∫ 6+e2x−125e9 log2(4)+625e18 log4(4)+ex(−5−x+50e9 log2(4))____________________________________________ 9+e2x−150e9 log2(4)+625e18 log4(4)+ex(−6+50e9 log2(4)) dx [1101]

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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(190\) vs. \(2(23)=46\).
time = 0.49, antiderivative size = 190, normalized size of antiderivative = 8.26, number of steps used = 17, number of rules used = 12, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.140, Rules used = {6873, 6874, 2216, 2215, 2221, 2317, 2438, 2222, 2320, 36, 29, 31} \begin {gather*} -\frac {x^2}{2 \left (3-25 e^9 \log ^2(4)\right )}+x+\frac {(1-x)^2}{2 \left (3-25 e^9 \log ^2(4)\right )}+\frac {(1-x) \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}-\frac {\log \left (-e^x+3-25 e^9 \log ^2(4)\right )}{3-25 e^9 \log ^2(4)}+\frac {x \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}-\frac {x}{-e^x+3-25 e^9 \log ^2(4)}+\frac {x}{3-25 e^9 \log ^2(4)} \end {gather*}

Int[(6 + E^(2*x) - 125*E^9*Log[4]^2 + 625*E^18*Log[4]^4 + E^x*(-5 - x + 50*E^9*Log[4]^2))/(9 + E^(2*x) - 150*E

x + (1 - x)^2/(2*(3 - 25*E^9*Log[4]^2)) + x/(3 - 25*E^9*Log[4]^2) - x^2/(2*(3 - 25*E^9*Log[4]^2)) - x/(3 - E^x

- 25*E^9*Log[4]^2) - Log[3 - E^x - 25*E^9*Log[4]^2]/(3 - 25*E^9*Log[4]^2) + ((1 - x)*Log[1 - E^x/(3 - 25*E^9*

Log[4]^2)])/(3 - 25*E^9*Log[4]^2) + (x*Log[1 - E^x/(3 - 25*E^9*Log[4]^2)])/(3 - 25*E^9*Log[4]^2)

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Int[1/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Dist[b/(b*c - a*d), Int[1/(a + b*x), x], x] -

Dist[d/(b*c - a*d), Int[1/(c + d*x), x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0]

Int[((c_.) + (d_.)*(x_))^(m_.)/((a_) + (b_.)*((F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)), x_Symbol] :> Simp[(c

+ d*x)^(m + 1)/(a*d*(m + 1)), x] - Dist[b/a, Int[(c + d*x)^m*((F^(g*(e + f*x)))^n/(a + b*(F^(g*(e + f*x)))^n))

Int[((a_) + (b_.)*((F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.))^(p_)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Dis

t[1/a, Int[(c + d*x)^m*(a + b*(F^(g*(e + f*x)))^n)^(p + 1), x], x] - Dist[b/a, Int[(c + d*x)^m*(F^(g*(e + f*x)

))^n*(a + b*(F^(g*(e + f*x)))^n)^p, x], x] /; FreeQ[{F, a, b, c, d, e, f, g, n}, x] && ILtQ[p, 0] && IGtQ[m, 0

Int[(((F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.))/((a_) + (b_.)*((F_)^((g_.)*((e_.) +

(f_.)*(x_))))^(n_.)), x_Symbol] :> Simp[((c + d*x)^m/(b*f*g*n*Log[F]))*Log[1 + b*((F^(g*(e + f*x)))^n/a)], x]

- Dist[d*(m/(b*f*g*n*Log[F])), Int[(c + d*x)^(m - 1)*Log[1 + b*((F^(g*(e + f*x)))^n/a)], x], x] /; FreeQ[{F,

Int[((F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((a_.) + (b_.)*((F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.))^(p_.)*

((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[(c + d*x)^m*((a + b*(F^(g*(e + f*x)))^n)^(p + 1)/(b*f*g*n*(p + 1

)*Log[F])), x] - Dist[d*(m/(b*f*g*n*(p + 1)*Log[F])), Int[(c + d*x)^(m - 1)*(a + b*(F^(g*(e + f*x)))^n)^(p + 1

), x], x] /; FreeQ[{F, a, b, c, d, e, f, g, m, n, p}, x] && NeQ[p, -1]

Int[Log[(a_) + (b_.)*((F_)^((e_.)*((c_.) + (d_.)*(x_))))^(n_.)], x_Symbol] :> Dist[1/(d*e*n*Log[F]), Subst[Int

[Log[a + b*x]/x, x], x, (F^(e*(c + d*x)))^n], x] /; FreeQ[{F, a, b, c, d, e, n}, x] && GtQ[a, 0]

Int[u_, x_Symbol] :> With[{v = FunctionOfExponential[u, x]}, Dist[v/D[v, x], Subst[Int[FunctionOfExponentialFu

nction[u, x]/x, x], x, v], x]] /; FunctionOfExponentialQ[u, x] && !MatchQ[u, (w_)*((a_.)*(v_)^(n_))^(m_) /; F

reeQ[{a, m, n}, x] && IntegerQ[m*n]] && !MatchQ[u, E^((c_.)*((a_.) + (b_.)*x))*(F_)[v_] /; FreeQ[{a, b, c}, x

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> Simp[-PolyLog[2, (-c)*e*x^n]/n, x] /; FreeQ[{c, d,

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

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

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 x}+e^x \left (-5-x+50 e^9 \log ^2(4)\right )+6 \left (1+\frac {125}{6} e^9 \log ^2(4) \left (-1+5 e^9 \log ^2(4)\right )\right )}{\left (e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )\right )^2} \, dx\\ &=\int \left (1+\frac {x \left (-3+25 e^9 \log ^2(4)\right )}{\left (e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )\right )^2}+\frac {1-x}{e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )}\right ) \, dx\\ &=x+\left (-3+25 e^9 \log ^2(4)\right ) \int \frac {x}{\left (e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )\right )^2} \, dx+\int \frac {1-x}{e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )} \, dx\\ &=x+\frac {(1-x)^2}{2 \left (3-25 e^9 \log ^2(4)\right )}+\frac {\int \frac {e^x (1-x)}{e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )} \, dx}{3-25 e^9 \log ^2(4)}-\int \frac {e^x x}{\left (e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )\right )^2} \, dx+\int \frac {x}{e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )} \, dx\\ &=x+\frac {(1-x)^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x}{3-e^x-25 e^9 \log ^2(4)}+\frac {(1-x) \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}+\frac {\int \frac {e^x x}{e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )} \, dx}{3-25 e^9 \log ^2(4)}+\frac {\int \log \left (1-\frac {e^x}{3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )}\right ) \, dx}{3-25 e^9 \log ^2(4)}-\int \frac {1}{e^x-3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )} \, dx\\ &=x+\frac {(1-x)^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x}{3-e^x-25 e^9 \log ^2(4)}+\frac {(1-x) \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}+\frac {x \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}-\frac {\int \log \left (1-\frac {e^x}{3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )}\right ) \, dx}{3-25 e^9 \log ^2(4)}+\frac {\text {Subst}\left (\int \frac {\log \left (1-\frac {x}{3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )}\right )}{x} \, dx,x,e^x\right )}{3-25 e^9 \log ^2(4)}-\text {Subst}\left (\int \frac {1}{x \left (-3+x+25 e^9 \log ^2(4)\right )} \, dx,x,e^x\right )\\ &=x+\frac {(1-x)^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x}{3-e^x-25 e^9 \log ^2(4)}+\frac {(1-x) \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}+\frac {x \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}-\frac {\text {Li}_2\left (\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}-\frac {\text {Subst}\left (\int \frac {\log \left (1-\frac {x}{3 \left (1-\frac {25}{3} e^9 \log ^2(4)\right )}\right )}{x} \, dx,x,e^x\right )}{3-25 e^9 \log ^2(4)}-\frac {\text {Subst}\left (\int \frac {1}{x} \, dx,x,e^x\right )}{-3+25 e^9 \log ^2(4)}+\frac {\text {Subst}\left (\int \frac {1}{-3+x+25 e^9 \log ^2(4)} \, dx,x,e^x\right )}{-3+25 e^9 \log ^2(4)}\\ &=x+\frac {(1-x)^2}{2 \left (3-25 e^9 \log ^2(4)\right )}+\frac {x}{3-25 e^9 \log ^2(4)}-\frac {x^2}{2 \left (3-25 e^9 \log ^2(4)\right )}-\frac {x}{3-e^x-25 e^9 \log ^2(4)}-\frac {\log \left (3-e^x-25 e^9 \log ^2(4)\right )}{3-25 e^9 \log ^2(4)}+\frac {(1-x) \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}+\frac {x \log \left (1-\frac {e^x}{3-25 e^9 \log ^2(4)}\right )}{3-25 e^9 \log ^2(4)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.07, size = 20, normalized size = 0.87 \begin {gather*} x+\frac {x}{-3+e^x+25 e^9 \log ^2(4)} \end {gather*}

Integrate[(6 + E^(2*x) - 125*E^9*Log[4]^2 + 625*E^18*Log[4]^4 + E^x*(-5 - x + 50*E^9*Log[4]^2))/(9 + E^(2*x) -

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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.36, size = 786, normalized size = 34.17


method	result	size

risch	\(x +\frac {x}{100 \,{\mathrm e}^{9} \ln \left (2\right )^{2}+{\mathrm e}^{x}-3}\)	\(19\)
norman	\(\frac {\left (100 \,{\mathrm e}^{9} \ln \left (2\right )^{2}-2\right ) x +{\mathrm e}^{x} x}{100 \,{\mathrm e}^{9} \ln \left (2\right )^{2}+{\mathrm e}^{x}-3}\)	\(33\)
default	\(\text {Expression too large to display}\)	\(786\)

int((exp(x)^2+(200*exp(9)*ln(2)^2-x-5)*exp(x)+10000*exp(9)^2*ln(2)^4-500*exp(9)*ln(2)^2+6)/(exp(x)^2+(200*exp(

9)*ln(2)^2-6)*exp(x)+10000*exp(9)^2*ln(2)^4-600*exp(9)*ln(2)^2+9),x,method=_RETURNVERBOSE)

-100/(100*exp(9)*ln(2)^2+exp(x)-3)*exp(9)*ln(2)^2+2/(100*exp(9)*ln(2)^2+exp(x)-3)+ln(100*exp(9)*ln(2)^2+exp(x)

-3)+(6/(100*exp(9)*ln(2)^2-3)+6/(100*exp(9)*ln(2)^2-3)*x+6/(10000*exp(9)^2*ln(2)^4-600*exp(9)*ln(2)^2+9)*x*exp

(x))/(100*exp(9)*ln(2)^2+exp(x)-3)-6/(10000*exp(9)^2*ln(2)^4-600*exp(9)*ln(2)^2+9)*ln(100*exp(9)*ln(2)^2+exp(x

)-3)+(-500*exp(9)*ln(2)^2/(100*exp(9)*ln(2)^2-3)-500*exp(9)*ln(2)^2/(100*exp(9)*ln(2)^2-3)*x-500/(10000*exp(9)

^2*ln(2)^4-600*exp(9)*ln(2)^2+9)*exp(9)*ln(2)^2*x*exp(x))/(100*exp(9)*ln(2)^2+exp(x)-3)+500/(10000*exp(9)^2*ln

(2)^4-600*exp(9)*ln(2)^2+9)*exp(9)*ln(2)^2*ln(100*exp(9)*ln(2)^2+exp(x)-3)+(10000*exp(9)^2*ln(2)^4/(100*exp(9)

*ln(2)^2-3)+10000*exp(9)^2*ln(2)^4/(100*exp(9)*ln(2)^2-3)*x+10000/(10000*exp(9)^2*ln(2)^4-600*exp(9)*ln(2)^2+9

)*exp(9)^2*ln(2)^4*x*exp(x))/(100*exp(9)*ln(2)^2+exp(x)-3)-10000/(10000*exp(9)^2*ln(2)^4-600*exp(9)*ln(2)^2+9)

*exp(9)^2*ln(2)^4*ln(100*exp(9)*ln(2)^2+exp(x)-3)-1/200*x*(ln((100*exp(9)*ln(2)^2-100*(exp(9)^2*ln(2)^4-exp(18

)*ln(2)^4)^(1/2)+exp(x)-3)/(100*exp(9)*ln(2)^2-100*(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)-3))-ln((100*exp(9)

*ln(2)^2+100*(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)+exp(x)-3)/(100*exp(9)*ln(2)^2+100*(exp(9)^2*ln(2)^4-exp(

18)*ln(2)^4)^(1/2)-3)))/(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)-1/200/(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2

)*dilog((100*exp(9)*ln(2)^2-100*(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)+exp(x)-3)/(100*exp(9)*ln(2)^2-100*(ex

p(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)-3))+1/200/(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)*dilog((100*exp(9)*ln(

2)^2+100*(exp(9)^2*ln(2)^4-exp(18)*ln(2)^4)^(1/2)+exp(x)-3)/(100*exp(9)*ln(2)^2+100*(exp(9)^2*ln(2)^4-exp(18)*

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 437 vs. \(2 (18) = 36\).
time = 0.50, size = 437, normalized size = 19.00 \begin {gather*} 10000 \, {\left (\frac {x}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + 9} - \frac {\log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right )}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + 9} + \frac {1}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + {\left (100 \, e^{9} \log \left (2\right )^{2} - 3\right )} e^{x} + 9}\right )} e^{18} \log \left (2\right )^{4} - 500 \, {\left (\frac {x}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + 9} - \frac {\log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right )}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + 9} + \frac {1}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + {\left (100 \, e^{9} \log \left (2\right )^{2} - 3\right )} e^{x} + 9}\right )} e^{9} \log \left (2\right )^{2} - \frac {200 \, e^{18} \log \left (2\right )^{2}}{100 \, e^{18} \log \left (2\right )^{2} - 3 \, e^{9} + e^{\left (x + 9\right )}} - \frac {x e^{x}}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + {\left (100 \, e^{9} \log \left (2\right )^{2} - 3\right )} e^{x} + 9} + \frac {100 \, e^{9} \log \left (2\right )^{2} - 3}{100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3} + \frac {6 \, x}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + 9} - \frac {6 \, \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right )}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + 9} + \frac {\log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right )}{100 \, e^{9} \log \left (2\right )^{2} - 3} + \frac {6}{10000 \, e^{18} \log \left (2\right )^{4} - 600 \, e^{9} \log \left (2\right )^{2} + {\left (100 \, e^{9} \log \left (2\right )^{2} - 3\right )} e^{x} + 9} + \frac {5}{100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3} + \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) \end {gather*}

integrate((exp(x)^2+(200*exp(9)*log(2)^2-x-5)*exp(x)+10000*exp(9)^2*log(2)^4-500*exp(9)*log(2)^2+6)/(exp(x)^2+

(200*exp(9)*log(2)^2-6)*exp(x)+10000*exp(9)^2*log(2)^4-600*exp(9)*log(2)^2+9),x, algorithm="maxima")

10000*(x/(10000*e^18*log(2)^4 - 600*e^9*log(2)^2 + 9) - log(100*e^9*log(2)^2 + e^x - 3)/(10000*e^18*log(2)^4 -

600*e^9*log(2)^2 + 9) + 1/(10000*e^18*log(2)^4 - 600*e^9*log(2)^2 + (100*e^9*log(2)^2 - 3)*e^x + 9))*e^18*log

(2)^4 - 500*(x/(10000*e^18*log(2)^4 - 600*e^9*log(2)^2 + 9) - log(100*e^9*log(2)^2 + e^x - 3)/(10000*e^18*log(

2)^4 - 600*e^9*log(2)^2 + 9) + 1/(10000*e^18*log(2)^4 - 600*e^9*log(2)^2 + (100*e^9*log(2)^2 - 3)*e^x + 9))*e^

9*log(2)^2 - 200*e^18*log(2)^2/(100*e^18*log(2)^2 - 3*e^9 + e^(x + 9)) - x*e^x/(10000*e^18*log(2)^4 - 600*e^9*

log(2)^2 + (100*e^9*log(2)^2 - 3)*e^x + 9) + (100*e^9*log(2)^2 - 3)/(100*e^9*log(2)^2 + e^x - 3) + 6*x/(10000*

e^18*log(2)^4 - 600*e^9*log(2)^2 + 9) - 6*log(100*e^9*log(2)^2 + e^x - 3)/(10000*e^18*log(2)^4 - 600*e^9*log(2

)^2 + 9) + log(100*e^9*log(2)^2 + e^x - 3)/(100*e^9*log(2)^2 - 3) + 6/(10000*e^18*log(2)^4 - 600*e^9*log(2)^2

+ (100*e^9*log(2)^2 - 3)*e^x + 9) + 5/(100*e^9*log(2)^2 + e^x - 3) + log(100*e^9*log(2)^2 + e^x - 3)

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Fricas [A]
time = 0.42, size = 32, normalized size = 1.39 \begin {gather*} \frac {100 \, x e^{9} \log \left (2\right )^{2} + x e^{x} - 2 \, x}{100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3} \end {gather*}

integrate((exp(x)^2+(200*exp(9)*log(2)^2-x-5)*exp(x)+10000*exp(9)^2*log(2)^4-500*exp(9)*log(2)^2+6)/(exp(x)^2+

(200*exp(9)*log(2)^2-6)*exp(x)+10000*exp(9)^2*log(2)^4-600*exp(9)*log(2)^2+9),x, algorithm="fricas")

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Sympy [A]
time = 0.04, size = 17, normalized size = 0.74 \begin {gather*} x + \frac {x}{e^{x} - 3 + 100 e^{9} \log {\left (2 \right )}^{2}} \end {gather*}

integrate((exp(x)**2+(200*exp(9)*ln(2)**2-x-5)*exp(x)+10000*exp(9)**2*ln(2)**4-500*exp(9)*ln(2)**2+6)/(exp(x)*

*2+(200*exp(9)*ln(2)**2-6)*exp(x)+10000*exp(9)**2*ln(2)**4-600*exp(9)*ln(2)**2+9),x)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 359 vs. \(2 (18) = 36\).
time = 0.40, size = 359, normalized size = 15.61 \begin {gather*} \frac {1000000 \, x e^{27} \log \left (2\right )^{6} + 1000000 \, e^{27} \log \left (2\right )^{6} \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) - 1000000 \, e^{27} \log \left (2\right )^{6} \log \left (-100 \, e^{9} \log \left (2\right )^{2} - e^{x} + 3\right ) - 80000 \, x e^{18} \log \left (2\right )^{4} + 10000 \, x e^{\left (x + 18\right )} \log \left (2\right )^{4} - 30000 \, e^{18} \log \left (2\right )^{4} \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) + 10000 \, e^{\left (x + 18\right )} \log \left (2\right )^{4} \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) + 30000 \, e^{18} \log \left (2\right )^{4} \log \left (-100 \, e^{9} \log \left (2\right )^{2} - e^{x} + 3\right ) - 10000 \, e^{\left (x + 18\right )} \log \left (2\right )^{4} \log \left (-100 \, e^{9} \log \left (2\right )^{2} - e^{x} + 3\right ) + 2100 \, x e^{9} \log \left (2\right )^{2} - 600 \, x e^{\left (x + 9\right )} \log \left (2\right )^{2} + 600 \, e^{9} \log \left (2\right )^{2} \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) - 600 \, e^{9} \log \left (2\right )^{2} \log \left (-100 \, e^{9} \log \left (2\right )^{2} - e^{x} + 3\right ) + 9 \, x e^{x} + 6 \, e^{x} \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) - 6 \, e^{x} \log \left (-100 \, e^{9} \log \left (2\right )^{2} - e^{x} + 3\right ) - 18 \, x - 18 \, \log \left (100 \, e^{9} \log \left (2\right )^{2} + e^{x} - 3\right ) + 18 \, \log \left (-100 \, e^{9} \log \left (2\right )^{2} - e^{x} + 3\right )}{1000000 \, e^{27} \log \left (2\right )^{6} - 90000 \, e^{18} \log \left (2\right )^{4} + 10000 \, e^{\left (x + 18\right )} \log \left (2\right )^{4} + 2700 \, e^{9} \log \left (2\right )^{2} - 600 \, e^{\left (x + 9\right )} \log \left (2\right )^{2} + 9 \, e^{x} - 27} \end {gather*}

integrate((exp(x)^2+(200*exp(9)*log(2)^2-x-5)*exp(x)+10000*exp(9)^2*log(2)^4-500*exp(9)*log(2)^2+6)/(exp(x)^2+

(200*exp(9)*log(2)^2-6)*exp(x)+10000*exp(9)^2*log(2)^4-600*exp(9)*log(2)^2+9),x, algorithm="giac")

(1000000*x*e^27*log(2)^6 + 1000000*e^27*log(2)^6*log(100*e^9*log(2)^2 + e^x - 3) - 1000000*e^27*log(2)^6*log(-

100*e^9*log(2)^2 - e^x + 3) - 80000*x*e^18*log(2)^4 + 10000*x*e^(x + 18)*log(2)^4 - 30000*e^18*log(2)^4*log(10

0*e^9*log(2)^2 + e^x - 3) + 10000*e^(x + 18)*log(2)^4*log(100*e^9*log(2)^2 + e^x - 3) + 30000*e^18*log(2)^4*lo

g(-100*e^9*log(2)^2 - e^x + 3) - 10000*e^(x + 18)*log(2)^4*log(-100*e^9*log(2)^2 - e^x + 3) + 2100*x*e^9*log(2

)^2 - 600*x*e^(x + 9)*log(2)^2 + 600*e^9*log(2)^2*log(100*e^9*log(2)^2 + e^x - 3) - 600*e^9*log(2)^2*log(-100*

e^9*log(2)^2 - e^x + 3) + 9*x*e^x + 6*e^x*log(100*e^9*log(2)^2 + e^x - 3) - 6*e^x*log(-100*e^9*log(2)^2 - e^x

+ 3) - 18*x - 18*log(100*e^9*log(2)^2 + e^x - 3) + 18*log(-100*e^9*log(2)^2 - e^x + 3))/(1000000*e^27*log(2)^6

- 90000*e^18*log(2)^4 + 10000*e^(x + 18)*log(2)^4 + 2700*e^9*log(2)^2 - 600*e^(x + 9)*log(2)^2 + 9*e^x - 27)

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Mupad [B]
time = 0.23, size = 18, normalized size = 0.78 \begin {gather*} x+\frac {x}{{\mathrm {e}}^x+100\,{\mathrm {e}}^9\,{\ln \left (2\right )}^2-3} \end {gather*}

int((exp(2*x) - 500*exp(9)*log(2)^2 + 10000*exp(18)*log(2)^4 - exp(x)*(x - 200*exp(9)*log(2)^2 + 5) + 6)/(exp(

2*x) + exp(x)*(200*exp(9)*log(2)^2 - 6) - 600*exp(9)*log(2)^2 + 10000*exp(18)*log(2)^4 + 9),x)

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3.12.1 \(\int \frac {6+e^{2 x}-125 e^9 \log ^2(4)+625 e^{18} \log ^4(4)+e^x (-5-x+50 e^9 \log ^2(4))}{9+e^{2 x}-150 e^9 \log ^2(4)+625 e^{18} \log ^4(4)+e^x (-6+50 e^9 \log ^2(4))} \, dx\) [1101]