3.37.35 \(\int \frac {-108 x^2+e^{\frac {e^x}{x}} (e^x (162-162 x)-162 x) \log (x)+(108 x^2-486 x^3) \log (x)+(36 x+(-36 x+216 x^2) \log (x)) \log (\frac {x}{2 \log (x)})-18 x \log (x) \log ^2(\frac {x}{2 \log (x)})}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+(-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)) \log (\frac {x}{2 \log (x)})+(18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)) \log ^2(\frac {x}{2 \log (x)})-12 x^4 \log (x) \log ^3(\frac {x}{2 \log (x)})+x^3 \log (x) \log ^4(\frac {x}{2 \log (x)})} \, dx\)

Optimal. Leaf size=35 \[ \frac {2}{x \left (e^{\frac {e^x}{x}}+\left (x-\frac {1}{3} \log \left (\frac {x}{2 \log (x)}\right )\right )^2\right )} \]

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Rubi [A]  time = 3.63, antiderivative size = 48, normalized size of antiderivative = 1.37, number of steps used = 3, number of rules used = 3, integrand size = 242, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {6688, 12, 6687} \begin {gather*} \frac {18}{x \left (9 \left (x^2+e^{\frac {e^x}{x}}\right )+\log ^2\left (\frac {x}{2 \log (x)}\right )-6 x \log \left (\frac {x}{2 \log (x)}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-108*x^2 + E^(E^x/x)*(E^x*(162 - 162*x) - 162*x)*Log[x] + (108*x^2 - 486*x^3)*Log[x] + (36*x + (-36*x + 2
16*x^2)*Log[x])*Log[x/(2*Log[x])] - 18*x*Log[x]*Log[x/(2*Log[x])]^2)/(81*E^((2*E^x)/x)*x^3*Log[x] + 162*E^(E^x
/x)*x^5*Log[x] + 81*x^7*Log[x] + (-108*E^(E^x/x)*x^4*Log[x] - 108*x^6*Log[x])*Log[x/(2*Log[x])] + (18*E^(E^x/x
)*x^3*Log[x] + 54*x^5*Log[x])*Log[x/(2*Log[x])]^2 - 12*x^4*Log[x]*Log[x/(2*Log[x])]^3 + x^3*Log[x]*Log[x/(2*Lo
g[x])]^4),x]

[Out]

18/(x*(9*(E^(E^x/x) + x^2) - 6*x*Log[x/(2*Log[x])] + Log[x/(2*Log[x])]^2))

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6687

Int[(u_)*(y_)^(m_.)*(z_)^(n_.), x_Symbol] :> With[{q = DerivativeDivides[y*z, u*z^(n - m), x]}, Simp[(q*y^(m +
1)*z^(m + 1))/(m + 1), x] /;  !FalseQ[q]] /; FreeQ[{m, n}, x] && NeQ[m, -1]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18 \left (-2 x \left (3 x-\log \left (\frac {x}{2 \log (x)}\right )\right )-\log (x) \left (9 e^{\frac {e^x}{x}+x} (-1+x)+9 e^{\frac {e^x}{x}} x+3 x^2 (-2+9 x)+2 (1-6 x) x \log \left (\frac {x}{2 \log (x)}\right )+x \log ^2\left (\frac {x}{2 \log (x)}\right )\right )\right )}{x^3 \log (x) \left (9 \left (e^{\frac {e^x}{x}}+x^2\right )-6 x \log \left (\frac {x}{2 \log (x)}\right )+\log ^2\left (\frac {x}{2 \log (x)}\right )\right )^2} \, dx\\ &=18 \int \frac {-2 x \left (3 x-\log \left (\frac {x}{2 \log (x)}\right )\right )-\log (x) \left (9 e^{\frac {e^x}{x}+x} (-1+x)+9 e^{\frac {e^x}{x}} x+3 x^2 (-2+9 x)+2 (1-6 x) x \log \left (\frac {x}{2 \log (x)}\right )+x \log ^2\left (\frac {x}{2 \log (x)}\right )\right )}{x^3 \log (x) \left (9 \left (e^{\frac {e^x}{x}}+x^2\right )-6 x \log \left (\frac {x}{2 \log (x)}\right )+\log ^2\left (\frac {x}{2 \log (x)}\right )\right )^2} \, dx\\ &=\frac {18}{x \left (9 \left (e^{\frac {e^x}{x}}+x^2\right )-6 x \log \left (\frac {x}{2 \log (x)}\right )+\log ^2\left (\frac {x}{2 \log (x)}\right )\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 49, normalized size = 1.40 \begin {gather*} \frac {18}{x \left (9 e^{\frac {e^x}{x}}+9 x^2-6 x \log \left (\frac {x}{2 \log (x)}\right )+\log ^2\left (\frac {x}{2 \log (x)}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-108*x^2 + E^(E^x/x)*(E^x*(162 - 162*x) - 162*x)*Log[x] + (108*x^2 - 486*x^3)*Log[x] + (36*x + (-36
*x + 216*x^2)*Log[x])*Log[x/(2*Log[x])] - 18*x*Log[x]*Log[x/(2*Log[x])]^2)/(81*E^((2*E^x)/x)*x^3*Log[x] + 162*
E^(E^x/x)*x^5*Log[x] + 81*x^7*Log[x] + (-108*E^(E^x/x)*x^4*Log[x] - 108*x^6*Log[x])*Log[x/(2*Log[x])] + (18*E^
(E^x/x)*x^3*Log[x] + 54*x^5*Log[x])*Log[x/(2*Log[x])]^2 - 12*x^4*Log[x]*Log[x/(2*Log[x])]^3 + x^3*Log[x]*Log[x
/(2*Log[x])]^4),x]

[Out]

18/(x*(9*E^(E^x/x) + 9*x^2 - 6*x*Log[x/(2*Log[x])] + Log[x/(2*Log[x])]^2))

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fricas [A]  time = 0.76, size = 45, normalized size = 1.29 \begin {gather*} \frac {18}{9 \, x^{3} - 6 \, x^{2} \log \left (\frac {x}{2 \, \log \relax (x)}\right ) + x \log \left (\frac {x}{2 \, \log \relax (x)}\right )^{2} + 9 \, x e^{\left (\frac {e^{x}}{x}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x*log(x)*log(1/2*x/log(x))^2+((216*x^2-36*x)*log(x)+36*x)*log(1/2*x/log(x))+((-162*x+162)*exp(x
)-162*x)*log(x)*exp(exp(x)/x)+(-486*x^3+108*x^2)*log(x)-108*x^2)/(x^3*log(x)*log(1/2*x/log(x))^4-12*x^4*log(x)
*log(1/2*x/log(x))^3+(18*x^3*log(x)*exp(exp(x)/x)+54*x^5*log(x))*log(1/2*x/log(x))^2+(-108*x^4*log(x)*exp(exp(
x)/x)-108*x^6*log(x))*log(1/2*x/log(x))+81*x^3*log(x)*exp(exp(x)/x)^2+162*x^5*log(x)*exp(exp(x)/x)+81*x^7*log(
x)),x, algorithm="fricas")

[Out]

18/(9*x^3 - 6*x^2*log(1/2*x/log(x)) + x*log(1/2*x/log(x))^2 + 9*x*e^(e^x/x))

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giac [B]  time = 1.32, size = 7627, normalized size = 217.91 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x*log(x)*log(1/2*x/log(x))^2+((216*x^2-36*x)*log(x)+36*x)*log(1/2*x/log(x))+((-162*x+162)*exp(x
)-162*x)*log(x)*exp(exp(x)/x)+(-486*x^3+108*x^2)*log(x)-108*x^2)/(x^3*log(x)*log(1/2*x/log(x))^4-12*x^4*log(x)
*log(1/2*x/log(x))^3+(18*x^3*log(x)*exp(exp(x)/x)+54*x^5*log(x))*log(1/2*x/log(x))^2+(-108*x^4*log(x)*exp(exp(
x)/x)-108*x^6*log(x))*log(1/2*x/log(x))+81*x^3*log(x)*exp(exp(x)/x)^2+162*x^5*log(x)*exp(exp(x)/x)+81*x^7*log(
x)),x, algorithm="giac")

[Out]

18*(27*x^4*e^(2*x)*log(x) - 54*x^4*e^x*log(x) + 27*x^3*e^(2*x)*log(2)*log(x) - 36*x^3*e^x*log(2)*log(x) + 9*x^
2*e^(2*x)*log(2)^2*log(x) - 6*x^2*e^x*log(2)^2*log(x) + x*e^(2*x)*log(2)^3*log(x) - 27*x^3*e^(2*x)*log(x)^2 +
36*x^3*e^x*log(x)^2 - 18*x^2*e^(2*x)*log(2)*log(x)^2 + 12*x^2*e^x*log(2)*log(x)^2 - 3*x*e^(2*x)*log(2)^2*log(x
)^2 + 9*x^2*e^(2*x)*log(x)^3 - 6*x^2*e^x*log(x)^3 + 3*x*e^(2*x)*log(2)*log(x)^3 - x*e^(2*x)*log(x)^4 + 27*x^3*
e^(2*x)*log(x)*log(log(x)) - 36*x^3*e^x*log(x)*log(log(x)) + 18*x^2*e^(2*x)*log(2)*log(x)*log(log(x)) - 12*x^2
*e^x*log(2)*log(x)*log(log(x)) + 3*x*e^(2*x)*log(2)^2*log(x)*log(log(x)) - 18*x^2*e^(2*x)*log(x)^2*log(log(x))
+ 12*x^2*e^x*log(x)^2*log(log(x)) - 6*x*e^(2*x)*log(2)*log(x)^2*log(log(x)) + 3*x*e^(2*x)*log(x)^3*log(log(x)
) + 9*x^2*e^(2*x)*log(x)*log(log(x))^2 - 6*x^2*e^x*log(x)*log(log(x))^2 + 3*x*e^(2*x)*log(2)*log(x)*log(log(x)
)^2 - 3*x*e^(2*x)*log(x)^2*log(log(x))^2 + x*e^(2*x)*log(x)*log(log(x))^3 - 27*x^3*e^(2*x)*log(x) + 18*x^3*e^x
*log(x) - 27*x^2*e^(2*x)*log(2)*log(x) + 12*x^2*e^x*log(2)*log(x) - 9*x*e^(2*x)*log(2)^2*log(x) + 2*x*e^x*log(
2)^2*log(x) - e^(2*x)*log(2)^3*log(x) + 27*x^2*e^(2*x)*log(x)^2 - 12*x^2*e^x*log(x)^2 + 18*x*e^(2*x)*log(2)*lo
g(x)^2 - 4*x*e^x*log(2)*log(x)^2 + 3*e^(2*x)*log(2)^2*log(x)^2 - 9*x*e^(2*x)*log(x)^3 + 2*x*e^x*log(x)^3 - 3*e
^(2*x)*log(2)*log(x)^3 + e^(2*x)*log(x)^4 - 27*x^2*e^(2*x)*log(x)*log(log(x)) + 12*x^2*e^x*log(x)*log(log(x))
- 18*x*e^(2*x)*log(2)*log(x)*log(log(x)) + 4*x*e^x*log(2)*log(x)*log(log(x)) - 3*e^(2*x)*log(2)^2*log(x)*log(l
og(x)) + 18*x*e^(2*x)*log(x)^2*log(log(x)) - 4*x*e^x*log(x)^2*log(log(x)) + 6*e^(2*x)*log(2)*log(x)^2*log(log(
x)) - 3*e^(2*x)*log(x)^3*log(log(x)) - 9*x*e^(2*x)*log(x)*log(log(x))^2 + 2*x*e^x*log(x)*log(log(x))^2 - 3*e^(
2*x)*log(2)*log(x)*log(log(x))^2 + 3*e^(2*x)*log(x)^2*log(log(x))^2 - e^(2*x)*log(x)*log(log(x))^3 - 18*x^3*e^
x - 12*x^2*e^x*log(2) - 2*x*e^x*log(2)^2 + 27*x^2*e^(2*x + e^x/x)*log(x) + 12*x^2*e^x*log(x) - 54*x^2*e^((x^2
+ e^x)/x)*log(x) + 9*x*e^(2*x + e^x/x)*log(2)*log(x) + 4*x*e^x*log(2)*log(x) - 9*x*e^(2*x + e^x/x)*log(x)^2 -
2*x*e^x*log(x)^2 - 12*x^2*e^x*log(log(x)) - 4*x*e^x*log(2)*log(log(x)) + 9*x*e^(2*x + e^x/x)*log(x)*log(log(x)
) + 4*x*e^x*log(x)*log(log(x)) - 2*x*e^x*log(log(x))^2 - 27*x*e^(2*x + e^x/x)*log(x) + 18*x*e^((x^2 + e^x)/x)*
log(x) - 9*e^(2*x + e^x/x)*log(2)*log(x) + 9*e^(2*x + e^x/x)*log(x)^2 - 9*e^(2*x + e^x/x)*log(x)*log(log(x)) -
18*x*e^((x^2 + e^x)/x))/(243*x^7*e^(2*x)*log(x) - 486*x^7*e^x*log(x) + 405*x^6*e^(2*x)*log(2)*log(x) - 648*x^
6*e^x*log(2)*log(x) + 270*x^5*e^(2*x)*log(2)^2*log(x) - 324*x^5*e^x*log(2)^2*log(x) + 90*x^4*e^(2*x)*log(2)^3*
log(x) - 72*x^4*e^x*log(2)^3*log(x) + 15*x^3*e^(2*x)*log(2)^4*log(x) - 6*x^3*e^x*log(2)^4*log(x) + x^2*e^(2*x)
*log(2)^5*log(x) - 405*x^6*e^(2*x)*log(x)^2 + 648*x^6*e^x*log(x)^2 - 540*x^5*e^(2*x)*log(2)*log(x)^2 + 648*x^5
*e^x*log(2)*log(x)^2 - 270*x^4*e^(2*x)*log(2)^2*log(x)^2 + 216*x^4*e^x*log(2)^2*log(x)^2 - 60*x^3*e^(2*x)*log(
2)^3*log(x)^2 + 24*x^3*e^x*log(2)^3*log(x)^2 - 5*x^2*e^(2*x)*log(2)^4*log(x)^2 + 270*x^5*e^(2*x)*log(x)^3 - 32
4*x^5*e^x*log(x)^3 + 270*x^4*e^(2*x)*log(2)*log(x)^3 - 216*x^4*e^x*log(2)*log(x)^3 + 90*x^3*e^(2*x)*log(2)^2*l
og(x)^3 - 36*x^3*e^x*log(2)^2*log(x)^3 + 10*x^2*e^(2*x)*log(2)^3*log(x)^3 - 90*x^4*e^(2*x)*log(x)^4 + 72*x^4*e
^x*log(x)^4 - 60*x^3*e^(2*x)*log(2)*log(x)^4 + 24*x^3*e^x*log(2)*log(x)^4 - 10*x^2*e^(2*x)*log(2)^2*log(x)^4 +
15*x^3*e^(2*x)*log(x)^5 - 6*x^3*e^x*log(x)^5 + 5*x^2*e^(2*x)*log(2)*log(x)^5 - x^2*e^(2*x)*log(x)^6 + 405*x^6
*e^(2*x)*log(x)*log(log(x)) - 648*x^6*e^x*log(x)*log(log(x)) + 540*x^5*e^(2*x)*log(2)*log(x)*log(log(x)) - 648
*x^5*e^x*log(2)*log(x)*log(log(x)) + 270*x^4*e^(2*x)*log(2)^2*log(x)*log(log(x)) - 216*x^4*e^x*log(2)^2*log(x)
*log(log(x)) + 60*x^3*e^(2*x)*log(2)^3*log(x)*log(log(x)) - 24*x^3*e^x*log(2)^3*log(x)*log(log(x)) + 5*x^2*e^(
2*x)*log(2)^4*log(x)*log(log(x)) - 540*x^5*e^(2*x)*log(x)^2*log(log(x)) + 648*x^5*e^x*log(x)^2*log(log(x)) - 5
40*x^4*e^(2*x)*log(2)*log(x)^2*log(log(x)) + 432*x^4*e^x*log(2)*log(x)^2*log(log(x)) - 180*x^3*e^(2*x)*log(2)^
2*log(x)^2*log(log(x)) + 72*x^3*e^x*log(2)^2*log(x)^2*log(log(x)) - 20*x^2*e^(2*x)*log(2)^3*log(x)^2*log(log(x
)) + 270*x^4*e^(2*x)*log(x)^3*log(log(x)) - 216*x^4*e^x*log(x)^3*log(log(x)) + 180*x^3*e^(2*x)*log(2)*log(x)^3
*log(log(x)) - 72*x^3*e^x*log(2)*log(x)^3*log(log(x)) + 30*x^2*e^(2*x)*log(2)^2*log(x)^3*log(log(x)) - 60*x^3*
e^(2*x)*log(x)^4*log(log(x)) + 24*x^3*e^x*log(x)^4*log(log(x)) - 20*x^2*e^(2*x)*log(2)*log(x)^4*log(log(x)) +
5*x^2*e^(2*x)*log(x)^5*log(log(x)) + 270*x^5*e^(2*x)*log(x)*log(log(x))^2 - 324*x^5*e^x*log(x)*log(log(x))^2 +
270*x^4*e^(2*x)*log(2)*log(x)*log(log(x))^2 - 216*x^4*e^x*log(2)*log(x)*log(log(x))^2 + 90*x^3*e^(2*x)*log(2)
^2*log(x)*log(log(x))^2 - 36*x^3*e^x*log(2)^2*log(x)*log(log(x))^2 + 10*x^2*e^(2*x)*log(2)^3*log(x)*log(log(x)
)^2 - 270*x^4*e^(2*x)*log(x)^2*log(log(x))^2 + 216*x^4*e^x*log(x)^2*log(log(x))^2 - 180*x^3*e^(2*x)*log(2)*log
(x)^2*log(log(x))^2 + 72*x^3*e^x*log(2)*log(x)^2*log(log(x))^2 - 30*x^2*e^(2*x)*log(2)^2*log(x)^2*log(log(x))^
2 + 90*x^3*e^(2*x)*log(x)^3*log(log(x))^2 - 36*x^3*e^x*log(x)^3*log(log(x))^2 + 30*x^2*e^(2*x)*log(2)*log(x)^3
*log(log(x))^2 - 10*x^2*e^(2*x)*log(x)^4*log(log(x))^2 + 90*x^4*e^(2*x)*log(x)*log(log(x))^3 - 72*x^4*e^x*log(
x)*log(log(x))^3 + 60*x^3*e^(2*x)*log(2)*log(x)*log(log(x))^3 - 24*x^3*e^x*log(2)*log(x)*log(log(x))^3 + 10*x^
2*e^(2*x)*log(2)^2*log(x)*log(log(x))^3 - 60*x^3*e^(2*x)*log(x)^2*log(log(x))^3 + 24*x^3*e^x*log(x)^2*log(log(
x))^3 - 20*x^2*e^(2*x)*log(2)*log(x)^2*log(log(x))^3 + 10*x^2*e^(2*x)*log(x)^3*log(log(x))^3 + 15*x^3*e^(2*x)*
log(x)*log(log(x))^4 - 6*x^3*e^x*log(x)*log(log(x))^4 + 5*x^2*e^(2*x)*log(2)*log(x)*log(log(x))^4 - 5*x^2*e^(2
*x)*log(x)^2*log(log(x))^4 + x^2*e^(2*x)*log(x)*log(log(x))^5 - 243*x^6*e^(2*x)*log(x) + 162*x^6*e^x*log(x) -
405*x^5*e^(2*x)*log(2)*log(x) + 216*x^5*e^x*log(2)*log(x) - 270*x^4*e^(2*x)*log(2)^2*log(x) + 108*x^4*e^x*log(
2)^2*log(x) - 90*x^3*e^(2*x)*log(2)^3*log(x) + 24*x^3*e^x*log(2)^3*log(x) - 15*x^2*e^(2*x)*log(2)^4*log(x) + 2
*x^2*e^x*log(2)^4*log(x) - x*e^(2*x)*log(2)^5*log(x) + 405*x^5*e^(2*x)*log(x)^2 - 216*x^5*e^x*log(x)^2 + 540*x
^4*e^(2*x)*log(2)*log(x)^2 - 216*x^4*e^x*log(2)*log(x)^2 + 270*x^3*e^(2*x)*log(2)^2*log(x)^2 - 72*x^3*e^x*log(
2)^2*log(x)^2 + 60*x^2*e^(2*x)*log(2)^3*log(x)^2 - 8*x^2*e^x*log(2)^3*log(x)^2 + 5*x*e^(2*x)*log(2)^4*log(x)^2
- 270*x^4*e^(2*x)*log(x)^3 + 108*x^4*e^x*log(x)^3 - 270*x^3*e^(2*x)*log(2)*log(x)^3 + 72*x^3*e^x*log(2)*log(x
)^3 - 90*x^2*e^(2*x)*log(2)^2*log(x)^3 + 12*x^2*e^x*log(2)^2*log(x)^3 - 10*x*e^(2*x)*log(2)^3*log(x)^3 + 90*x^
3*e^(2*x)*log(x)^4 - 24*x^3*e^x*log(x)^4 + 60*x^2*e^(2*x)*log(2)*log(x)^4 - 8*x^2*e^x*log(2)*log(x)^4 + 10*x*e
^(2*x)*log(2)^2*log(x)^4 - 15*x^2*e^(2*x)*log(x)^5 + 2*x^2*e^x*log(x)^5 - 5*x*e^(2*x)*log(2)*log(x)^5 + x*e^(2
*x)*log(x)^6 - 405*x^5*e^(2*x)*log(x)*log(log(x)) + 216*x^5*e^x*log(x)*log(log(x)) - 540*x^4*e^(2*x)*log(2)*lo
g(x)*log(log(x)) + 216*x^4*e^x*log(2)*log(x)*log(log(x)) - 270*x^3*e^(2*x)*log(2)^2*log(x)*log(log(x)) + 72*x^
3*e^x*log(2)^2*log(x)*log(log(x)) - 60*x^2*e^(2*x)*log(2)^3*log(x)*log(log(x)) + 8*x^2*e^x*log(2)^3*log(x)*log
(log(x)) - 5*x*e^(2*x)*log(2)^4*log(x)*log(log(x)) + 540*x^4*e^(2*x)*log(x)^2*log(log(x)) - 216*x^4*e^x*log(x)
^2*log(log(x)) + 540*x^3*e^(2*x)*log(2)*log(x)^2*log(log(x)) - 144*x^3*e^x*log(2)*log(x)^2*log(log(x)) + 180*x
^2*e^(2*x)*log(2)^2*log(x)^2*log(log(x)) - 24*x^2*e^x*log(2)^2*log(x)^2*log(log(x)) + 20*x*e^(2*x)*log(2)^3*lo
g(x)^2*log(log(x)) - 270*x^3*e^(2*x)*log(x)^3*log(log(x)) + 72*x^3*e^x*log(x)^3*log(log(x)) - 180*x^2*e^(2*x)*
log(2)*log(x)^3*log(log(x)) + 24*x^2*e^x*log(2)*log(x)^3*log(log(x)) - 30*x*e^(2*x)*log(2)^2*log(x)^3*log(log(
x)) + 60*x^2*e^(2*x)*log(x)^4*log(log(x)) - 8*x^2*e^x*log(x)^4*log(log(x)) + 20*x*e^(2*x)*log(2)*log(x)^4*log(
log(x)) - 5*x*e^(2*x)*log(x)^5*log(log(x)) - 270*x^4*e^(2*x)*log(x)*log(log(x))^2 + 108*x^4*e^x*log(x)*log(log
(x))^2 - 270*x^3*e^(2*x)*log(2)*log(x)*log(log(x))^2 + 72*x^3*e^x*log(2)*log(x)*log(log(x))^2 - 90*x^2*e^(2*x)
*log(2)^2*log(x)*log(log(x))^2 + 12*x^2*e^x*log(2)^2*log(x)*log(log(x))^2 - 10*x*e^(2*x)*log(2)^3*log(x)*log(l
og(x))^2 + 270*x^3*e^(2*x)*log(x)^2*log(log(x))^2 - 72*x^3*e^x*log(x)^2*log(log(x))^2 + 180*x^2*e^(2*x)*log(2)
*log(x)^2*log(log(x))^2 - 24*x^2*e^x*log(2)*log(x)^2*log(log(x))^2 + 30*x*e^(2*x)*log(2)^2*log(x)^2*log(log(x)
)^2 - 90*x^2*e^(2*x)*log(x)^3*log(log(x))^2 + 12*x^2*e^x*log(x)^3*log(log(x))^2 - 30*x*e^(2*x)*log(2)*log(x)^3
*log(log(x))^2 + 10*x*e^(2*x)*log(x)^4*log(log(x))^2 - 90*x^3*e^(2*x)*log(x)*log(log(x))^3 + 24*x^3*e^x*log(x)
*log(log(x))^3 - 60*x^2*e^(2*x)*log(2)*log(x)*log(log(x))^3 + 8*x^2*e^x*log(2)*log(x)*log(log(x))^3 - 10*x*e^(
2*x)*log(2)^2*log(x)*log(log(x))^3 + 60*x^2*e^(2*x)*log(x)^2*log(log(x))^3 - 8*x^2*e^x*log(x)^2*log(log(x))^3
+ 20*x*e^(2*x)*log(2)*log(x)^2*log(log(x))^3 - 10*x*e^(2*x)*log(x)^3*log(log(x))^3 - 15*x^2*e^(2*x)*log(x)*log
(log(x))^4 + 2*x^2*e^x*log(x)*log(log(x))^4 - 5*x*e^(2*x)*log(2)*log(x)*log(log(x))^4 + 5*x*e^(2*x)*log(x)^2*l
og(log(x))^4 - x*e^(2*x)*log(x)*log(log(x))^5 - 162*x^6*e^x - 216*x^5*e^x*log(2) - 108*x^4*e^x*log(2)^2 - 24*x
^3*e^x*log(2)^3 - 2*x^2*e^x*log(2)^4 + 243*x^5*e^(2*x + e^x/x)*log(x) + 243*x^5*e^(x + (x^2 + e^x)/x)*log(x) -
486*x^5*e^(x + e^x/x)*log(x) + 216*x^5*e^x*log(x) - 486*x^5*e^((x^2 + e^x)/x)*log(x) + 243*x^4*e^(2*x + e^x/x
)*log(2)*log(x) + 243*x^4*e^(x + (x^2 + e^x)/x)*log(2)*log(x) - 324*x^4*e^(x + e^x/x)*log(2)*log(x) + 216*x^4*
e^x*log(2)*log(x) - 324*x^4*e^((x^2 + e^x)/x)*log(2)*log(x) + 81*x^3*e^(2*x + e^x/x)*log(2)^2*log(x) + 81*x^3*
e^(x + (x^2 + e^x)/x)*log(2)^2*log(x) - 54*x^3*e^(x + e^x/x)*log(2)^2*log(x) + 72*x^3*e^x*log(2)^2*log(x) - 54
*x^3*e^((x^2 + e^x)/x)*log(2)^2*log(x) + 9*x^2*e^(2*x + e^x/x)*log(2)^3*log(x) + 9*x^2*e^(x + (x^2 + e^x)/x)*l
og(2)^3*log(x) + 8*x^2*e^x*log(2)^3*log(x) - 243*x^4*e^(2*x + e^x/x)*log(x)^2 - 243*x^4*e^(x + (x^2 + e^x)/x)*
log(x)^2 + 324*x^4*e^(x + e^x/x)*log(x)^2 - 108*x^4*e^x*log(x)^2 + 324*x^4*e^((x^2 + e^x)/x)*log(x)^2 - 162*x^
3*e^(2*x + e^x/x)*log(2)*log(x)^2 - 162*x^3*e^(x + (x^2 + e^x)/x)*log(2)*log(x)^2 + 108*x^3*e^(x + e^x/x)*log(
2)*log(x)^2 - 72*x^3*e^x*log(2)*log(x)^2 + 108*x^3*e^((x^2 + e^x)/x)*log(2)*log(x)^2 - 27*x^2*e^(2*x + e^x/x)*
log(2)^2*log(x)^2 - 27*x^2*e^(x + (x^2 + e^x)/x)*log(2)^2*log(x)^2 - 12*x^2*e^x*log(2)^2*log(x)^2 + 81*x^3*e^(
2*x + e^x/x)*log(x)^3 + 81*x^3*e^(x + (x^2 + e^x)/x)*log(x)^3 - 54*x^3*e^(x + e^x/x)*log(x)^3 + 24*x^3*e^x*log
(x)^3 - 54*x^3*e^((x^2 + e^x)/x)*log(x)^3 + 27*x^2*e^(2*x + e^x/x)*log(2)*log(x)^3 + 27*x^2*e^(x + (x^2 + e^x)
/x)*log(2)*log(x)^3 + 8*x^2*e^x*log(2)*log(x)^3 - 9*x^2*e^(2*x + e^x/x)*log(x)^4 - 9*x^2*e^(x + (x^2 + e^x)/x)
*log(x)^4 - 2*x^2*e^x*log(x)^4 - 216*x^5*e^x*log(log(x)) - 216*x^4*e^x*log(2)*log(log(x)) - 72*x^3*e^x*log(2)^
2*log(log(x)) - 8*x^2*e^x*log(2)^3*log(log(x)) + 243*x^4*e^(2*x + e^x/x)*log(x)*log(log(x)) + 243*x^4*e^(x + (
x^2 + e^x)/x)*log(x)*log(log(x)) - 324*x^4*e^(x + e^x/x)*log(x)*log(log(x)) + 216*x^4*e^x*log(x)*log(log(x)) -
324*x^4*e^((x^2 + e^x)/x)*log(x)*log(log(x)) + 162*x^3*e^(2*x + e^x/x)*log(2)*log(x)*log(log(x)) + 162*x^3*e^
(x + (x^2 + e^x)/x)*log(2)*log(x)*log(log(x)) - 108*x^3*e^(x + e^x/x)*log(2)*log(x)*log(log(x)) + 144*x^3*e^x*
log(2)*log(x)*log(log(x)) - 108*x^3*e^((x^2 + e^x)/x)*log(2)*log(x)*log(log(x)) + 27*x^2*e^(2*x + e^x/x)*log(2
)^2*log(x)*log(log(x)) + 27*x^2*e^(x + (x^2 + e^x)/x)*log(2)^2*log(x)*log(log(x)) + 24*x^2*e^x*log(2)^2*log(x)
*log(log(x)) - 162*x^3*e^(2*x + e^x/x)*log(x)^2*log(log(x)) - 162*x^3*e^(x + (x^2 + e^x)/x)*log(x)^2*log(log(x
)) + 108*x^3*e^(x + e^x/x)*log(x)^2*log(log(x)) - 72*x^3*e^x*log(x)^2*log(log(x)) + 108*x^3*e^((x^2 + e^x)/x)*
log(x)^2*log(log(x)) - 54*x^2*e^(2*x + e^x/x)*log(2)*log(x)^2*log(log(x)) - 54*x^2*e^(x + (x^2 + e^x)/x)*log(2
)*log(x)^2*log(log(x)) - 24*x^2*e^x*log(2)*log(x)^2*log(log(x)) + 27*x^2*e^(2*x + e^x/x)*log(x)^3*log(log(x))
+ 27*x^2*e^(x + (x^2 + e^x)/x)*log(x)^3*log(log(x)) + 8*x^2*e^x*log(x)^3*log(log(x)) - 108*x^4*e^x*log(log(x))
^2 - 72*x^3*e^x*log(2)*log(log(x))^2 - 12*x^2*e^x*log(2)^2*log(log(x))^2 + 81*x^3*e^(2*x + e^x/x)*log(x)*log(l
og(x))^2 + 81*x^3*e^(x + (x^2 + e^x)/x)*log(x)*log(log(x))^2 - 54*x^3*e^(x + e^x/x)*log(x)*log(log(x))^2 + 72*
x^3*e^x*log(x)*log(log(x))^2 - 54*x^3*e^((x^2 + e^x)/x)*log(x)*log(log(x))^2 + 27*x^2*e^(2*x + e^x/x)*log(2)*l
og(x)*log(log(x))^2 + 27*x^2*e^(x + (x^2 + e^x)/x)*log(2)*log(x)*log(log(x))^2 + 24*x^2*e^x*log(2)*log(x)*log(
log(x))^2 - 27*x^2*e^(2*x + e^x/x)*log(x)^2*log(log(x))^2 - 27*x^2*e^(x + (x^2 + e^x)/x)*log(x)^2*log(log(x))^
2 - 12*x^2*e^x*log(x)^2*log(log(x))^2 - 24*x^3*e^x*log(log(x))^3 - 8*x^2*e^x*log(2)*log(log(x))^3 + 9*x^2*e^(2
*x + e^x/x)*log(x)*log(log(x))^3 + 9*x^2*e^(x + (x^2 + e^x)/x)*log(x)*log(log(x))^3 + 8*x^2*e^x*log(x)*log(log
(x))^3 - 2*x^2*e^x*log(log(x))^4 - 243*x^4*e^(2*x + e^x/x)*log(x) - 243*x^4*e^(x + (x^2 + e^x)/x)*log(x) + 162
*x^4*e^(x + e^x/x)*log(x) + 162*x^4*e^((x^2 + e^x)/x)*log(x) - 243*x^3*e^(2*x + e^x/x)*log(2)*log(x) - 243*x^3
*e^(x + (x^2 + e^x)/x)*log(2)*log(x) + 108*x^3*e^(x + e^x/x)*log(2)*log(x) + 108*x^3*e^((x^2 + e^x)/x)*log(2)*
log(x) - 81*x^2*e^(2*x + e^x/x)*log(2)^2*log(x) - 81*x^2*e^(x + (x^2 + e^x)/x)*log(2)^2*log(x) + 18*x^2*e^(x +
e^x/x)*log(2)^2*log(x) + 18*x^2*e^((x^2 + e^x)/x)*log(2)^2*log(x) - 9*x*e^(2*x + e^x/x)*log(2)^3*log(x) - 9*x
*e^(x + (x^2 + e^x)/x)*log(2)^3*log(x) + 243*x^3*e^(2*x + e^x/x)*log(x)^2 + 243*x^3*e^(x + (x^2 + e^x)/x)*log(
x)^2 - 108*x^3*e^(x + e^x/x)*log(x)^2 - 108*x^3*e^((x^2 + e^x)/x)*log(x)^2 + 162*x^2*e^(2*x + e^x/x)*log(2)*lo
g(x)^2 + 162*x^2*e^(x + (x^2 + e^x)/x)*log(2)*log(x)^2 - 36*x^2*e^(x + e^x/x)*log(2)*log(x)^2 - 36*x^2*e^((x^2
+ e^x)/x)*log(2)*log(x)^2 + 27*x*e^(2*x + e^x/x)*log(2)^2*log(x)^2 + 27*x*e^(x + (x^2 + e^x)/x)*log(2)^2*log(
x)^2 - 81*x^2*e^(2*x + e^x/x)*log(x)^3 - 81*x^2*e^(x + (x^2 + e^x)/x)*log(x)^3 + 18*x^2*e^(x + e^x/x)*log(x)^3
+ 18*x^2*e^((x^2 + e^x)/x)*log(x)^3 - 27*x*e^(2*x + e^x/x)*log(2)*log(x)^3 - 27*x*e^(x + (x^2 + e^x)/x)*log(2
)*log(x)^3 + 9*x*e^(2*x + e^x/x)*log(x)^4 + 9*x*e^(x + (x^2 + e^x)/x)*log(x)^4 - 243*x^3*e^(2*x + e^x/x)*log(x
)*log(log(x)) - 243*x^3*e^(x + (x^2 + e^x)/x)*log(x)*log(log(x)) + 108*x^3*e^(x + e^x/x)*log(x)*log(log(x)) +
108*x^3*e^((x^2 + e^x)/x)*log(x)*log(log(x)) - 162*x^2*e^(2*x + e^x/x)*log(2)*log(x)*log(log(x)) - 162*x^2*e^(
x + (x^2 + e^x)/x)*log(2)*log(x)*log(log(x)) + 36*x^2*e^(x + e^x/x)*log(2)*log(x)*log(log(x)) + 36*x^2*e^((x^2
+ e^x)/x)*log(2)*log(x)*log(log(x)) - 27*x*e^(2*x + e^x/x)*log(2)^2*log(x)*log(log(x)) - 27*x*e^(x + (x^2 + e
^x)/x)*log(2)^2*log(x)*log(log(x)) + 162*x^2*e^(2*x + e^x/x)*log(x)^2*log(log(x)) + 162*x^2*e^(x + (x^2 + e^x)
/x)*log(x)^2*log(log(x)) - 36*x^2*e^(x + e^x/x)*log(x)^2*log(log(x)) - 36*x^2*e^((x^2 + e^x)/x)*log(x)^2*log(l
og(x)) + 54*x*e^(2*x + e^x/x)*log(2)*log(x)^2*log(log(x)) + 54*x*e^(x + (x^2 + e^x)/x)*log(2)*log(x)^2*log(log
(x)) - 27*x*e^(2*x + e^x/x)*log(x)^3*log(log(x)) - 27*x*e^(x + (x^2 + e^x)/x)*log(x)^3*log(log(x)) - 81*x^2*e^
(2*x + e^x/x)*log(x)*log(log(x))^2 - 81*x^2*e^(x + (x^2 + e^x)/x)*log(x)*log(log(x))^2 + 18*x^2*e^(x + e^x/x)*
log(x)*log(log(x))^2 + 18*x^2*e^((x^2 + e^x)/x)*log(x)*log(log(x))^2 - 27*x*e^(2*x + e^x/x)*log(2)*log(x)*log(
log(x))^2 - 27*x*e^(x + (x^2 + e^x)/x)*log(2)*log(x)*log(log(x))^2 + 27*x*e^(2*x + e^x/x)*log(x)^2*log(log(x))
^2 + 27*x*e^(x + (x^2 + e^x)/x)*log(x)^2*log(log(x))^2 - 9*x*e^(2*x + e^x/x)*log(x)*log(log(x))^3 - 9*x*e^(x +
(x^2 + e^x)/x)*log(x)*log(log(x))^3 - 162*x^4*e^(x + e^x/x) - 162*x^4*e^((x^2 + e^x)/x) - 108*x^3*e^(x + e^x/
x)*log(2) - 108*x^3*e^((x^2 + e^x)/x)*log(2) - 18*x^2*e^(x + e^x/x)*log(2)^2 - 18*x^2*e^((x^2 + e^x)/x)*log(2)
^2 + 243*x^3*e^(x + (x^2 + e^x)/x + e^x/x)*log(x) + 108*x^3*e^(x + e^x/x)*log(x) - 486*x^3*e^((x^2 + e^x)/x +
e^x/x)*log(x) + 108*x^3*e^((x^2 + e^x)/x)*log(x) + 81*x^2*e^(x + (x^2 + e^x)/x + e^x/x)*log(2)*log(x) + 36*x^2
*e^(x + e^x/x)*log(2)*log(x) + 36*x^2*e^((x^2 + e^x)/x)*log(2)*log(x) - 81*x^2*e^(x + (x^2 + e^x)/x + e^x/x)*l
og(x)^2 - 18*x^2*e^(x + e^x/x)*log(x)^2 - 18*x^2*e^((x^2 + e^x)/x)*log(x)^2 - 108*x^3*e^(x + e^x/x)*log(log(x)
) - 108*x^3*e^((x^2 + e^x)/x)*log(log(x)) - 36*x^2*e^(x + e^x/x)*log(2)*log(log(x)) - 36*x^2*e^((x^2 + e^x)/x)
*log(2)*log(log(x)) + 81*x^2*e^(x + (x^2 + e^x)/x + e^x/x)*log(x)*log(log(x)) + 36*x^2*e^(x + e^x/x)*log(x)*lo
g(log(x)) + 36*x^2*e^((x^2 + e^x)/x)*log(x)*log(log(x)) - 18*x^2*e^(x + e^x/x)*log(log(x))^2 - 18*x^2*e^((x^2
+ e^x)/x)*log(log(x))^2 - 243*x^2*e^(x + (x^2 + e^x)/x + e^x/x)*log(x) + 162*x^2*e^((x^2 + e^x)/x + e^x/x)*log
(x) - 81*x*e^(x + (x^2 + e^x)/x + e^x/x)*log(2)*log(x) + 81*x*e^(x + (x^2 + e^x)/x + e^x/x)*log(x)^2 - 81*x*e^
(x + (x^2 + e^x)/x + e^x/x)*log(x)*log(log(x)) - 162*x^2*e^((x^2 + e^x)/x + e^x/x))

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maple [C]  time = 6.09, size = 676, normalized size = 19.31

method	result	size
risch	\(-\frac {72}{x \left (-8 \ln \relax (2) \ln \left (\ln \relax (x )\right )-24 x \ln \left (\ln \relax (x )\right )-4 \ln \relax (2)^{2}-4 \ln \left (\ln \relax (x )\right )^{2}-4 \ln \relax (x )^{2}-36 x^{2}+8 \ln \relax (2) \ln \relax (x )+8 \ln \relax (x ) \ln \left (\ln \relax (x )\right )-24 x \ln \relax (2)+24 x \ln \relax (x )-4 i \ln \relax (2) \pi \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{3}+\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right )^{2} \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}-2 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{3}-2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right )^{2} \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{3}+4 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{4}-4 i \ln \left (\ln \relax (x )\right ) \pi \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{3}+4 i \ln \relax (x ) \pi \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{3}-12 i \pi x \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{3}-36 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{x}}+\pi ^{2} \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{6}-12 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )-4 i \ln \relax (2) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )+4 i \ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )-4 i \ln \left (\ln \relax (x )\right ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )+4 i \ln \relax (2) \pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}+12 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}+4 i \ln \left (\ln \relax (x )\right ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}+4 i \ln \left (\ln \relax (x )\right ) \pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}+4 i \ln \relax (2) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}+12 i \pi x \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}-4 i \ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}-4 i \ln \relax (x ) \pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{2}-2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{5}-2 \pi ^{2} \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{5}+\pi ^{2} \mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right )^{2} \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{4}+\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )}\right )^{4}\right )}\)	\(676\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-18*x*ln(x)*ln(1/2*x/ln(x))^2+((216*x^2-36*x)*ln(x)+36*x)*ln(1/2*x/ln(x))+((-162*x+162)*exp(x)-162*x)*ln(
x)*exp(exp(x)/x)+(-486*x^3+108*x^2)*ln(x)-108*x^2)/(x^3*ln(x)*ln(1/2*x/ln(x))^4-12*x^4*ln(x)*ln(1/2*x/ln(x))^3
+(18*x^3*ln(x)*exp(exp(x)/x)+54*x^5*ln(x))*ln(1/2*x/ln(x))^2+(-108*x^4*ln(x)*exp(exp(x)/x)-108*x^6*ln(x))*ln(1
/2*x/ln(x))+81*x^3*ln(x)*exp(exp(x)/x)^2+162*x^5*ln(x)*exp(exp(x)/x)+81*x^7*ln(x)),x,method=_RETURNVERBOSE)

[Out]

-72/x/(12*I*Pi*x*csgn(I/ln(x))*csgn(I*x/ln(x))^2-4*I*ln(x)*Pi*csgn(I*x)*csgn(I*x/ln(x))^2-4*I*ln(x)*Pi*csgn(I/
ln(x))*csgn(I*x/ln(x))^2+4*I*ln(ln(x))*Pi*csgn(I*x)*csgn(I*x/ln(x))^2+4*I*ln(ln(x))*Pi*csgn(I/ln(x))*csgn(I*x/
ln(x))^2+4*I*ln(2)*Pi*csgn(I*x)*csgn(I*x/ln(x))^2+4*I*ln(2)*Pi*csgn(I/ln(x))*csgn(I*x/ln(x))^2+12*I*Pi*x*csgn(
I*x)*csgn(I*x/ln(x))^2-12*I*Pi*x*csgn(I*x)*csgn(I/ln(x))*csgn(I*x/ln(x))-4*I*ln(2)*Pi*csgn(I*x)*csgn(I/ln(x))*
csgn(I*x/ln(x))+4*I*ln(x)*Pi*csgn(I*x)*csgn(I/ln(x))*csgn(I*x/ln(x))-4*I*ln(ln(x))*Pi*csgn(I*x)*csgn(I/ln(x))*
csgn(I*x/ln(x))-8*ln(2)*ln(ln(x))-24*x*ln(ln(x))-4*ln(2)^2-4*ln(ln(x))^2-4*ln(x)^2-36*x^2+8*ln(2)*ln(x)+8*ln(x
)*ln(ln(x))-24*x*ln(2)+24*x*ln(x)-4*I*ln(ln(x))*Pi*csgn(I*x/ln(x))^3+4*I*ln(x)*Pi*csgn(I*x/ln(x))^3-12*I*Pi*x*
csgn(I*x/ln(x))^3-4*I*ln(2)*Pi*csgn(I*x/ln(x))^3+Pi^2*csgn(I*x)^2*csgn(I/ln(x))^2*csgn(I*x/ln(x))^2-2*Pi^2*csg
n(I*x)^2*csgn(I/ln(x))*csgn(I*x/ln(x))^3-2*Pi^2*csgn(I*x)*csgn(I/ln(x))^2*csgn(I*x/ln(x))^3+4*Pi^2*csgn(I*x)*c
sgn(I/ln(x))*csgn(I*x/ln(x))^4-2*Pi^2*csgn(I*x)*csgn(I*x/ln(x))^5-2*Pi^2*csgn(I/ln(x))*csgn(I*x/ln(x))^5-36*ex
p(exp(x)/x)+Pi^2*csgn(I*x/ln(x))^6+Pi^2*csgn(I/ln(x))^2*csgn(I*x/ln(x))^4+Pi^2*csgn(I*x)^2*csgn(I*x/ln(x))^4)

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maxima [B]  time = 1.46, size = 80, normalized size = 2.29 \begin {gather*} \frac {18}{9 \, x^{3} + 6 \, x^{2} \log \relax (2) + x \log \relax (2)^{2} + x \log \relax (x)^{2} + x \log \left (\log \relax (x)\right )^{2} + 9 \, x e^{\left (\frac {e^{x}}{x}\right )} - 2 \, {\left (3 \, x^{2} + x \log \relax (2)\right )} \log \relax (x) + 2 \, {\left (3 \, x^{2} + x \log \relax (2) - x \log \relax (x)\right )} \log \left (\log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x*log(x)*log(1/2*x/log(x))^2+((216*x^2-36*x)*log(x)+36*x)*log(1/2*x/log(x))+((-162*x+162)*exp(x
)-162*x)*log(x)*exp(exp(x)/x)+(-486*x^3+108*x^2)*log(x)-108*x^2)/(x^3*log(x)*log(1/2*x/log(x))^4-12*x^4*log(x)
*log(1/2*x/log(x))^3+(18*x^3*log(x)*exp(exp(x)/x)+54*x^5*log(x))*log(1/2*x/log(x))^2+(-108*x^4*log(x)*exp(exp(
x)/x)-108*x^6*log(x))*log(1/2*x/log(x))+81*x^3*log(x)*exp(exp(x)/x)^2+162*x^5*log(x)*exp(exp(x)/x)+81*x^7*log(
x)),x, algorithm="maxima")

[Out]

18/(9*x^3 + 6*x^2*log(2) + x*log(2)^2 + x*log(x)^2 + x*log(log(x))^2 + 9*x*e^(e^x/x) - 2*(3*x^2 + x*log(2))*lo
g(x) + 2*(3*x^2 + x*log(2) - x*log(x))*log(log(x)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {108\,x^2-\ln \left (\frac {x}{2\,\ln \relax (x)}\right )\,\left (36\,x-\ln \relax (x)\,\left (36\,x-216\,x^2\right )\right )-\ln \relax (x)\,\left (108\,x^2-486\,x^3\right )+{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \relax (x)\,\left (162\,x+{\mathrm {e}}^x\,\left (162\,x-162\right )\right )+18\,x\,{\ln \left (\frac {x}{2\,\ln \relax (x)}\right )}^2\,\ln \relax (x)}{81\,x^7\,\ln \relax (x)+{\ln \left (\frac {x}{2\,\ln \relax (x)}\right )}^2\,\left (54\,x^5\,\ln \relax (x)+18\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \relax (x)\right )-\ln \left (\frac {x}{2\,\ln \relax (x)}\right )\,\left (108\,x^6\,\ln \relax (x)+108\,x^4\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \relax (x)\right )+x^3\,{\ln \left (\frac {x}{2\,\ln \relax (x)}\right )}^4\,\ln \relax (x)-12\,x^4\,{\ln \left (\frac {x}{2\,\ln \relax (x)}\right )}^3\,\ln \relax (x)+81\,x^3\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^x}{x}}\,\ln \relax (x)+162\,x^5\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \relax (x)} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(108*x^2 - log(x/(2*log(x)))*(36*x - log(x)*(36*x - 216*x^2)) - log(x)*(108*x^2 - 486*x^3) + exp(exp(x)/x
)*log(x)*(162*x + exp(x)*(162*x - 162)) + 18*x*log(x/(2*log(x)))^2*log(x))/(81*x^7*log(x) + log(x/(2*log(x)))^
2*(54*x^5*log(x) + 18*x^3*exp(exp(x)/x)*log(x)) - log(x/(2*log(x)))*(108*x^6*log(x) + 108*x^4*exp(exp(x)/x)*lo
g(x)) + x^3*log(x/(2*log(x)))^4*log(x) - 12*x^4*log(x/(2*log(x)))^3*log(x) + 81*x^3*exp((2*exp(x))/x)*log(x) +
162*x^5*exp(exp(x)/x)*log(x)),x)

[Out]

int(-(108*x^2 - log(x/(2*log(x)))*(36*x - log(x)*(36*x - 216*x^2)) - log(x)*(108*x^2 - 486*x^3) + exp(exp(x)/x
)*log(x)*(162*x + exp(x)*(162*x - 162)) + 18*x*log(x/(2*log(x)))^2*log(x))/(81*x^7*log(x) + log(x/(2*log(x)))^
2*(54*x^5*log(x) + 18*x^3*exp(exp(x)/x)*log(x)) - log(x/(2*log(x)))*(108*x^6*log(x) + 108*x^4*exp(exp(x)/x)*lo
g(x)) + x^3*log(x/(2*log(x)))^4*log(x) - 12*x^4*log(x/(2*log(x)))^3*log(x) + 81*x^3*exp((2*exp(x))/x)*log(x) +
162*x^5*exp(exp(x)/x)*log(x)), x)

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sympy [A]  time = 0.78, size = 41, normalized size = 1.17 \begin {gather*} \frac {18}{9 x^{3} - 6 x^{2} \log {\left (\frac {x}{2 \log {\relax (x )}} \right )} + 9 x e^{\frac {e^{x}}{x}} + x \log {\left (\frac {x}{2 \log {\relax (x )}} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x*ln(x)*ln(1/2*x/ln(x))**2+((216*x**2-36*x)*ln(x)+36*x)*ln(1/2*x/ln(x))+((-162*x+162)*exp(x)-16
2*x)*ln(x)*exp(exp(x)/x)+(-486*x**3+108*x**2)*ln(x)-108*x**2)/(x**3*ln(x)*ln(1/2*x/ln(x))**4-12*x**4*ln(x)*ln(
1/2*x/ln(x))**3+(18*x**3*ln(x)*exp(exp(x)/x)+54*x**5*ln(x))*ln(1/2*x/ln(x))**2+(-108*x**4*ln(x)*exp(exp(x)/x)-
108*x**6*ln(x))*ln(1/2*x/ln(x))+81*x**3*ln(x)*exp(exp(x)/x)**2+162*x**5*ln(x)*exp(exp(x)/x)+81*x**7*ln(x)),x)

[Out]

18/(9*x**3 - 6*x**2*log(x/(2*log(x))) + 9*x*exp(exp(x)/x) + x*log(x/(2*log(x)))**2)

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