 \left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right ) \, dx\\ &=\frac {2}{5} \int \frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+10 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 e^{e^x} x \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+30 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-15 x^3 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (e^{e^x} x^3+5 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )+15 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx\\ &=\frac {2}{5} \int \frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 (-2+x) \left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (\frac {e^{e^x} x^3}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}+5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.38, size = 35, normalized size = 1.00 \begin {gather*} x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((2*E^(E^x + x)*x^4 + 12*x^5 + (-12*x^5 + 6*x^6 + E^E^x*(-4*x^3 + 2*x^4))*Log[(E^E^x + 3*x^2)/3]*Log
[Log[(E^E^x + 3*x^2)/3]])*Log[(x^2 - 5*E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^E^x + 3*x^2)/3]])] + (
(-2*E^E^x*x^3 - 6*x^5)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]] + (10*E^(E^x + x)*x + 30*E^x*x^3)*Lo
g[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]]^2)*Log[(x^2 - 5*E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log
[(E^E^x + 3*x^2)/3]])]^2)/((-(E^E^x*x^2) - 3*x^4)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]] + (5*E^(E
^x + x) + 15*E^x*x^2)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]]^2),x]

[Out]

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

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fricas [B]  time = 0.75, size = 64, normalized size = 1.83 \begin {gather*} x^{2} \log \left (\frac {{\left (x^{2} - 5 \, e^{x} \log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )} e^{\left (-x\right )}}{\log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))^2+(
-2*x^3*exp(exp(x))-6*x^5)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2)))*log((-5*exp(x)*log(log(1/3*e
xp(exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3)*exp(exp(x))+6*x^6-12*x^5)*log(1/
3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*log((-5*exp(x)*log(log(1/3*e
xp(exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(exp(x))+15*exp(x)*x^2)*log(1/3*exp
(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))^2+(-exp(exp(x))*x^2-3*x^4)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*ex
p(exp(x))+x^2))),x, algorithm="fricas")

[Out]

x^2*log((x^2 - 5*e^x*log(log(1/3*(3*x^2*e^x + e^(x + e^x))*e^(-x))))*e^(-x)/log(log(1/3*(3*x^2*e^x + e^(x + e^
x))*e^(-x))))^2

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giac [B]  time = 0.56, size = 211, normalized size = 6.03 \begin {gather*} x^{4} - 2 \, x^{3} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) - 2 \, x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) \log \left (\log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))^2+(
-2*x^3*exp(exp(x))-6*x^5)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2)))*log((-5*exp(x)*log(log(1/3*e
xp(exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3)*exp(exp(x))+6*x^6-12*x^5)*log(1/
3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*log((-5*exp(x)*log(log(1/3*e
xp(exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(exp(x))+15*exp(x)*x^2)*log(1/3*exp
(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))^2+(-exp(exp(x))*x^2-3*x^4)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*ex
p(exp(x))+x^2))),x, algorithm="giac")

[Out]

x^4 - 2*x^3*log(x^2 - 5*e^x*log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x)))) + x^2*log(x^2 - 5*e^x*log(-l
og(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x))))^2 + 2*x^3*log(log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-
x)))) - 2*x^2*log(x^2 - 5*e^x*log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x))))*log(log(-log(3) + log((3*x
^2*e^x + e^(x + e^x))*e^(-x)))) + x^2*log(log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x))))^2

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maple [C]  time = 1.36, size = 5397, normalized size = 154.20

method	result	size
risch	\(\text {Expression too large to display}\)	\(5397\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*ln(1/3*exp(exp(x))+x^2)*ln(ln(1/3*exp(exp(x))+x^2))^2+(-2*x^3*ex
p(exp(x))-6*x^5)*ln(1/3*exp(exp(x))+x^2)*ln(ln(1/3*exp(exp(x))+x^2)))*ln((-5*exp(x)*ln(ln(1/3*exp(exp(x))+x^2)
)+x^2)/exp(x)/ln(ln(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3)*exp(exp(x))+6*x^6-12*x^5)*ln(1/3*exp(exp(x))+x^2)
*ln(ln(1/3*exp(exp(x))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*ln((-5*exp(x)*ln(ln(1/3*exp(exp(x))+x^2))+x^2)/e
xp(x)/ln(ln(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(exp(x))+15*exp(x)*x^2)*ln(1/3*exp(exp(x))+x^2)*ln(ln(1/3*ex
p(exp(x))+x^2))^2+(-exp(exp(x))*x^2-3*x^4)*ln(1/3*exp(exp(x))+x^2)*ln(ln(1/3*exp(exp(x))+x^2))),x,method=_RETU
RNVERBOSE)

[Out]

result too large to display

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maxima [B]  time = 1.29, size = 132, normalized size = 3.77 \begin {gather*} x^{4} + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} - 2 \, {\left (x^{3} + x^{2} \log \left (\log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )\right )} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))^2+(
-2*x^3*exp(exp(x))-6*x^5)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2)))*log((-5*exp(x)*log(log(1/3*e
xp(exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3)*exp(exp(x))+6*x^6-12*x^5)*log(1/
3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*log((-5*exp(x)*log(log(1/3*e
xp(exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(exp(x))+15*exp(x)*x^2)*log(1/3*exp
(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2))^2+(-exp(exp(x))*x^2-3*x^4)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*ex
p(exp(x))+x^2))),x, algorithm="maxima")

[Out]

x^4 + x^2*log(x^2 - 5*e^x*log(-log(3) + log(3*x^2 + e^(e^x))))^2 + 2*x^3*log(log(-log(3) + log(3*x^2 + e^(e^x)
))) + x^2*log(log(-log(3) + log(3*x^2 + e^(e^x))))^2 - 2*(x^3 + x^2*log(log(-log(3) + log(3*x^2 + e^(e^x)))))*
log(x^2 - 5*e^x*log(-log(3) + log(3*x^2 + e^(e^x))))

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mupad [B]  time = 6.20, size = 45, normalized size = 1.29 \begin {gather*} x^2\,{\ln \left (-\frac {5\,\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )-x^2\,{\mathrm {e}}^{-x}}{\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )}\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log((exp(-x)*(x^2 - 5*exp(x)*log(log(exp(exp(x))/3 + x^2))))/log(log(exp(exp(x))/3 + x^2)))*(12*x^5 + 2*
x^4*exp(exp(x))*exp(x) - log(exp(exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))*(exp(exp(x))*(4*x^3 - 2*x^4) +
12*x^5 - 6*x^6)) + log((exp(-x)*(x^2 - 5*exp(x)*log(log(exp(exp(x))/3 + x^2))))/log(log(exp(exp(x))/3 + x^2))
)^2*(log(exp(exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))^2*(30*x^3*exp(x) + 10*x*exp(exp(x))*exp(x)) - log(
exp(exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))*(2*x^3*exp(exp(x)) + 6*x^5)))/(log(exp(exp(x))/3 + x^2)*log
(log(exp(exp(x))/3 + x^2))*(x^2*exp(exp(x)) + 3*x^4) - log(exp(exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))^
2*(15*x^2*exp(x) + 5*exp(exp(x))*exp(x))),x)

[Out]

x^2*log(-(5*log(log(exp(exp(x))/3 + x^2)) - x^2*exp(-x))/log(log(exp(exp(x))/3 + x^2)))^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((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x**3)*ln(1/3*exp(exp(x))+x**2)*ln(ln(1/3*exp(exp(x))+x**2))**2+
(-2*x**3*exp(exp(x))-6*x**5)*ln(1/3*exp(exp(x))+x**2)*ln(ln(1/3*exp(exp(x))+x**2)))*ln((-5*exp(x)*ln(ln(1/3*ex
p(exp(x))+x**2))+x**2)/exp(x)/ln(ln(1/3*exp(exp(x))+x**2)))**2+(((2*x**4-4*x**3)*exp(exp(x))+6*x**6-12*x**5)*l
n(1/3*exp(exp(x))+x**2)*ln(ln(1/3*exp(exp(x))+x**2))+2*x**4*exp(x)*exp(exp(x))+12*x**5)*ln((-5*exp(x)*ln(ln(1/
3*exp(exp(x))+x**2))+x**2)/exp(x)/ln(ln(1/3*exp(exp(x))+x**2))))/((5*exp(x)*exp(exp(x))+15*exp(x)*x**2)*ln(1/3
*exp(exp(x))+x**2)*ln(ln(1/3*exp(exp(x))+x**2))**2+(-exp(exp(x))*x**2-3*x**4)*ln(1/3*exp(exp(x))+x**2)*ln(ln(1
/3*exp(exp(x))+x**2))),x)

[Out]

Timed out

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