∫ ex(−4+2x) log(−2+x)+(−exx+ex(−2+x) log(−2+x)) log(x2)+ex(2x2−x3) log2(x2)+(ex(−2+x) log(−2+x) log(x2)+ex(−2x2+x3) log2(x2)) log(log(−2+x)+x2 log(x2) x log(x2) )+(ex(2−3x+x2) log(−2+x) log(x2)+ex(2x2−3x3+x4) log2(x2)) log(log(−2+x)+x2 log(x2) x log(x2) ) log( x______________ log (log(−2+x)+x2 log(x2) x log(x2) )) ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ((−2x2+x3) log(−2+x) log(x2)+(−2x4+x5) log2(x2)) log(log(−2+x)+x2 log(x2) x log(x2) ) dx

3.73.63 $\int \frac {e^x (-4+2 x) \log (-2+x)+(-e^x x+e^x (-2+x) \log (-2+x)) \log (x^2)+e^x (2 x^2-x^3) \log ^2(x^2)+(e^x (-2+x) \log (-2+x) \log (x^2)+e^x (-2 x^2+x^3) \log ^2(x^2)) \log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)})+(e^x (2-3 x+x^2) \log (-2+x) \log (x^2)+e^x (2 x^2-3 x^3+x^4) \log ^2(x^2)) \log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)}) \log (\frac {x}{\log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)})})}{((-2 x^2+x^3) \log (-2+x) \log (x^2)+(-2 x^4+x^5) \log ^2(x^2)) \log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)})} \, dx$

Optimal. Leaf size=29 \[ \frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x} \]

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Rubi [A] time = 116.15, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 57, number of rules used = 6, integrand size = 281, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.021, Rules used = {6688, 6742, 2177, 2178, 2197, 2555} \begin {gather*} \frac {e^x \log \left (\frac {x}{\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )}{x} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

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

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

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

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

[Out]

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

Rule 2177

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

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

(e + f*x)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && LtQ[m, -1] && IntegerQ[2*m] && !$UseGamma ===

True

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral

Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] && !$UseGamma === True

Rule 2197

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> With[{b = Coefficient[v, x, 1], d = Coefficient[u, x, 0],

e = Coefficient[u, x, 1], f = Coefficient[w, x, 0], g = Coefficient[w, x, 1]}, Simp[(g*u^(m + 1)*F^(c*v))/(b*c

*e*Log[F]), x] /; EqQ[e*g*(m + 1) - b*c*(e*f - d*g)*Log[F], 0]] /; FreeQ[{F, c, m}, x] && LinearQ[{u, v, w}, x

]

Rule 2555

Int[Log[u_]*(v_), x_Symbol] :> With[{w = IntHide[v, x]}, Dist[Log[u], w, x] - Int[SimplifyIntegrand[w*Simplify

[D[u, x]/u], x], x] /; InverseFunctionFreeQ[w, x]] /; ProductQ[u]

Rule 6688

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

Rule 6742

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (-2 (-2+x) \log (-2+x)-(-x+(-2+x) \log (-2+x)) \log \left (x^2\right )+(-2+x) x^2 \log ^2\left (x^2\right )-(-2+x) \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )-\left (2-3 x+x^2\right ) \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )\right )}{(2-x) x^2 \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )} \, dx\\ &=\int \left (\frac {e^x \left (-4 \log (-2+x)+2 x \log (-2+x)-x \log \left (x^2\right )-2 \log (-2+x) \log \left (x^2\right )+x \log (-2+x) \log \left (x^2\right )+2 x^2 \log ^2\left (x^2\right )-x^3 \log ^2\left (x^2\right )-2 \log (-2+x) \log \left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )+x \log (-2+x) \log \left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )-2 x^2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )+x^3 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )\right )}{(-2+x) x^2 \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}+\frac {e^x (-1+x) \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x^2}\right ) \, dx\\ &=\int \frac {e^x \left (-4 \log (-2+x)+2 x \log (-2+x)-x \log \left (x^2\right )-2 \log (-2+x) \log \left (x^2\right )+x \log (-2+x) \log \left (x^2\right )+2 x^2 \log ^2\left (x^2\right )-x^3 \log ^2\left (x^2\right )-2 \log (-2+x) \log \left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )+x \log (-2+x) \log \left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )-2 x^2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )+x^3 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )\right )}{(-2+x) x^2 \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )} \, dx+\int \frac {e^x (-1+x) \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x^2} \, dx\\ &=\frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x}+\int \frac {e^x \left (-x \log \left (x^2\right ) \left (-1+(-2+x) x \log \left (x^2\right ) \left (-1+\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )\right )\right )-(-2+x) \log (-2+x) \left (2+\log \left (x^2\right ) \left (1+\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )\right )\right )\right )}{(2-x) x^2 \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )} \, dx-\int \frac {e^x \left (x \log \left (x^2\right ) \left (-1+(-2+x) x \log \left (x^2\right ) \left (-1+\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )\right )\right )+(-2+x) \log (-2+x) \left (2+\log \left (x^2\right ) \left (1+\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )\right )\right )\right )}{(-2+x) x^2 \log \left (x^2\right ) \left (\log (-2+x)+x^2 \log \left (x^2\right )\right ) \log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )} \, dx\\ &=\frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.48, size = 29, normalized size = 1.00 \begin {gather*} \frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

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

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

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

g[-2 + x]*Log[x^2] + (-2*x^4 + x^5)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2])/(x*Log[x^2])]),x]

[Out]

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

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fricas [A] time = 0.68, size = 35, normalized size = 1.21 \begin {gather*} \frac {e^{x} \log \left (\frac {x}{\log \left (\frac {x^{2} \log \left (x^{2}\right ) + \log \left (x - 2\right )}{x \log \left (x^{2}\right )}\right )}\right )}{x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^4-3*x^3+2*x^2)*exp(x)*log(x^2)^2+(x^2-3*x+2)*exp(x)*log(x-2)*log(x^2))*log((x^2*log(x^2)+log(x-

2))/x/log(x^2))*log(x/log((x^2*log(x^2)+log(x-2))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(x-2)*exp(x)*log

(x-2)*log(x^2))*log((x^2*log(x^2)+log(x-2))/x/log(x^2))+(-x^3+2*x^2)*exp(x)*log(x^2)^2+((x-2)*exp(x)*log(x-2)-

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

g(x^2)+log(x-2))/x/log(x^2)),x, algorithm="fricas")

[Out]

e^x*log(x/log((x^2*log(x^2) + log(x - 2))/(x*log(x^2))))/x

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giac [B] time = 14.03, size = 2231, normalized size = 76.93 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^4-3*x^3+2*x^2)*exp(x)*log(x^2)^2+(x^2-3*x+2)*exp(x)*log(x-2)*log(x^2))*log((x^2*log(x^2)+log(x-

2))/x/log(x^2))*log(x/log((x^2*log(x^2)+log(x-2))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(x-2)*exp(x)*log

(x-2)*log(x^2))*log((x^2*log(x^2)+log(x-2))/x/log(x^2))+(-x^3+2*x^2)*exp(x)*log(x^2)^2+((x-2)*exp(x)*log(x-2)-

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

g(x^2)+log(x-2))/x/log(x^2)),x, algorithm="giac")

[Out]

-1/2*(e^x*log(-1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2)

)*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn(x^2*log(x^2) + log(abs(x - 2)))*sgn(log(x^2)) + 1/2*p

i^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(-pi + 2*pi*flo

or(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn(x^2*log(x^2) + log(abs(x - 2))) + 1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*

sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x^2*log(x^2) + log(abs(x - 2)))*sgn(x) + 1/2*pi^

2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(-pi + 2*pi*floor

(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn(log(x^2)) - 1/2*pi^2*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn

(x)*sgn(log(x^2)) - 1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x

- 2))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x)) - 1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1)

+ 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x^2*log(x^2) + log(abs(x - 2))) - pi*arctan(-1/2*(pi - 4*pi

*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2))/(x^2*log(x^2) + log(abs(x - 2))))*sg

n(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x^2*log(x^2) + log(a

bs(x - 2))) + pi*arctan(-(pi - 2*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2))*sgn(-pi + 4*pi*x^2*floor(-1/

2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x^2*log(x^2) + log(abs(x - 2))) - 1/2*pi^2*sgn

(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x) + 1/2*pi^2*sgn(-pi

+ 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn(x) + 1/2*pi^2*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x

))*sgn(log(x^2)) + pi*arctan(-1/2*(pi - 4*pi*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(

x - 2))/(x^2*log(x^2) + log(abs(x - 2))))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn(log(x^2)) - p

i*arctan(-(pi - 2*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*

sgn(x))*sgn(log(x^2)) + 1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*s

gn(x - 2)) + pi*arctan(-1/2*(pi - 4*pi*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2)

)/(x^2*log(x^2) + log(abs(x - 2))))*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + p

i*sgn(x - 2)) - pi*arctan(-(pi - 2*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2))*sgn(-pi + 4*pi*x^2*floor(-

1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2)) - 1/2*pi^2*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1)

+ pi*sgn(x)) - pi*arctan(-1/2*(pi - 4*pi*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x -

2))/(x^2*log(x^2) + log(abs(x - 2))))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x)) + pi*arctan(-(pi - 2

*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x)) - 1/2*pi^

2*sgn(x^2*log(x^2) + log(abs(x - 2))) - 1/2*pi^2*sgn(x) - pi*arctan(-1/2*(pi - 4*pi*x^2*floor(-1/2*sgn(x) + 1)

- 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2))/(x^2*log(x^2) + log(abs(x - 2))))*sgn(x) + pi*arctan(-(pi - 2*p

i*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2))*sgn(x) - 1/2*pi^2*sgn(log(x^2)) + 3/2*pi^2 + pi*arctan(-1/2*(p

i - 4*pi*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2))/(x^2*log(x^2) + log(abs(x -

2)))) + arctan(-1/2*(pi - 4*pi*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2))/(x^2*l

og(x^2) + log(abs(x - 2))))^2 - pi*arctan(-(pi - 2*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2)) - 2*arctan

(-1/2*(pi - 4*pi*x^2*floor(-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2))/(x^2*log(x^2) + log(

abs(x - 2))))*arctan(-(pi - 2*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2)) + arctan(-(pi - 2*pi*floor(-1/2

*sgn(x) + 1) - pi*sgn(x))/log(x^2))^2 + 1/4*log(4*pi^2*x^4*floor(-1/2*sgn(x) + 1)^2 + 4*pi^2*x^4*floor(-1/2*sg

n(x) + 1)*sgn(x) - 4*pi^2*x^4*floor(-1/2*sgn(x) + 1) - 2*pi^2*x^4*sgn(x) + 2*pi^2*x^4 + x^4*log(x^2)^2 + 2*pi^

2*x^2*floor(-1/2*sgn(x) + 1)*sgn(x - 2) + pi^2*x^2*sgn(x - 2)*sgn(x) - 2*pi^2*x^2*floor(-1/2*sgn(x) + 1) - pi^

2*x^2*sgn(x - 2) - pi^2*x^2*sgn(x) + pi^2*x^2 + 2*x^2*log(x^2)*log(abs(x - 2)) - 1/2*pi^2*sgn(x - 2) + 1/2*pi^

2 + log(abs(x - 2))^2)^2 - log(4*pi^2*x^4*floor(-1/2*sgn(x) + 1)^2 + 4*pi^2*x^4*floor(-1/2*sgn(x) + 1)*sgn(x)

- 4*pi^2*x^4*floor(-1/2*sgn(x) + 1) - 2*pi^2*x^4*sgn(x) + 2*pi^2*x^4 + x^4*log(x^2)^2 + 2*pi^2*x^2*floor(-1/2*

sgn(x) + 1)*sgn(x - 2) + pi^2*x^2*sgn(x - 2)*sgn(x) - 2*pi^2*x^2*floor(-1/2*sgn(x) + 1) - pi^2*x^2*sgn(x - 2)

- pi^2*x^2*sgn(x) + pi^2*x^2 + 2*x^2*log(x^2)*log(abs(x - 2)) - 1/2*pi^2*sgn(x - 2) + 1/2*pi^2 + log(abs(x - 2

))^2)*log(abs(x)) + log(abs(x))^2 - log(4*pi^2*x^4*floor(-1/2*sgn(x) + 1)^2 + 4*pi^2*x^4*floor(-1/2*sgn(x) + 1

)*sgn(x) - 4*pi^2*x^4*floor(-1/2*sgn(x) + 1) - 2*pi^2*x^4*sgn(x) + 2*pi^2*x^4 + x^4*log(x^2)^2 + 2*pi^2*x^2*fl

oor(-1/2*sgn(x) + 1)*sgn(x - 2) + pi^2*x^2*sgn(x - 2)*sgn(x) - 2*pi^2*x^2*floor(-1/2*sgn(x) + 1) - pi^2*x^2*sg

n(x - 2) - pi^2*x^2*sgn(x) + pi^2*x^2 + 2*x^2*log(x^2)*log(abs(x - 2)) - 1/2*pi^2*sgn(x - 2) + 1/2*pi^2 + log(

abs(x - 2))^2)*log(abs(log(x^2))) + 2*log(abs(x))*log(abs(log(x^2))) + log(abs(log(x^2)))^2) - 2*e^x*log(abs(x

)))/x

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maple [C] time = 6.43, size = 22245, normalized size = 767.07


method	result	size

risch	$\text {Expression too large to display}$	$22245$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

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

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

xp(x)*ln(x-2))/((x^5-2*x^4)*ln(x^2)^2+(x^3-2*x^2)*ln(x-2)*ln(x^2))/ln((x^2*ln(x^2)+ln(x-2))/x/ln(x^2)),x,metho

d=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [A] time = 0.58, size = 42, normalized size = 1.45 \begin {gather*} \frac {e^{x} \log \relax (x) - e^{x} \log \left (-\log \relax (2) + \log \left (2 \, x^{2} \log \relax (x) + \log \left (x - 2\right )\right ) - \log \relax (x) - \log \left (\log \relax (x)\right )\right )}{x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^4-3*x^3+2*x^2)*exp(x)*log(x^2)^2+(x^2-3*x+2)*exp(x)*log(x-2)*log(x^2))*log((x^2*log(x^2)+log(x-

2))/x/log(x^2))*log(x/log((x^2*log(x^2)+log(x-2))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(x-2)*exp(x)*log

(x-2)*log(x^2))*log((x^2*log(x^2)+log(x-2))/x/log(x^2))+(-x^3+2*x^2)*exp(x)*log(x^2)^2+((x-2)*exp(x)*log(x-2)-

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

g(x^2)+log(x-2))/x/log(x^2)),x, algorithm="maxima")

[Out]

(e^x*log(x) - e^x*log(-log(2) + log(2*x^2*log(x) + log(x - 2)) - log(x) - log(log(x))))/x

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \left (\frac {x}{\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )}\right )\,\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )\,\left ({\mathrm {e}}^x\,\left (x^4-3\,x^3+2\,x^2\right )\,{\ln \left (x^2\right )}^2+\ln \left (x-2\right )\,{\mathrm {e}}^x\,\left (x^2-3\,x+2\right )\,\ln \left (x^2\right )\right )-\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )\,\left ({\ln \left (x^2\right )}^2\,{\mathrm {e}}^x\,\left (2\,x^2-x^3\right )-\ln \left (x-2\right )\,\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (x-2\right )\right )-\ln \left (x^2\right )\,\left (x\,{\mathrm {e}}^x-\ln \left (x-2\right )\,{\mathrm {e}}^x\,\left (x-2\right )\right )+{\ln \left (x^2\right )}^2\,{\mathrm {e}}^x\,\left (2\,x^2-x^3\right )+\ln \left (x-2\right )\,{\mathrm {e}}^x\,\left (2\,x-4\right )}{\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )\,\left (\left (2\,x^4-x^5\right )\,{\ln \left (x^2\right )}^2+\ln \left (x-2\right )\,\left (2\,x^2-x^3\right )\,\ln \left (x^2\right )\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x/log((log(x - 2) + x^2*log(x^2))/(x*log(x^2))))*log((log(x - 2) + x^2*log(x^2))/(x*log(x^2)))*(log(

x^2)^2*exp(x)*(2*x^2 - 3*x^3 + x^4) + log(x - 2)*log(x^2)*exp(x)*(x^2 - 3*x + 2)) - log((log(x - 2) + x^2*log(

x^2))/(x*log(x^2)))*(log(x^2)^2*exp(x)*(2*x^2 - x^3) - log(x - 2)*log(x^2)*exp(x)*(x - 2)) - log(x^2)*(x*exp(x

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

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

[Out]

int(-(log(x/log((log(x - 2) + x^2*log(x^2))/(x*log(x^2))))*log((log(x - 2) + x^2*log(x^2))/(x*log(x^2)))*(log(

x^2)^2*exp(x)*(2*x^2 - 3*x^3 + x^4) + log(x - 2)*log(x^2)*exp(x)*(x^2 - 3*x + 2)) - log((log(x - 2) + x^2*log(

x^2))/(x*log(x^2)))*(log(x^2)^2*exp(x)*(2*x^2 - x^3) - log(x - 2)*log(x^2)*exp(x)*(x - 2)) - log(x^2)*(x*exp(x

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

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

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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**4-3*x**3+2*x**2)*exp(x)*ln(x**2)**2+(x**2-3*x+2)*exp(x)*ln(x-2)*ln(x**2))*ln((x**2*ln(x**2)+ln

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

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

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

x**2*ln(x**2)+ln(x-2))/x/ln(x**2)),x)

[Out]

Timed out

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