3.39.73 \(\int \frac {\log (x)+e^{e^{3 x}} (-2 e^5+(2-2 e^5+6 e^{5+3 x} x) \log (x)+(2-6 e^{3 x} x) \log ^2(x))+e^{e^{3 x}} (-e^5+(1-e^5+3 e^{5+3 x} x) \log (x)+(1-3 e^{3 x} x) \log ^2(x)) \log (-e^5+\log (x))+(2 e^5+(-2+2 e^5) \log (x)-2 \log ^2(x)+(e^5+(-1+e^5) \log (x)-\log ^2(x)) \log (-e^5+\log (x))) \log (2+\log (-e^5+\log (x)))}{e^{e^{3 x}} (2 e^5 x \log (x)-2 x \log ^2(x))+e^{e^{3 x}} (e^5 x \log (x)-x \log ^2(x)) \log (-e^5+\log (x))+(-2 e^5 x \log (x)+2 x \log ^2(x)+(-e^5 x \log (x)+x \log ^2(x)) \log (-e^5+\log (x))) \log (2+\log (-e^5+\log (x)))} \, dx\)

Optimal. Leaf size=31 \[ \log \left (\frac {e^{e^{3 x}}-\log \left (2+\log \left (-e^5+\log (x)\right )\right )}{x \log (x)}\right ) \]

________________________________________________________________________________________

Rubi [F]  time = 19.00, 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 {\log (x)+e^{e^{3 x}} \left (-2 e^5+\left (2-2 e^5+6 e^{5+3 x} x\right ) \log (x)+\left (2-6 e^{3 x} x\right ) \log ^2(x)\right )+e^{e^{3 x}} \left (-e^5+\left (1-e^5+3 e^{5+3 x} x\right ) \log (x)+\left (1-3 e^{3 x} x\right ) \log ^2(x)\right ) \log \left (-e^5+\log (x)\right )+\left (2 e^5+\left (-2+2 e^5\right ) \log (x)-2 \log ^2(x)+\left (e^5+\left (-1+e^5\right ) \log (x)-\log ^2(x)\right ) \log \left (-e^5+\log (x)\right )\right ) \log \left (2+\log \left (-e^5+\log (x)\right )\right )}{e^{e^{3 x}} \left (2 e^5 x \log (x)-2 x \log ^2(x)\right )+e^{e^{3 x}} \left (e^5 x \log (x)-x \log ^2(x)\right ) \log \left (-e^5+\log (x)\right )+\left (-2 e^5 x \log (x)+2 x \log ^2(x)+\left (-e^5 x \log (x)+x \log ^2(x)\right ) \log \left (-e^5+\log (x)\right )\right ) \log \left (2+\log \left (-e^5+\log (x)\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

3*Defer[Int][E^(E^(3*x) + 3*x)/(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]]), x] - 2*Defer[Int][E^E^(3*x)/(x*(2 +
Log[-E^5 + Log[x]])*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x] + Defer[Int][1/(x*(E^5 - Log[x])*(2 + Log[-
E^5 + Log[x]])*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x] - 2*Defer[Int][E^E^(3*x)/(x*Log[x]*(2 + Log[-E^5
+ Log[x]])*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x] - Defer[Int][(E^E^(3*x)*Log[-E^5 + Log[x]])/(x*(2 +
Log[-E^5 + Log[x]])*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x] - Defer[Int][(E^E^(3*x)*Log[-E^5 + Log[x]]
)/(x*Log[x]*(2 + Log[-E^5 + Log[x]])*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x] + Defer[Int][Log[2 + Log[-
E^5 + Log[x]]]/(x*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x] + Defer[Int][Log[2 + Log[-E^5 + Log[x]]]/(x*L
og[x]*(E^E^(3*x) - Log[2 + Log[-E^5 + Log[x]]])), x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.47, size = 33, normalized size = 1.06 \begin {gather*} -\log (x)-\log (\log (x))+\log \left (e^{e^{3 x}}-\log \left (2+\log \left (-e^5+\log (x)\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.93, size = 30, normalized size = 0.97 \begin {gather*} -\log \relax (x) + \log \left (-e^{\left (e^{\left (3 \, x\right )}\right )} + \log \left (\log \left (-e^{5} + \log \relax (x)\right ) + 2\right )\right ) - \log \left (\log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-log(x)^2+(exp(5)-1)*log(x)+exp(5))*log(log(x)-exp(5))-2*log(x)^2+(2*exp(5)-2)*log(x)+2*exp(5))*l
og(log(log(x)-exp(5))+2)+((-3*x*exp(3*x)+1)*log(x)^2+(3*x*exp(5)*exp(3*x)+1-exp(5))*log(x)-exp(5))*exp(exp(3*x
))*log(log(x)-exp(5))+((-6*x*exp(3*x)+2)*log(x)^2+(6*x*exp(5)*exp(3*x)-2*exp(5)+2)*log(x)-2*exp(5))*exp(exp(3*
x))+log(x))/(((x*log(x)^2-x*exp(5)*log(x))*log(log(x)-exp(5))+2*x*log(x)^2-2*x*exp(5)*log(x))*log(log(log(x)-e
xp(5))+2)+(-x*log(x)^2+x*exp(5)*log(x))*exp(exp(3*x))*log(log(x)-exp(5))+(-2*x*log(x)^2+2*x*exp(5)*log(x))*exp
(exp(3*x))),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [A]  time = 0.18, size = 41, normalized size = 1.32 \begin {gather*} -3 \, x + \log \left (-e^{\left (3 \, x\right )} \log \left (\log \left (-e^{5} + \log \relax (x)\right ) + 2\right ) + e^{\left (3 \, x + e^{\left (3 \, x\right )}\right )}\right ) - \log \relax (x) - \log \left (\log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-log(x)^2+(exp(5)-1)*log(x)+exp(5))*log(log(x)-exp(5))-2*log(x)^2+(2*exp(5)-2)*log(x)+2*exp(5))*l
og(log(log(x)-exp(5))+2)+((-3*x*exp(3*x)+1)*log(x)^2+(3*x*exp(5)*exp(3*x)+1-exp(5))*log(x)-exp(5))*exp(exp(3*x
))*log(log(x)-exp(5))+((-6*x*exp(3*x)+2)*log(x)^2+(6*x*exp(5)*exp(3*x)-2*exp(5)+2)*log(x)-2*exp(5))*exp(exp(3*
x))+log(x))/(((x*log(x)^2-x*exp(5)*log(x))*log(log(x)-exp(5))+2*x*log(x)^2-2*x*exp(5)*log(x))*log(log(log(x)-e
xp(5))+2)+(-x*log(x)^2+x*exp(5)*log(x))*exp(exp(3*x))*log(log(x)-exp(5))+(-2*x*log(x)^2+2*x*exp(5)*log(x))*exp
(exp(3*x))),x, algorithm="giac")

[Out]

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

________________________________________________________________________________________

maple [A]  time = 0.12, size = 31, normalized size = 1.00

method	result	size
risch	\(-\ln \relax (x )-\ln \left (\ln \relax (x )\right )+\ln \left (\ln \left (\ln \left (\ln \relax (x )-{\mathrm e}^{5}\right )+2\right )-{\mathrm e}^{{\mathrm e}^{3 x}}\right )\)	\(31\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-ln(x)^2+(exp(5)-1)*ln(x)+exp(5))*ln(ln(x)-exp(5))-2*ln(x)^2+(2*exp(5)-2)*ln(x)+2*exp(5))*ln(ln(ln(x)-e
xp(5))+2)+((-3*x*exp(3*x)+1)*ln(x)^2+(3*x*exp(5)*exp(3*x)+1-exp(5))*ln(x)-exp(5))*exp(exp(3*x))*ln(ln(x)-exp(5
))+((-6*x*exp(3*x)+2)*ln(x)^2+(6*x*exp(5)*exp(3*x)-2*exp(5)+2)*ln(x)-2*exp(5))*exp(exp(3*x))+ln(x))/(((x*ln(x)
^2-x*exp(5)*ln(x))*ln(ln(x)-exp(5))+2*x*ln(x)^2-2*x*exp(5)*ln(x))*ln(ln(ln(x)-exp(5))+2)+(-x*ln(x)^2+x*exp(5)*
ln(x))*exp(exp(3*x))*ln(ln(x)-exp(5))+(-2*x*ln(x)^2+2*x*exp(5)*ln(x))*exp(exp(3*x))),x,method=_RETURNVERBOSE)

[Out]

-ln(x)-ln(ln(x))+ln(ln(ln(ln(x)-exp(5))+2)-exp(exp(3*x)))

________________________________________________________________________________________

maxima [A]  time = 0.48, size = 30, normalized size = 0.97 \begin {gather*} -\log \relax (x) + \log \left (-e^{\left (e^{\left (3 \, x\right )}\right )} + \log \left (\log \left (-e^{5} + \log \relax (x)\right ) + 2\right )\right ) - \log \left (\log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-log(x)^2+(exp(5)-1)*log(x)+exp(5))*log(log(x)-exp(5))-2*log(x)^2+(2*exp(5)-2)*log(x)+2*exp(5))*l
og(log(log(x)-exp(5))+2)+((-3*x*exp(3*x)+1)*log(x)^2+(3*x*exp(5)*exp(3*x)+1-exp(5))*log(x)-exp(5))*exp(exp(3*x
))*log(log(x)-exp(5))+((-6*x*exp(3*x)+2)*log(x)^2+(6*x*exp(5)*exp(3*x)-2*exp(5)+2)*log(x)-2*exp(5))*exp(exp(3*
x))+log(x))/(((x*log(x)^2-x*exp(5)*log(x))*log(log(x)-exp(5))+2*x*log(x)^2-2*x*exp(5)*log(x))*log(log(log(x)-e
xp(5))+2)+(-x*log(x)^2+x*exp(5)*log(x))*exp(exp(3*x))*log(log(x)-exp(5))+(-2*x*log(x)^2+2*x*exp(5)*log(x))*exp
(exp(3*x))),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 3.10, size = 30, normalized size = 0.97 \begin {gather*} \ln \left (\ln \left (\ln \left (\ln \relax (x)-{\mathrm {e}}^5\right )+2\right )-{\mathrm {e}}^{{\mathrm {e}}^{3\,x}}\right )-\ln \left (\ln \relax (x)\right )-\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x) + log(log(log(x) - exp(5)) + 2)*(2*exp(5) - 2*log(x)^2 + log(log(x) - exp(5))*(exp(5) + log(x)*(e
xp(5) - 1) - log(x)^2) + log(x)*(2*exp(5) - 2)) - exp(exp(3*x))*(2*exp(5) + log(x)^2*(6*x*exp(3*x) - 2) - log(
x)*(6*x*exp(3*x)*exp(5) - 2*exp(5) + 2)) - exp(exp(3*x))*log(log(x) - exp(5))*(exp(5) + log(x)^2*(3*x*exp(3*x)
- 1) - log(x)*(3*x*exp(3*x)*exp(5) - exp(5) + 1)))/(exp(exp(3*x))*(2*x*log(x)^2 - 2*x*exp(5)*log(x)) - log(lo
g(log(x) - exp(5)) + 2)*(2*x*log(x)^2 + log(log(x) - exp(5))*(x*log(x)^2 - x*exp(5)*log(x)) - 2*x*exp(5)*log(x
)) + exp(exp(3*x))*log(log(x) - exp(5))*(x*log(x)^2 - x*exp(5)*log(x))),x)

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 11.97, size = 27, normalized size = 0.87 \begin {gather*} - \log {\relax (x )} + \log {\left (e^{e^{3 x}} - \log {\left (\log {\left (\log {\relax (x )} - e^{5} \right )} + 2 \right )} \right )} - \log {\left (\log {\relax (x )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-ln(x)**2+(exp(5)-1)*ln(x)+exp(5))*ln(ln(x)-exp(5))-2*ln(x)**2+(2*exp(5)-2)*ln(x)+2*exp(5))*ln(ln
(ln(x)-exp(5))+2)+((-3*x*exp(3*x)+1)*ln(x)**2+(3*x*exp(5)*exp(3*x)+1-exp(5))*ln(x)-exp(5))*exp(exp(3*x))*ln(ln
(x)-exp(5))+((-6*x*exp(3*x)+2)*ln(x)**2+(6*x*exp(5)*exp(3*x)-2*exp(5)+2)*ln(x)-2*exp(5))*exp(exp(3*x))+ln(x))/
(((x*ln(x)**2-x*exp(5)*ln(x))*ln(ln(x)-exp(5))+2*x*ln(x)**2-2*x*exp(5)*ln(x))*ln(ln(ln(x)-exp(5))+2)+(-x*ln(x)
**2+x*exp(5)*ln(x))*exp(exp(3*x))*ln(ln(x)-exp(5))+(-2*x*ln(x)**2+2*x*exp(5)*ln(x))*exp(exp(3*x))),x)

[Out]

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

________________________________________________________________________________________