∫ (−12x2−2exx2) log(x)+2x2 log(x) log( 3____ x log(x))+e9+log2(6+ex−log( 3____xlog (x))) (6+(6+6exx) log(x)+(−2+(−2−2exx) log(x)) log(6+ex−log( 3____xlog (x)))) _____________________________________________________________________________________________________________________________________ (6+ex−log( 3____xlog (x)))6 ______________________________________________________________________________________________________________________________________________________________________________________________________________(−6x−ex x) log(x)+x log(x) log( 3___

3.53.97 \(\int \frac {(-12 x^2-2 e^x x^2) \log (x)+2 x^2 \log (x) \log (\frac {3}{x \log (x)})+\frac {e^{9+\log ^2(6+e^x-\log (\frac {3}{x \log (x)}))} (6+(6+6 e^x x) \log (x)+(-2+(-2-2 e^x x) \log (x)) \log (6+e^x-\log (\frac {3}{x \log (x)})))}{(6+e^x-\log (\frac {3}{x \log (x)}))^6}}{(-6 x-e^x x) \log (x)+x \log (x) \log (\frac {3}{x \log (x)})} \, dx\)

Optimal. Leaf size=29 \[ 5+e^{\left (-3+\log \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )\right )^2}+x^2 \]

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Rubi [B] time = 10.94, antiderivative size = 93, normalized size of antiderivative = 3.21, number of steps used = 4, number of rules used = 3, integrand size = 155, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6741, 6742, 2288} \begin {gather*} x^2+\frac {e^{\log ^2\left (e^x-\log \left (\frac {3}{x \log (x)}\right )+6\right )+9} \left (e^x x \log (x)+\log (x)+1\right )}{x \log (x) \left (x \left (\frac {1}{x^2 \log ^2(x)}+\frac {1}{x^2 \log (x)}\right ) \log (x)+e^x\right ) \left (e^x-\log \left (\frac {3}{x \log (x)}\right )+6\right )^6} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[((-12*x^2 - 2*E^x*x^2)*Log[x] + 2*x^2*Log[x]*Log[3/(x*Log[x])] + (E^(9 + Log[6 + E^x - Log[3/(x*Log[x])]]^

2)*(6 + (6 + 6*E^x*x)*Log[x] + (-2 + (-2 - 2*E^x*x)*Log[x])*Log[6 + E^x - Log[3/(x*Log[x])]]))/(6 + E^x - Log[

3/(x*Log[x])])^6)/((-6*x - E^x*x)*Log[x] + x*Log[x]*Log[3/(x*Log[x])]),x]

[Out]

x^2 + (E^(9 + Log[6 + E^x - Log[3/(x*Log[x])]]^2)*(1 + Log[x] + E^x*x*Log[x]))/(x*Log[x]*(E^x + x*(1/(x^2*Log[

x]^2) + 1/(x^2*Log[x]))*Log[x])*(6 + E^x - Log[3/(x*Log[x])])^6)

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,

x], w*y]] /; FreeQ[F, x]

Rule 6741

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

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 {-\left (\left (-12 x^2-2 e^x x^2\right ) \log (x)\right )-2 x^2 \log (x) \log \left (\frac {3}{x \log (x)}\right )-\frac {e^{9+\log ^2\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )} \left (6+\left (6+6 e^x x\right ) \log (x)+\left (-2+\left (-2-2 e^x x\right ) \log (x)\right ) \log \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )\right )}{\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )^6}}{x \log (x) \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )} \, dx\\ &=\int \left (2 x+\frac {2 e^{9+\log ^2\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )} \left (1+\log (x)+e^x x \log (x)\right ) \left (-3+\log \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )\right )}{x \log (x) \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )^7}\right ) \, dx\\ &=x^2+2 \int \frac {e^{9+\log ^2\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )} \left (1+\log (x)+e^x x \log (x)\right ) \left (-3+\log \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )\right )}{x \log (x) \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )^7} \, dx\\ &=x^2+\frac {e^{9+\log ^2\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )} \left (1+\log (x)+e^x x \log (x)\right )}{x \log (x) \left (e^x+x \left (\frac {1}{x^2 \log ^2(x)}+\frac {1}{x^2 \log (x)}\right ) \log (x)\right ) \left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )^6}\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.45, size = 48, normalized size = 1.66 \begin {gather*} x^2+\frac {e^{9+\log ^2\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )}}{\left (6+e^x-\log \left (\frac {3}{x \log (x)}\right )\right )^6} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((-12*x^2 - 2*E^x*x^2)*Log[x] + 2*x^2*Log[x]*Log[3/(x*Log[x])] + (E^(9 + Log[6 + E^x - Log[3/(x*Log[

x])]]^2)*(6 + (6 + 6*E^x*x)*Log[x] + (-2 + (-2 - 2*E^x*x)*Log[x])*Log[6 + E^x - Log[3/(x*Log[x])]]))/(6 + E^x

- Log[3/(x*Log[x])])^6)/((-6*x - E^x*x)*Log[x] + x*Log[x]*Log[3/(x*Log[x])]),x]

[Out]

x^2 + E^(9 + Log[6 + E^x - Log[3/(x*Log[x])]]^2)/(6 + E^x - Log[3/(x*Log[x])])^6

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fricas [A] time = 0.55, size = 45, normalized size = 1.55 \begin {gather*} x^{2} + e^{\left (\log \left (e^{x} - \log \left (\frac {3}{x \log \relax (x)}\right ) + 6\right )^{2} - 6 \, \log \left (e^{x} - \log \left (\frac {3}{x \log \relax (x)}\right ) + 6\right ) + 9\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*exp(x)*x-2)*log(x)-2)*log(-log(3/x/log(x))+exp(x)+6)+(6*exp(x)*x+6)*log(x)+6)*exp(log(-log(3/

x/log(x))+exp(x)+6)^2-6*log(-log(3/x/log(x))+exp(x)+6)+9)+2*x^2*log(x)*log(3/x/log(x))+(-2*exp(x)*x^2-12*x^2)*

log(x))/(x*log(x)*log(3/x/log(x))+(-exp(x)*x-6*x)*log(x)),x, algorithm="fricas")

[Out]

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

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*exp(x)*x-2)*log(x)-2)*log(-log(3/x/log(x))+exp(x)+6)+(6*exp(x)*x+6)*log(x)+6)*exp(log(-log(3/

x/log(x))+exp(x)+6)^2-6*log(-log(3/x/log(x))+exp(x)+6)+9)+2*x^2*log(x)*log(3/x/log(x))+(-2*exp(x)*x^2-12*x^2)*

log(x))/(x*log(x)*log(3/x/log(x))+(-exp(x)*x-6*x)*log(x)),x, algorithm="giac")

[Out]

undef

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maple [C] time = 0.31, size = 156, normalized size = 5.38


method	result	size

risch	\(x^{2}+\frac {{\mathrm e}^{9} {\mathrm e}^{\ln \left (-\ln \relax (3)+\ln \relax (x )+\ln \left (\ln \relax (x )\right )+\frac {i \pi \,\mathrm {csgn}\left (\frac {i}{x \ln \relax (x )}\right ) \left (-\mathrm {csgn}\left (\frac {i}{x \ln \relax (x )}\right )+\mathrm {csgn}\left (\frac {i}{x}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i}{x \ln \relax (x )}\right )+\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right )\right )}{2}+6+{\mathrm e}^{x}\right )^{2}}}{\left (-\ln \relax (3)+\ln \relax (x )+\ln \left (\ln \relax (x )\right )+\frac {i \pi \,\mathrm {csgn}\left (\frac {i}{x \ln \relax (x )}\right ) \left (-\mathrm {csgn}\left (\frac {i}{x \ln \relax (x )}\right )+\mathrm {csgn}\left (\frac {i}{x}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i}{x \ln \relax (x )}\right )+\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right )\right )}{2}+6+{\mathrm e}^{x}\right )^{6}}\)	\(156\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((((-2*exp(x)*x-2)*ln(x)-2)*ln(-ln(3/x/ln(x))+exp(x)+6)+(6*exp(x)*x+6)*ln(x)+6)*exp(ln(-ln(3/x/ln(x))+exp(

x)+6)^2-6*ln(-ln(3/x/ln(x))+exp(x)+6)+9)+2*x^2*ln(x)*ln(3/x/ln(x))+(-2*exp(x)*x^2-12*x^2)*ln(x))/(x*ln(x)*ln(3

/x/ln(x))+(-exp(x)*x-6*x)*ln(x)),x,method=_RETURNVERBOSE)

[Out]

x^2+1/(-ln(3)+ln(x)+ln(ln(x))+1/2*I*Pi*csgn(I/x/ln(x))*(-csgn(I/x/ln(x))+csgn(I/x))*(-csgn(I/x/ln(x))+csgn(I/l

n(x)))+6+exp(x))^6*exp(9)*exp(ln(-ln(3)+ln(x)+ln(ln(x))+1/2*I*Pi*csgn(I/x/ln(x))*(-csgn(I/x/ln(x))+csgn(I/x))*

(-csgn(I/x/ln(x))+csgn(I/ln(x)))+6+exp(x))^2)

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maxima [B] time = 0.73, size = 2490, normalized size = 85.86 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*exp(x)*x-2)*log(x)-2)*log(-log(3/x/log(x))+exp(x)+6)+(6*exp(x)*x+6)*log(x)+6)*exp(log(-log(3/

x/log(x))+exp(x)+6)^2-6*log(-log(3/x/log(x))+exp(x)+6)+9)+2*x^2*log(x)*log(3/x/log(x))+(-2*exp(x)*x^2-12*x^2)*

log(x))/(x*log(x)*log(3/x/log(x))+(-exp(x)*x-6*x)*log(x)),x, algorithm="maxima")

[Out]

-(6*x^2*(log(3) - 6)*log(x)^5 - x^2*log(x)^6 - x^2*log(log(x))^6 - 15*(log(3)^2 - 12*log(3) + 36)*x^2*log(x)^4

+ 20*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*x^2*log(x)^3 + 6*(x^2*(log(3) - 6) - x^2*e^x - x^2*log(x))*l

og(log(x))^5 - 15*(log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 864*log(3) + 1296)*x^2*log(x)^2 + 15*(2*x^2*(log(3)

- 6)*log(x) - x^2*log(x)^2 - (log(3)^2 - 12*log(3) + 36)*x^2 - x^2*e^(2*x) + 2*(x^2*(log(3) - 6) - x^2*log(x)

)*e^x)*log(log(x))^4 + 6*(log(3)^5 - 30*log(3)^4 + 360*log(3)^3 - 2160*log(3)^2 + 6480*log(3) - 7776)*x^2*log(

x) + 20*(3*x^2*(log(3) - 6)*log(x)^2 - x^2*log(x)^3 - 3*(log(3)^2 - 12*log(3) + 36)*x^2*log(x) + (log(3)^3 - 1

8*log(3)^2 + 108*log(3) - 216)*x^2 - x^2*e^(3*x) + 3*(x^2*(log(3) - 6) - x^2*log(x))*e^(2*x) + 3*(2*x^2*(log(3

) - 6)*log(x) - x^2*log(x)^2 - (log(3)^2 - 12*log(3) + 36)*x^2)*e^x)*log(log(x))^3 - (log(3)^6 - 36*log(3)^5 +

540*log(3)^4 - 4320*log(3)^3 + 19440*log(3)^2 - 46656*log(3) + 46656)*x^2 - x^2*e^(6*x) + 15*(4*x^2*(log(3) -

6)*log(x)^3 - x^2*log(x)^4 - 6*(log(3)^2 - 12*log(3) + 36)*x^2*log(x)^2 + 4*(log(3)^3 - 18*log(3)^2 + 108*log

(3) - 216)*x^2*log(x) - (log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 864*log(3) + 1296)*x^2 - x^2*e^(4*x) + 4*(x^2

*(log(3) - 6) - x^2*log(x))*e^(3*x) + 6*(2*x^2*(log(3) - 6)*log(x) - x^2*log(x)^2 - (log(3)^2 - 12*log(3) + 36

)*x^2)*e^(2*x) + 4*(3*x^2*(log(3) - 6)*log(x)^2 - x^2*log(x)^3 - 3*(log(3)^2 - 12*log(3) + 36)*x^2*log(x) + (l

og(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*x^2)*e^x)*log(log(x))^2 + 6*(x^2*(log(3) - 6) - x^2*log(x))*e^(5*x)

+ 15*(2*x^2*(log(3) - 6)*log(x) - x^2*log(x)^2 - (log(3)^2 - 12*log(3) + 36)*x^2)*e^(4*x) + 20*(3*x^2*(log(3)

- 6)*log(x)^2 - x^2*log(x)^3 - 3*(log(3)^2 - 12*log(3) + 36)*x^2*log(x) + (log(3)^3 - 18*log(3)^2 + 108*log(3)

- 216)*x^2)*e^(3*x) + 15*(4*x^2*(log(3) - 6)*log(x)^3 - x^2*log(x)^4 - 6*(log(3)^2 - 12*log(3) + 36)*x^2*log(

x)^2 + 4*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*x^2*log(x) - (log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 864

*log(3) + 1296)*x^2)*e^(2*x) + 6*(5*x^2*(log(3) - 6)*log(x)^4 - x^2*log(x)^5 - 10*(log(3)^2 - 12*log(3) + 36)*

x^2*log(x)^3 + 10*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*x^2*log(x)^2 - 5*(log(3)^4 - 24*log(3)^3 + 216*l

og(3)^2 - 864*log(3) + 1296)*x^2*log(x) + (log(3)^5 - 30*log(3)^4 + 360*log(3)^3 - 2160*log(3)^2 + 6480*log(3)

- 7776)*x^2)*e^x + 6*(5*x^2*(log(3) - 6)*log(x)^4 - x^2*log(x)^5 - 10*(log(3)^2 - 12*log(3) + 36)*x^2*log(x)^

3 + 10*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*x^2*log(x)^2 - 5*(log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 8

64*log(3) + 1296)*x^2*log(x) + (log(3)^5 - 30*log(3)^4 + 360*log(3)^3 - 2160*log(3)^2 + 6480*log(3) - 7776)*x^

2 - x^2*e^(5*x) + 5*(x^2*(log(3) - 6) - x^2*log(x))*e^(4*x) + 10*(2*x^2*(log(3) - 6)*log(x) - x^2*log(x)^2 - (

log(3)^2 - 12*log(3) + 36)*x^2)*e^(3*x) + 10*(3*x^2*(log(3) - 6)*log(x)^2 - x^2*log(x)^3 - 3*(log(3)^2 - 12*lo

g(3) + 36)*x^2*log(x) + (log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*x^2)*e^(2*x) + 5*(4*x^2*(log(3) - 6)*log(x

)^3 - x^2*log(x)^4 - 6*(log(3)^2 - 12*log(3) + 36)*x^2*log(x)^2 + 4*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216

)*x^2*log(x) - (log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 864*log(3) + 1296)*x^2)*e^x)*log(log(x)) - e^(log(e^x

- log(3) + log(x) + log(log(x)) + 6)^2 + 9))/(log(3)^6 - 6*(log(3) - 6)*log(x)^5 + log(x)^6 + 6*(e^x - log(3)

+ log(x) + 6)*log(log(x))^5 + log(log(x))^6 - 36*log(3)^5 + 15*(log(3)^2 - 12*log(3) + 36)*log(x)^4 - 15*(2*(l

og(3) - log(x) - 6)*e^x - log(3)^2 + 2*(log(3) - 6)*log(x) - log(x)^2 - e^(2*x) + 12*log(3) - 36)*log(log(x))^

4 + 540*log(3)^4 - 20*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*log(x)^3 - 20*(log(3)^3 + 3*(log(3) - 6)*log

(x)^2 - log(x)^3 + 3*(log(3) - log(x) - 6)*e^(2*x) - 3*(log(3)^2 - 2*(log(3) - 6)*log(x) + log(x)^2 - 12*log(3

) + 36)*e^x - 18*log(3)^2 - 3*(log(3)^2 - 12*log(3) + 36)*log(x) - e^(3*x) + 108*log(3) - 216)*log(log(x))^3 -

4320*log(3)^3 + 15*(log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 864*log(3) + 1296)*log(x)^2 + 15*(log(3)^4 - 4*(l

og(3) - 6)*log(x)^3 + log(x)^4 - 24*log(3)^3 + 6*(log(3)^2 - 12*log(3) + 36)*log(x)^2 - 4*(log(3) - log(x) - 6

)*e^(3*x) + 6*(log(3)^2 - 2*(log(3) - 6)*log(x) + log(x)^2 - 12*log(3) + 36)*e^(2*x) - 4*(log(3)^3 + 3*(log(3)

- 6)*log(x)^2 - log(x)^3 - 18*log(3)^2 - 3*(log(3)^2 - 12*log(3) + 36)*log(x) + 108*log(3) - 216)*e^x + 216*l

og(3)^2 - 4*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*log(x) + e^(4*x) - 864*log(3) + 1296)*log(log(x))^2 -

6*(log(3) - log(x) - 6)*e^(5*x) + 15*(log(3)^2 - 2*(log(3) - 6)*log(x) + log(x)^2 - 12*log(3) + 36)*e^(4*x) -

20*(log(3)^3 + 3*(log(3) - 6)*log(x)^2 - log(x)^3 - 18*log(3)^2 - 3*(log(3)^2 - 12*log(3) + 36)*log(x) + 108*l

og(3) - 216)*e^(3*x) + 15*(log(3)^4 - 4*(log(3) - 6)*log(x)^3 + log(x)^4 - 24*log(3)^3 + 6*(log(3)^2 - 12*log(

3) + 36)*log(x)^2 + 216*log(3)^2 - 4*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*log(x) - 864*log(3) + 1296)*e

^(2*x) - 6*(log(3)^5 + 5*(log(3) - 6)*log(x)^4 - log(x)^5 - 30*log(3)^4 - 10*(log(3)^2 - 12*log(3) + 36)*log(x

)^3 + 360*log(3)^3 + 10*(log(3)^3 - 18*log(3)^2 + 108*log(3) - 216)*log(x)^2 - 2160*log(3)^2 - 5*(log(3)^4 - 2

4*log(3)^3 + 216*log(3)^2 - 864*log(3) + 1296)*log(x) + 6480*log(3) - 7776)*e^x + 19440*log(3)^2 - 6*(log(3)^5

- 30*log(3)^4 + 360*log(3)^3 - 2160*log(3)^2 + 6480*log(3) - 7776)*log(x) - 6*(log(3)^5 + 5*(log(3) - 6)*log(

x)^4 - log(x)^5 - 30*log(3)^4 - 10*(log(3)^2 - 12*log(3) + 36)*log(x)^3 + 360*log(3)^3 + 10*(log(3)^3 - 18*log

(3)^2 + 108*log(3) - 216)*log(x)^2 + 5*(log(3) - log(x) - 6)*e^(4*x) - 10*(log(3)^2 - 2*(log(3) - 6)*log(x) +

log(x)^2 - 12*log(3) + 36)*e^(3*x) + 10*(log(3)^3 + 3*(log(3) - 6)*log(x)^2 - log(x)^3 - 18*log(3)^2 - 3*(log(

3)^2 - 12*log(3) + 36)*log(x) + 108*log(3) - 216)*e^(2*x) - 5*(log(3)^4 - 4*(log(3) - 6)*log(x)^3 + log(x)^4 -

24*log(3)^3 + 6*(log(3)^2 - 12*log(3) + 36)*log(x)^2 + 216*log(3)^2 - 4*(log(3)^3 - 18*log(3)^2 + 108*log(3)

- 216)*log(x) - 864*log(3) + 1296)*e^x - 2160*log(3)^2 - 5*(log(3)^4 - 24*log(3)^3 + 216*log(3)^2 - 864*log(3)

+ 1296)*log(x) - e^(5*x) + 6480*log(3) - 7776)*log(log(x)) + e^(6*x) - 46656*log(3) + 46656)

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mupad [B] time = 4.29, size = 1132, normalized size = 39.03 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(log(exp(x) - log(3/(x*log(x))) + 6)^2 - 6*log(exp(x) - log(3/(x*log(x))) + 6) + 9)*(log(x)*(6*x*exp(

x) + 6) - log(exp(x) - log(3/(x*log(x))) + 6)*(log(x)*(2*x*exp(x) + 2) + 2) + 6) - log(x)*(2*x^2*exp(x) + 12*x

^2) + 2*x^2*log(x)*log(3/(x*log(x))))/(log(x)*(6*x + x*exp(x)) - x*log(x)*log(3/(x*log(x)))),x)

[Out]

x^2 + (exp(9)*exp(log(exp(x) - log(3) - log(1/(x*log(x))) + 6)^2))/(19440*exp(2*x) + 4320*exp(3*x) + 540*exp(4

*x) + 36*exp(5*x) + exp(6*x) - 46656*log(3) + 46656*exp(x) - 46656*log(1/(x*log(x))) - 12960*exp(2*x)*log(3) -

2160*exp(3*x)*log(3) - 180*exp(4*x)*log(3) - 6*exp(5*x)*log(3) + 12960*exp(x)*log(3)^2 - 2160*exp(x)*log(3)^3

+ 180*exp(x)*log(3)^4 - 6*exp(x)*log(3)^5 - 12960*log(3)*log(1/(x*log(x)))^2 - 12960*log(3)^2*log(1/(x*log(x)

)) + 2160*log(3)*log(1/(x*log(x)))^3 + 2160*log(3)^3*log(1/(x*log(x))) - 180*log(3)*log(1/(x*log(x)))^4 - 180*

log(3)^4*log(1/(x*log(x))) + 6*log(3)*log(1/(x*log(x)))^5 + 6*log(3)^5*log(1/(x*log(x))) - 38880*exp(x)*log(1/

(x*log(x))) + 19440*log(1/(x*log(x)))^2 - 4320*log(1/(x*log(x)))^3 + 540*log(1/(x*log(x)))^4 - 36*log(1/(x*log

(x)))^5 + log(1/(x*log(x)))^6 + 3240*exp(2*x)*log(3)^2 - 360*exp(2*x)*log(3)^3 + 360*exp(3*x)*log(3)^2 + 15*ex

p(2*x)*log(3)^4 - 20*exp(3*x)*log(3)^3 + 15*exp(4*x)*log(3)^2 + 3240*log(3)^2*log(1/(x*log(x)))^2 - 360*log(3)

^2*log(1/(x*log(x)))^3 - 360*log(3)^3*log(1/(x*log(x)))^2 + 15*log(3)^2*log(1/(x*log(x)))^4 + 20*log(3)^3*log(

1/(x*log(x)))^3 + 15*log(3)^4*log(1/(x*log(x)))^2 - 12960*exp(2*x)*log(1/(x*log(x))) - 2160*exp(3*x)*log(1/(x*

log(x))) - 180*exp(4*x)*log(1/(x*log(x))) - 6*exp(5*x)*log(1/(x*log(x))) + 12960*exp(x)*log(1/(x*log(x)))^2 -

2160*exp(x)*log(1/(x*log(x)))^3 + 180*exp(x)*log(1/(x*log(x)))^4 - 6*exp(x)*log(1/(x*log(x)))^5 - 38880*exp(x)

*log(3) + 38880*log(3)*log(1/(x*log(x))) + 19440*log(3)^2 - 4320*log(3)^3 + 540*log(3)^4 - 36*log(3)^5 + log(3

)^6 + 3240*exp(2*x)*log(1/(x*log(x)))^2 - 360*exp(2*x)*log(1/(x*log(x)))^3 + 360*exp(3*x)*log(1/(x*log(x)))^2

+ 15*exp(2*x)*log(1/(x*log(x)))^4 - 20*exp(3*x)*log(1/(x*log(x)))^3 + 15*exp(4*x)*log(1/(x*log(x)))^2 - 1080*e

xp(2*x)*log(3)*log(1/(x*log(x)))^2 - 1080*exp(2*x)*log(3)^2*log(1/(x*log(x))) + 60*exp(2*x)*log(3)*log(1/(x*lo

g(x)))^3 + 60*exp(2*x)*log(3)^3*log(1/(x*log(x))) - 60*exp(3*x)*log(3)*log(1/(x*log(x)))^2 - 60*exp(3*x)*log(3

)^2*log(1/(x*log(x))) + 1080*exp(x)*log(3)^2*log(1/(x*log(x)))^2 - 60*exp(x)*log(3)^2*log(1/(x*log(x)))^3 - 60

*exp(x)*log(3)^3*log(1/(x*log(x)))^2 + 25920*exp(x)*log(3)*log(1/(x*log(x))) + 90*exp(2*x)*log(3)^2*log(1/(x*l

og(x)))^2 + 6480*exp(2*x)*log(3)*log(1/(x*log(x))) + 720*exp(3*x)*log(3)*log(1/(x*log(x))) + 30*exp(4*x)*log(3

)*log(1/(x*log(x))) - 6480*exp(x)*log(3)*log(1/(x*log(x)))^2 - 6480*exp(x)*log(3)^2*log(1/(x*log(x))) + 720*ex

p(x)*log(3)*log(1/(x*log(x)))^3 + 720*exp(x)*log(3)^3*log(1/(x*log(x))) - 30*exp(x)*log(3)*log(1/(x*log(x)))^4

- 30*exp(x)*log(3)^4*log(1/(x*log(x))) + 46656)

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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(((((-2*exp(x)*x-2)*ln(x)-2)*ln(-ln(3/x/ln(x))+exp(x)+6)+(6*exp(x)*x+6)*ln(x)+6)*exp(ln(-ln(3/x/ln(x)

)+exp(x)+6)**2-6*ln(-ln(3/x/ln(x))+exp(x)+6)+9)+2*x**2*ln(x)*ln(3/x/ln(x))+(-2*exp(x)*x**2-12*x**2)*ln(x))/(x*

ln(x)*ln(3/x/ln(x))+(-exp(x)*x-6*x)*ln(x)),x)

[Out]

Timed out

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