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

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

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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} $$\begin{array}{c}\frac{e^x\log \left(\frac{x}{\log (\frac{\log (x-2)}{x\log \left(x^2\right)}+x)}\right)}{x}\end{array}$$

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{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^x(-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)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})-(2-3x+x^2)\log \left(x^2\right)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})\log \left(\frac{x}{\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}\right))}{(2-x)x^2\log \left(x^2\right)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}dx\\ & =\int (\frac{e^x(-4\log (-2+x)+2x\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)+2x^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 (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})+x\log (-2+x)\log \left(x^2\right)\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})-2x^2{\log }^2\left(x^2\right)\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})+x^3{\log }^2\left(x^2\right)\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)}))}{(-2+x)x^2\log \left(x^2\right)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}+\frac{e^x(-1+x)\log \left(\frac{x}{\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}\right)}{x^2})dx\\ & =\int \frac{e^x(-4\log (-2+x)+2x\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)+2x^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 (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})+x\log (-2+x)\log \left(x^2\right)\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})-2x^2{\log }^2\left(x^2\right)\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})+x^3{\log }^2\left(x^2\right)\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)}))}{(-2+x)x^2\log \left(x^2\right)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}dx+\int \frac{e^x(-1+x)\log \left(\frac{x}{\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}\right)}{x^2}dx\\ & =\frac{e^x\log \left(\frac{x}{\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}\right)}{x}+\int \frac{e^x(-x\log \left(x^2\right)(-1+(-2+x)x\log \left(x^2\right)(-1+\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})))-(-2+x)\log (-2+x)(2+\log \left(x^2\right)(1+\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)}))))}{(2-x)x^2\log \left(x^2\right)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}dx-\int \frac{e^x(x\log \left(x^2\right)(-1+(-2+x)x\log \left(x^2\right)(-1+\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})))+(-2+x)\log (-2+x)(2+\log \left(x^2\right)(1+\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)}))))}{(-2+x)x^2\log \left(x^2\right)(\log (-2+x)+x^2\log \left(x^2\right))\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}dx\\ & =\frac{e^x\log \left(\frac{x}{\log (x+\frac{\log (-2+x)}{x\log \left(x^2\right)})}\right)}{x}\end{array}\end{array}$$

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

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 $$\begin{array}{c}\frac{e^x\log \left(\frac{x}{\log \left(\frac{x^2\log \left(x^2\right)+\log (x-2)}{x\log \left(x^2\right)}\right)}\right)}{x}\end{array}$$

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 $$\begin{array}{c}\frac{e^x\log (x)-e^x\log (-\log (2)+\log (2x^2\log (x)+\log (x-2))-\log (x)-\log (\log (x)))}{x}\end{array}$$

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 $$\begin{array}{c}\int -\frac{\ln \left(\frac{x}{\ln \left(\frac{\ln (x-2)+x^2\ln \left(x^2\right)}{x\ln \left(x^2\right)}\right)}\right)\ln \left(\frac{\ln (x-2)+x^2\ln \left(x^2\right)}{x\ln \left(x^2\right)}\right)({\mathrm{e}}^x(x^4-3x^3+2x^2){\ln \left(x^2\right)}^2+\ln (x-2){\mathrm{e}}^x(x^2-3x+2)\ln \left(x^2\right))-\ln \left(\frac{\ln (x-2)+x^2\ln \left(x^2\right)}{x\ln \left(x^2\right)}\right)({\ln \left(x^2\right)}^2{\mathrm{e}}^x(2x^2-x^3)-\ln (x-2)\ln \left(x^2\right){\mathrm{e}}^x(x-2))-\ln \left(x^2\right)(x{\mathrm{e}}^x-\ln (x-2){\mathrm{e}}^x(x-2))+{\ln \left(x^2\right)}^2{\mathrm{e}}^x(2x^2-x^3)+\ln (x-2){\mathrm{e}}^x(2x-4)}{\ln \left(\frac{\ln (x-2)+x^2\ln \left(x^2\right)}{x\ln \left(x^2\right)}\right)((2x^4-x^5){\ln \left(x^2\right)}^2+\ln (x-2)(2x^2-x^3)\ln \left(x^2\right))}dx\end{array}$$

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 $$\begin{array}{c}\text{Timed out}\end{array}$$

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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