\(\int \frac {3 x+e^{e^5+x^2} (36-24 x^2)+e^{x^2} (36 x-24 x^3)+(e^{e^5+x^2} (-9+6 x^2)+e^{x^2} (-9 x+6 x^3)) \log (e^{e^5}+x)+(36 e^{e^5}+36 x+(-9 e^{e^5}-9 x) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))+(12 e^{e^5+x^2}+12 e^{x^2} x+(-3 e^{e^5+x^2}-3 e^{x^2} x) \log (e^{e^5}+x)+(12 e^{e^5}+12 x+(-3 e^{e^5}-3 x) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log (\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+(4 e^{e^5+x^2} x^2+4 e^{x^2} x^3) \log (e^{e^5}+x)+(-16 e^{e^5} x^2-16 x^3+(4 e^{e^5} x^2+4 x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))+(-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+(4 e^{e^5+x^2} x^2+4 e^{x^2} x^3) \log (e^{e^5}+x)+(-16 e^{e^5} x^2-16 x^3+(4 e^{e^5} x^2+4 x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log (\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})+(-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+(e^{e^5+x^2} x^2+e^{x^2} x^3) \log (e^{e^5}+x)+(-4 e^{e^5} x^2-4 x^3+(e^{e^5} x^2+x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log ^2(\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})} \, dx\) [9269]

Optimal result

Integrand size = 618, antiderivative size = 31 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \]

[Out]

3/(2+ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2))))/x

Rubi [A] (verified)

Time = 2.62 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {6820, 12, 6819} \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \left (\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+2\right )} \]

[In]

Int[(3*x + E^(E^5 + x^2)*(36 - 24*x^2) + E^x^2*(36*x - 24*x^3) + (E^(E^5 + x^2)*(-9 + 6*x^2) + E^x^2*(-9*x + 6
*x^3))*Log[E^E^5 + x] + (36*E^E^5 + 36*x + (-9*E^E^5 - 9*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (12*E^(
E^5 + x^2) + 12*E^x^2*x + (-3*E^(E^5 + x^2) - 3*E^x^2*x)*Log[E^E^5 + x] + (12*E^E^5 + 12*x + (-3*E^E^5 - 3*x)*
Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])])/(-16*E^(E^5 + x^2)*x^2 -
16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4
*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (-16*E^(E^5 + x^2)*x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2
+ 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E
^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])] + (-4*E^(E^5 + x^2)*x^2 - 4*E^x^2*x^3 + (E^(E^5 + x^2)*x
^2 + E^x^2*x^3)*Log[E^E^5 + x] + (-4*E^E^5*x^2 - 4*x^3 + (E^E^5*x^2 + x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5
+ x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]^2),x]

[Out]

3/(x*(2 + Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]))

Rule 12

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

Rule 6819

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 6820

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

Rubi steps \begin{align*} \text {integral}& = \int \frac {3 \left (-12 e^{e^5+x^2}-x-12 e^{x^2} x+8 e^{e^5+x^2} x^2+8 e^{x^2} x^3-4 e^{e^5+x^2} \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 e^{x^2} x \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 \left (e^{e^5}+x\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\left (e^{e^5}+x\right ) \log \left (e^{e^5}+x\right ) \left (e^{x^2} \left (-3+2 x^2-\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )\right )\right )}{x^2 \left (e^{e^5}+x\right ) \left (4-\log \left (e^{e^5}+x\right )\right ) \left (e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )^2} \, dx \\ & = 3 \int \frac {-12 e^{e^5+x^2}-x-12 e^{x^2} x+8 e^{e^5+x^2} x^2+8 e^{x^2} x^3-4 e^{e^5+x^2} \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 e^{x^2} x \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 \left (e^{e^5}+x\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\left (e^{e^5}+x\right ) \log \left (e^{e^5}+x\right ) \left (e^{x^2} \left (-3+2 x^2-\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )\right )}{x^2 \left (e^{e^5}+x\right ) \left (4-\log \left (e^{e^5}+x\right )\right ) \left (e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )^2} \, dx \\ & = \frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.50 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \]

[In]

Integrate[(3*x + E^(E^5 + x^2)*(36 - 24*x^2) + E^x^2*(36*x - 24*x^3) + (E^(E^5 + x^2)*(-9 + 6*x^2) + E^x^2*(-9
*x + 6*x^3))*Log[E^E^5 + x] + (36*E^E^5 + 36*x + (-9*E^E^5 - 9*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (
12*E^(E^5 + x^2) + 12*E^x^2*x + (-3*E^(E^5 + x^2) - 3*E^x^2*x)*Log[E^E^5 + x] + (12*E^E^5 + 12*x + (-3*E^E^5 -
3*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])])/(-16*E^(E^5 + x^2)*
x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x
^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (-16*E^(E^5 + x^2)*x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2
)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 +
Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])] + (-4*E^(E^5 + x^2)*x^2 - 4*E^x^2*x^3 + (E^(E^5 +
x^2)*x^2 + E^x^2*x^3)*Log[E^E^5 + x] + (-4*E^E^5*x^2 - 4*x^3 + (E^E^5*x^2 + x^3)*Log[E^E^5 + x])*Log[-4 + Log[
E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]^2),x]

[Out]

3/(x*(2 + Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]))

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.26 (sec) , antiderivative size = 185, normalized size of antiderivative = 5.97

\[-\frac {6 i}{x \left (\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) {\operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )}^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) \operatorname {csgn}\left (i x \right )-\pi {\operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )}^{3}+\pi {\operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )}^{2} \operatorname {csgn}\left (i x \right )-2 i \ln \left (x \right )+2 i \ln \left (\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}\right )-4 i\right )}\]

[In]

int(((((-3*exp(exp(5))-3*x)*ln(exp(exp(5))+x)+12*exp(exp(5))+12*x)*ln(ln(exp(exp(5))+x)-4)+(-3*exp(x^2)*exp(ex
p(5))-3*exp(x^2)*x)*ln(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp
(x^2)))+((-9*exp(exp(5))-9*x)*ln(exp(exp(5))+x)+36*exp(exp(5))+36*x)*ln(ln(exp(exp(5))+x)-4)+((6*x^2-9)*exp(x^
2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*ln(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3+36*x)*exp(x^
2)+3*x)/((((x^2*exp(exp(5))+x^3)*ln(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*ln(ln(exp(exp(5))+x)-4)+(x^2*exp(x
^2)*exp(exp(5))+x^3*exp(x^2))*ln(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2))*ln(x/(ln(ln(exp(exp
(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*ln(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*ln(ln(exp(exp
(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*ln(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*ex
p(x^2))*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*ln(exp(exp(5))+x)-16*x^2*exp(exp(5
))-16*x^3)*ln(ln(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*ln(exp(exp(5))+x)-16*x^2*exp(x^
2)*exp(exp(5))-16*x^3*exp(x^2)),x)

[Out]

-6*I/x/(Pi*csgn(I/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))^2-Pi*csgn(I
/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I*x)-Pi*csgn(I*x/(ln(ln
(exp(exp(5))+x)-4)+exp(x^2)))^3+Pi*csgn(I*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))^2*csgn(I*x)-2*I*ln(x)+2*I*ln(l
n(ln(exp(exp(5))+x)-4)+exp(x^2))-4*I)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.26 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \log \left (\frac {x e^{\left (e^{5}\right )}}{e^{\left (e^{5}\right )} \log \left (\log \left (x + e^{\left (e^{5}\right )}\right ) - 4\right ) + e^{\left (x^{2} + e^{5}\right )}}\right ) + 2 \, x} \]

[In]

integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(log(exp(exp(5))+x)-4)+(-3*exp(x^
2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(
5))+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x)*log(log(exp(exp(5))+x)-4)+(
(6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24
*x^3+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*log(log(exp(exp(
5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2)
)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(
5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*ex
p(x^2)*exp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*log
(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2
))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="fricas")

[Out]

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

Sympy [F(-1)]

Timed out. \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\text {Timed out} \]

[In]

integrate(((((-3*exp(exp(5))-3*x)*ln(exp(exp(5))+x)+12*exp(exp(5))+12*x)*ln(ln(exp(exp(5))+x)-4)+(-3*exp(x**2)
*exp(exp(5))-3*exp(x**2)*x)*ln(exp(exp(5))+x)+12*exp(x**2)*exp(exp(5))+12*exp(x**2)*x)*ln(x/(ln(ln(exp(exp(5))
+x)-4)+exp(x**2)))+((-9*exp(exp(5))-9*x)*ln(exp(exp(5))+x)+36*exp(exp(5))+36*x)*ln(ln(exp(exp(5))+x)-4)+((6*x*
*2-9)*exp(x**2)*exp(exp(5))+(6*x**3-9*x)*exp(x**2))*ln(exp(exp(5))+x)+(-24*x**2+36)*exp(x**2)*exp(exp(5))+(-24
*x**3+36*x)*exp(x**2)+3*x)/((((x**2*exp(exp(5))+x**3)*ln(exp(exp(5))+x)-4*x**2*exp(exp(5))-4*x**3)*ln(ln(exp(e
xp(5))+x)-4)+(x**2*exp(x**2)*exp(exp(5))+x**3*exp(x**2))*ln(exp(exp(5))+x)-4*x**2*exp(x**2)*exp(exp(5))-4*x**3
*exp(x**2))*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x**2)))**2+(((4*x**2*exp(exp(5))+4*x**3)*ln(exp(exp(5))+x)-16*x*
*2*exp(exp(5))-16*x**3)*ln(ln(exp(exp(5))+x)-4)+(4*x**2*exp(x**2)*exp(exp(5))+4*x**3*exp(x**2))*ln(exp(exp(5))
+x)-16*x**2*exp(x**2)*exp(exp(5))-16*x**3*exp(x**2))*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x**2)))+((4*x**2*exp(ex
p(5))+4*x**3)*ln(exp(exp(5))+x)-16*x**2*exp(exp(5))-16*x**3)*ln(ln(exp(exp(5))+x)-4)+(4*x**2*exp(x**2)*exp(exp
(5))+4*x**3*exp(x**2))*ln(exp(exp(5))+x)-16*x**2*exp(x**2)*exp(exp(5))-16*x**3*exp(x**2)),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.44 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.97 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \log \left (x\right ) - x \log \left (e^{\left (x^{2}\right )} + \log \left (\log \left (x + e^{\left (e^{5}\right )}\right ) - 4\right )\right ) + 2 \, x} \]

[In]

integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(log(exp(exp(5))+x)-4)+(-3*exp(x^
2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(
5))+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x)*log(log(exp(exp(5))+x)-4)+(
(6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24
*x^3+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*log(log(exp(exp(
5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2)
)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(
5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*ex
p(x^2)*exp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*log
(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2
))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="maxima")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1938 vs. \(2 (28) = 56\).

Time = 24.85 (sec) , antiderivative size = 1938, normalized size of antiderivative = 62.52 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\text {Too large to display} \]

[In]

integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(log(exp(exp(5))+x)-4)+(-3*exp(x^
2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(
5))+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x)*log(log(exp(exp(5))+x)-4)+(
(6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24
*x^3+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*log(log(exp(exp(
5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2)
)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(
5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*ex
p(x^2)*exp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*log
(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2
))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="giac")

[Out]

3*(2*x^3*e^(x^2)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) + 2*x^3*e^(2*x^2)*log(x + e^(e^5)) - 8*x^3*e^(x^2)
*log(log(x + e^(e^5)) - 4) + 2*x^2*e^(x^2 + e^5)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) - 8*x^3*e^(2*x^2)
+ 2*x^2*e^(2*x^2 + e^5)*log(x + e^(e^5)) - 8*x^2*e^(x^2 + e^5)*log(log(x + e^(e^5)) - 4) - 2*x*e^(x^2)*log(x +
e^(e^5))*log(log(x + e^(e^5)) - 4) - x*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4)^2 - e^(e^5)*log(x + e^(e^5)
)*log(log(x + e^(e^5)) - 4)^2 - 8*x^2*e^(2*x^2 + e^5) - x*e^(2*x^2)*log(x + e^(e^5)) + 8*x*e^(x^2)*log(log(x +
e^(e^5)) - 4) - 2*e^(x^2 + e^5)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) + 4*x*log(log(x + e^(e^5)) - 4)^2
+ 4*e^(e^5)*log(log(x + e^(e^5)) - 4)^2 + 4*x*e^(2*x^2) + x*e^(x^2) - e^(2*x^2 + e^5)*log(x + e^(e^5)) + x*log
(log(x + e^(e^5)) - 4) + 8*e^(x^2 + e^5)*log(log(x + e^(e^5)) - 4) + 4*e^(2*x^2 + e^5))/(2*x^4*e^(x^2)*log(x +
e^(e^5))*log(x)*log(log(x + e^(e^5)) - 4) - 2*x^4*e^(x^2)*log(x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5))
- 4))*log(log(x + e^(e^5)) - 4) + 2*x^4*e^(2*x^2)*log(x + e^(e^5))*log(x) - 2*x^4*e^(2*x^2)*log(x + e^(e^5))*
log(e^(x^2) + log(log(x + e^(e^5)) - 4)) + 4*x^4*e^(x^2)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) - 8*x^4*e^
(x^2)*log(x)*log(log(x + e^(e^5)) - 4) + 2*x^3*e^(x^2 + e^5)*log(x + e^(e^5))*log(x)*log(log(x + e^(e^5)) - 4)
+ 8*x^4*e^(x^2)*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) - 2*x^3*e^(x^2 + e^5)*log(
x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) + 4*x^4*e^(2*x^2)*log(x + e^(e
^5)) - 8*x^4*e^(2*x^2)*log(x) + 2*x^3*e^(2*x^2 + e^5)*log(x + e^(e^5))*log(x) + 8*x^4*e^(2*x^2)*log(e^(x^2) +
log(log(x + e^(e^5)) - 4)) - 2*x^3*e^(2*x^2 + e^5)*log(x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5)) - 4)) -
16*x^4*e^(x^2)*log(log(x + e^(e^5)) - 4) + 4*x^3*e^(x^2 + e^5)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) - 8
*x^3*e^(x^2 + e^5)*log(x)*log(log(x + e^(e^5)) - 4) - 2*x^2*e^(x^2)*log(x + e^(e^5))*log(x)*log(log(x + e^(e^5
)) - 4) + 8*x^3*e^(x^2 + e^5)*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) + 2*x^2*e^(x^
2)*log(x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) - x^2*log(x + e^(e^5))*
log(x)*log(log(x + e^(e^5)) - 4)^2 - x*e^(e^5)*log(x + e^(e^5))*log(x)*log(log(x + e^(e^5)) - 4)^2 + x^2*log(x
+ e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4)^2 + x*e^(e^5)*log(x + e^(e^5))*
log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4)^2 - 16*x^4*e^(2*x^2) + 4*x^3*e^(2*x^2 + e^5
)*log(x + e^(e^5)) - 8*x^3*e^(2*x^2 + e^5)*log(x) - x^2*e^(2*x^2)*log(x + e^(e^5))*log(x) + 8*x^3*e^(2*x^2 + e
^5)*log(e^(x^2) + log(log(x + e^(e^5)) - 4)) + x^2*e^(2*x^2)*log(x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5
)) - 4)) - 16*x^3*e^(x^2 + e^5)*log(log(x + e^(e^5)) - 4) - 4*x^2*e^(x^2)*log(x + e^(e^5))*log(log(x + e^(e^5)
) - 4) + 8*x^2*e^(x^2)*log(x)*log(log(x + e^(e^5)) - 4) - 2*x*e^(x^2 + e^5)*log(x + e^(e^5))*log(x)*log(log(x
+ e^(e^5)) - 4) - 8*x^2*e^(x^2)*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) + 2*x*e^(x^
2 + e^5)*log(x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) - 2*x^2*log(x + e
^(e^5))*log(log(x + e^(e^5)) - 4)^2 - 2*x*e^(e^5)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4)^2 + 4*x^2*log(x)*
log(log(x + e^(e^5)) - 4)^2 + 4*x*e^(e^5)*log(x)*log(log(x + e^(e^5)) - 4)^2 - 4*x^2*log(e^(x^2) + log(log(x +
e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4)^2 - 4*x*e^(e^5)*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x +
e^(e^5)) - 4)^2 - 16*x^3*e^(2*x^2 + e^5) - 2*x^2*e^(2*x^2)*log(x + e^(e^5)) + 4*x^2*e^(2*x^2)*log(x) + x^2*e^
(x^2)*log(x) - x*e^(2*x^2 + e^5)*log(x + e^(e^5))*log(x) - 4*x^2*e^(2*x^2)*log(e^(x^2) + log(log(x + e^(e^5))
- 4)) - x^2*e^(x^2)*log(e^(x^2) + log(log(x + e^(e^5)) - 4)) + x*e^(2*x^2 + e^5)*log(x + e^(e^5))*log(e^(x^2)
+ log(log(x + e^(e^5)) - 4)) + 16*x^2*e^(x^2)*log(log(x + e^(e^5)) - 4) - 4*x*e^(x^2 + e^5)*log(x + e^(e^5))*l
og(log(x + e^(e^5)) - 4) + x^2*log(x)*log(log(x + e^(e^5)) - 4) + 8*x*e^(x^2 + e^5)*log(x)*log(log(x + e^(e^5)
) - 4) - x^2*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) - 8*x*e^(x^2 + e^5)*log(e^(x^2
) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) + 8*x^2*log(log(x + e^(e^5)) - 4)^2 + 8*x*e^(e^5)*log
(log(x + e^(e^5)) - 4)^2 + 8*x^2*e^(2*x^2) + 2*x^2*e^(x^2) - 2*x*e^(2*x^2 + e^5)*log(x + e^(e^5)) + 4*x*e^(2*x
^2 + e^5)*log(x) - 4*x*e^(2*x^2 + e^5)*log(e^(x^2) + log(log(x + e^(e^5)) - 4)) + 2*x^2*log(log(x + e^(e^5)) -
4) + 16*x*e^(x^2 + e^5)*log(log(x + e^(e^5)) - 4) + 8*x*e^(2*x^2 + e^5))

Mupad [F(-1)]

Timed out. \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\int -\frac {3\,x+\ln \left (\frac {x}{{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )}\right )\,\left (12\,x\,{\mathrm {e}}^{x^2}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (3\,x\,{\mathrm {e}}^{x^2}+3\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+12\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (12\,x+12\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (3\,x+3\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )\right )\right )+{\mathrm {e}}^{x^2}\,\left (36\,x-24\,x^3\right )+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (36\,x+36\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (9\,x+9\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )\right )-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left ({\mathrm {e}}^{x^2}\,\left (9\,x-6\,x^3\right )-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\,\left (6\,x^2-9\right )\right )-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\,\left (24\,x^2-36\right )}{16\,x^3\,{\mathrm {e}}^{x^2}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3\,{\mathrm {e}}^{x^2}+4\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (16\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3+4\,{\mathrm {e}}^{{\mathrm {e}}^5}\,x^2\right )+16\,x^3\right )+\ln \left (\frac {x}{{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )}\right )\,\left (16\,x^3\,{\mathrm {e}}^{x^2}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3\,{\mathrm {e}}^{x^2}+4\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (16\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3+4\,{\mathrm {e}}^{{\mathrm {e}}^5}\,x^2\right )+16\,x^3\right )+16\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+{\ln \left (\frac {x}{{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )}\right )}^2\,\left (4\,x^3\,{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (4\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (x^3+{\mathrm {e}}^{{\mathrm {e}}^5}\,x^2\right )+4\,x^3\right )-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (x^3\,{\mathrm {e}}^{x^2}+x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+4\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+16\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}} \,d x \]

[In]

int(-(3*x + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(12*x*exp(x^2) - log(x + exp(exp(5)))*(3*x*exp(x
^2) + 3*exp(x^2)*exp(exp(5))) + 12*exp(x^2)*exp(exp(5)) + log(log(x + exp(exp(5))) - 4)*(12*x + 12*exp(exp(5))
- log(x + exp(exp(5)))*(3*x + 3*exp(exp(5))))) + exp(x^2)*(36*x - 24*x^3) + log(log(x + exp(exp(5))) - 4)*(36
*x + 36*exp(exp(5)) - log(x + exp(exp(5)))*(9*x + 9*exp(exp(5)))) - log(x + exp(exp(5)))*(exp(x^2)*(9*x - 6*x^
3) - exp(x^2)*exp(exp(5))*(6*x^2 - 9)) - exp(x^2)*exp(exp(5))*(24*x^2 - 36))/(16*x^3*exp(x^2) - log(x + exp(ex
p(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5))) - 4)*(16*x^2*exp(exp(5)) - log
(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(1
6*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5)))
- 4)*(16*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + 16*x^2*exp(x^2)*exp(e
xp(5))) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))^2*(4*x^3*exp(x^2) + log(log(x + exp(exp(5))) - 4)*
(4*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(x^2*exp(exp(5)) + x^3) + 4*x^3) - log(x + exp(exp(5)))*(x^3*exp(x^2
) + x^2*exp(x^2)*exp(exp(5))) + 4*x^2*exp(x^2)*exp(exp(5))) + 16*x^2*exp(x^2)*exp(exp(5))),x)

[Out]

int(-(3*x + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(12*x*exp(x^2) - log(x + exp(exp(5)))*(3*x*exp(x
^2) + 3*exp(x^2)*exp(exp(5))) + 12*exp(x^2)*exp(exp(5)) + log(log(x + exp(exp(5))) - 4)*(12*x + 12*exp(exp(5))
- log(x + exp(exp(5)))*(3*x + 3*exp(exp(5))))) + exp(x^2)*(36*x - 24*x^3) + log(log(x + exp(exp(5))) - 4)*(36
*x + 36*exp(exp(5)) - log(x + exp(exp(5)))*(9*x + 9*exp(exp(5)))) - log(x + exp(exp(5)))*(exp(x^2)*(9*x - 6*x^
3) - exp(x^2)*exp(exp(5))*(6*x^2 - 9)) - exp(x^2)*exp(exp(5))*(24*x^2 - 36))/(16*x^3*exp(x^2) - log(x + exp(ex
p(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5))) - 4)*(16*x^2*exp(exp(5)) - log
(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(1
6*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5)))
- 4)*(16*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + 16*x^2*exp(x^2)*exp(e
xp(5))) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))^2*(4*x^3*exp(x^2) + log(log(x + exp(exp(5))) - 4)*
(4*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(x^2*exp(exp(5)) + x^3) + 4*x^3) - log(x + exp(exp(5)))*(x^3*exp(x^2
) + x^2*exp(x^2)*exp(exp(5))) + 4*x^2*exp(x^2)*exp(exp(5))) + 16*x^2*exp(x^2)*exp(exp(5))), x)