3.73.63 \(\int \frac {e^x (-4+2 x) \log (-2+x)+(-e^x x+e^x (-2+x) \log (-2+x)) \log (x^2)+e^x (2 x^2-x^3) \log ^2(x^2)+(e^x (-2+x) \log (-2+x) \log (x^2)+e^x (-2 x^2+x^3) \log ^2(x^2)) \log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)})+(e^x (2-3 x+x^2) \log (-2+x) \log (x^2)+e^x (2 x^2-3 x^3+x^4) \log ^2(x^2)) \log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)}) \log (\frac {x}{\log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)})})}{((-2 x^2+x^3) \log (-2+x) \log (x^2)+(-2 x^4+x^5) \log ^2(x^2)) \log (\frac {\log (-2+x)+x^2 \log (x^2)}{x \log (x^2)})} \, dx\) [7263]
Optimal. Leaf size=29 \[ \frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x} \]
[Out]
exp(x)/x*ln(x/ln(ln(-2+x)/x/ln(x^2)+x))
________________________________________________________________________________________
Rubi [A]
time = 118.69, 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 = {6820, 6874,
2208, 2209, 2228, 2635} \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 2208
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] && !TrueQ[$UseGamm
a]
Rule 2209
Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - c*(f/d)))/d)*ExpInteg
ralEi[f*g*(c + d*x)*(Log[F]/d)], x] /; FreeQ[{F, c, d, e, f, g}, x] && !TrueQ[$UseGamma]
Rule 2228
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 2635
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 6820
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rule 6874
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*}
________________________________________________________________________________________
Mathematica [A]
time = 0.52, 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
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 17.22, 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
________________________________________________________________________________________
Maxima [A]
time = 0.62, size = 42, normalized size = 1.45 \begin {gather*} \frac {e^{x} \log \left (x\right ) - e^{x} \log \left (-\log \left (2\right ) + \log \left (2 \, x^{2} \log \left (x\right ) + \log \left (x - 2\right )\right ) - \log \left (x\right ) - \log \left (\log \left (x\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(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-
2+x))/x/log(x^2))*log(x/log((x^2*log(x^2)+log(-2+x))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(-2+x)*exp(x)
*log(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))+(-x^3+2*x^2)*exp(x)*log(x^2)^2+((-2+x)*exp(x)*lo
g(-2+x)-exp(x)*x)*log(x^2)+(2*x-4)*exp(x)*log(-2+x))/((x^5-2*x^4)*log(x^2)^2+(x^3-2*x^2)*log(-2+x)*log(x^2))/l
og((x^2*log(x^2)+log(-2+x))/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
________________________________________________________________________________________
Fricas [A]
time = 0.40, 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(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-
2+x))/x/log(x^2))*log(x/log((x^2*log(x^2)+log(-2+x))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(-2+x)*exp(x)
*log(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))+(-x^3+2*x^2)*exp(x)*log(x^2)^2+((-2+x)*exp(x)*lo
g(-2+x)-exp(x)*x)*log(x^2)+(2*x-4)*exp(x)*log(-2+x))/((x^5-2*x^4)*log(x^2)^2+(x^3-2*x^2)*log(-2+x)*log(x^2))/l
og((x^2*log(x^2)+log(-2+x))/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
________________________________________________________________________________________
Sympy [F(-1)] Timed out
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(-2+x)*ln(x**2))*ln((x**2*ln(x**2)+l
n(-2+x))/x/ln(x**2))*ln(x/ln((x**2*ln(x**2)+ln(-2+x))/x/ln(x**2)))+((x**3-2*x**2)*exp(x)*ln(x**2)**2+(-2+x)*ex
p(x)*ln(-2+x)*ln(x**2))*ln((x**2*ln(x**2)+ln(-2+x))/x/ln(x**2))+(-x**3+2*x**2)*exp(x)*ln(x**2)**2+((-2+x)*exp(
x)*ln(-2+x)-exp(x)*x)*ln(x**2)+(2*x-4)*exp(x)*ln(-2+x))/((x**5-2*x**4)*ln(x**2)**2+(x**3-2*x**2)*ln(-2+x)*ln(x
**2))/ln((x**2*ln(x**2)+ln(-2+x))/x/ln(x**2)),x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 2231 vs.
\(2 (28) = 56\).
time = 6.17, size = 2231, normalized size = 76.93 \begin {gather*} \text {Too large to display} \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(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-
2+x))/x/log(x^2))*log(x/log((x^2*log(x^2)+log(-2+x))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(-2+x)*exp(x)
*log(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))+(-x^3+2*x^2)*exp(x)*log(x^2)^2+((-2+x)*exp(x)*lo
g(-2+x)-exp(x)*x)*log(x^2)+(2*x-4)*exp(x)*log(-2+x))/((x^5-2*x^4)*log(x^2)^2+(x^3-2*x^2)*log(-2+x)*log(x^2))/l
og((x^2*log(x^2)+log(-2+x))/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(...
________________________________________________________________________________________
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)
________________________________________________________________________________________