3.57.36 \(\int \frac {(-\log (2)+9 e^{3 x} \log (2)) \log (x)+(3 \log (2)-27 e^{3 x} \log (2)) \log (x) \log (\log (x))+(-3 \log (2)+27 e^{3 x} \log (2)) \log (x) \log ^2(\log (x))+(\log (2)-9 e^{3 x} \log (2)) \log (x) \log ^3(\log (x))+e^{\frac {2 x}{\log (2)-2 \log (2) \log (\log (x))+\log (2) \log ^2(\log (x))}} (12 x+(6 x+3 \log (2)) \log (x)+(-6 x-9 \log (2)) \log (x) \log (\log (x))+9 \log (2) \log (x) \log ^2(\log (x))-3 \log (2) \log (x) \log ^3(\log (x)))}{-3 \log (2) \log (x)+9 \log (2) \log (x) \log (\log (x))-9 \log (2) \log (x) \log ^2(\log (x))+3 \log (2) \log (x) \log ^3(\log (x))} \, dx\)

Optimal. Leaf size=32 \[ -e^{3 x}+\left (\frac {1}{3}-e^{\frac {2 x}{\log (2) (-1+\log (\log (x)))^2}}\right ) x \]

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Rubi [B]  time = 4.17, antiderivative size = 89, normalized size of antiderivative = 2.78, number of steps used = 26, number of rules used = 5, integrand size = 198, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6741, 12, 6742, 2194, 2288} \begin {gather*} \frac {x}{3}-e^{3 x}-\frac {e^{\frac {2 x}{\log (2) (1-\log (\log (x)))^2}} (2 x+x \log (x)-x \log (x) \log (\log (x)))}{\log (x) \left (\frac {1}{(1-\log (\log (x)))^2}+\frac {2}{(1-\log (\log (x)))^3 \log (x)}\right ) (1-\log (\log (x)))^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((-Log[2] + 9*E^(3*x)*Log[2])*Log[x] + (3*Log[2] - 27*E^(3*x)*Log[2])*Log[x]*Log[Log[x]] + (-3*Log[2] + 27
*E^(3*x)*Log[2])*Log[x]*Log[Log[x]]^2 + (Log[2] - 9*E^(3*x)*Log[2])*Log[x]*Log[Log[x]]^3 + E^((2*x)/(Log[2] -
2*Log[2]*Log[Log[x]] + Log[2]*Log[Log[x]]^2))*(12*x + (6*x + 3*Log[2])*Log[x] + (-6*x - 9*Log[2])*Log[x]*Log[L
og[x]] + 9*Log[2]*Log[x]*Log[Log[x]]^2 - 3*Log[2]*Log[x]*Log[Log[x]]^3))/(-3*Log[2]*Log[x] + 9*Log[2]*Log[x]*L
og[Log[x]] - 9*Log[2]*Log[x]*Log[Log[x]]^2 + 3*Log[2]*Log[x]*Log[Log[x]]^3),x]

[Out]

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

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

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 (-\log (2)+9 e^{3 x} \log (2)\right ) \log (x)\right )-\left (3 \log (2)-27 e^{3 x} \log (2)\right ) \log (x) \log (\log (x))-\left (-3 \log (2)+27 e^{3 x} \log (2)\right ) \log (x) \log ^2(\log (x))-\left (\log (2)-9 e^{3 x} \log (2)\right ) \log (x) \log ^3(\log (x))-\exp \left (\frac {2 x}{\log (2)-2 \log (2) \log (\log (x))+\log (2) \log ^2(\log (x))}\right ) \left (12 x+(6 x+3 \log (2)) \log (x)+(-6 x-9 \log (2)) \log (x) \log (\log (x))+9 \log (2) \log (x) \log ^2(\log (x))-3 \log (2) \log (x) \log ^3(\log (x))\right )}{3 \log (2) \log (x) (1-\log (\log (x)))^3} \, dx\\ &=\frac {\int \frac {-\left (\left (-\log (2)+9 e^{3 x} \log (2)\right ) \log (x)\right )-\left (3 \log (2)-27 e^{3 x} \log (2)\right ) \log (x) \log (\log (x))-\left (-3 \log (2)+27 e^{3 x} \log (2)\right ) \log (x) \log ^2(\log (x))-\left (\log (2)-9 e^{3 x} \log (2)\right ) \log (x) \log ^3(\log (x))-\exp \left (\frac {2 x}{\log (2)-2 \log (2) \log (\log (x))+\log (2) \log ^2(\log (x))}\right ) \left (12 x+(6 x+3 \log (2)) \log (x)+(-6 x-9 \log (2)) \log (x) \log (\log (x))+9 \log (2) \log (x) \log ^2(\log (x))-3 \log (2) \log (x) \log ^3(\log (x))\right )}{\log (x) (1-\log (\log (x)))^3} \, dx}{3 \log (2)}\\ &=\frac {\int \left (\frac {\left (-1+9 e^{3 x}\right ) \log (2)}{(-1+\log (\log (x)))^3}-\frac {3 \left (-1+9 e^{3 x}\right ) \log (2) \log (\log (x))}{(-1+\log (\log (x)))^3}+\frac {3 \left (-1+9 e^{3 x}\right ) \log (2) \log ^2(\log (x))}{(-1+\log (\log (x)))^3}-\frac {\left (-1+9 e^{3 x}\right ) \log (2) \log ^3(\log (x))}{(-1+\log (\log (x)))^3}+\frac {3 e^{\frac {2 x}{\log (2) (-1+\log (\log (x)))^2}} \left (-4 x-2 x \log (x)-\log (2) \log (x)+2 x \log (x) \log (\log (x))+\log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log (x) \log (\log (x))-\log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log (x) \log ^2(\log (x))+\log (2) \log (x) \log ^3(\log (x))\right )}{\log (x) (1-\log (\log (x)))^3}\right ) \, dx}{3 \log (2)}\\ &=\frac {1}{3} \int \frac {-1+9 e^{3 x}}{(-1+\log (\log (x)))^3} \, dx-\frac {1}{3} \int \frac {\left (-1+9 e^{3 x}\right ) \log ^3(\log (x))}{(-1+\log (\log (x)))^3} \, dx+\frac {\int \frac {e^{\frac {2 x}{\log (2) (-1+\log (\log (x)))^2}} \left (-4 x-2 x \log (x)-\log (2) \log (x)+2 x \log (x) \log (\log (x))+\log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log (x) \log (\log (x))-\log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log (x) \log ^2(\log (x))+\log (2) \log (x) \log ^3(\log (x))\right )}{\log (x) (1-\log (\log (x)))^3} \, dx}{\log (2)}-\int \frac {\left (-1+9 e^{3 x}\right ) \log (\log (x))}{(-1+\log (\log (x)))^3} \, dx+\int \frac {\left (-1+9 e^{3 x}\right ) \log ^2(\log (x))}{(-1+\log (\log (x)))^3} \, dx\\ &=-\frac {e^{\frac {2 x}{\log (2) (1-\log (\log (x)))^2}} (2 x+x \log (x)-x \log (x) \log (\log (x)))}{\log (x) \left (\frac {2}{\log (x) (1-\log (\log (x)))^3}+\frac {1}{(1-\log (\log (x)))^2}\right ) (1-\log (\log (x)))^3}+\frac {1}{3} \int \left (-\frac {1}{(-1+\log (\log (x)))^3}+\frac {9 e^{3 x}}{(-1+\log (\log (x)))^3}\right ) \, dx-\frac {1}{3} \int \left (-\frac {\log ^3(\log (x))}{(-1+\log (\log (x)))^3}+\frac {9 e^{3 x} \log ^3(\log (x))}{(-1+\log (\log (x)))^3}\right ) \, dx-\int \left (-\frac {\log (\log (x))}{(-1+\log (\log (x)))^3}+\frac {9 e^{3 x} \log (\log (x))}{(-1+\log (\log (x)))^3}\right ) \, dx+\int \left (-\frac {\log ^2(\log (x))}{(-1+\log (\log (x)))^3}+\frac {9 e^{3 x} \log ^2(\log (x))}{(-1+\log (\log (x)))^3}\right ) \, dx\\ &=-\frac {e^{\frac {2 x}{\log (2) (1-\log (\log (x)))^2}} (2 x+x \log (x)-x \log (x) \log (\log (x)))}{\log (x) \left (\frac {2}{\log (x) (1-\log (\log (x)))^3}+\frac {1}{(1-\log (\log (x)))^2}\right ) (1-\log (\log (x)))^3}-\frac {1}{3} \int \frac {1}{(-1+\log (\log (x)))^3} \, dx+\frac {1}{3} \int \frac {\log ^3(\log (x))}{(-1+\log (\log (x)))^3} \, dx+3 \int \frac {e^{3 x}}{(-1+\log (\log (x)))^3} \, dx-3 \int \frac {e^{3 x} \log ^3(\log (x))}{(-1+\log (\log (x)))^3} \, dx-9 \int \frac {e^{3 x} \log (\log (x))}{(-1+\log (\log (x)))^3} \, dx+9 \int \frac {e^{3 x} \log ^2(\log (x))}{(-1+\log (\log (x)))^3} \, dx+\int \frac {\log (\log (x))}{(-1+\log (\log (x)))^3} \, dx-\int \frac {\log ^2(\log (x))}{(-1+\log (\log (x)))^3} \, dx\\ &=-\frac {e^{\frac {2 x}{\log (2) (1-\log (\log (x)))^2}} (2 x+x \log (x)-x \log (x) \log (\log (x)))}{\log (x) \left (\frac {2}{\log (x) (1-\log (\log (x)))^3}+\frac {1}{(1-\log (\log (x)))^2}\right ) (1-\log (\log (x)))^3}+\frac {1}{3} \int \left (1+\frac {1}{(-1+\log (\log (x)))^3}+\frac {3}{(-1+\log (\log (x)))^2}+\frac {3}{-1+\log (\log (x))}\right ) \, dx-\frac {1}{3} \int \frac {1}{(-1+\log (\log (x)))^3} \, dx-3 \int \left (e^{3 x}+\frac {e^{3 x}}{(-1+\log (\log (x)))^3}+\frac {3 e^{3 x}}{(-1+\log (\log (x)))^2}+\frac {3 e^{3 x}}{-1+\log (\log (x))}\right ) \, dx+3 \int \frac {e^{3 x}}{(-1+\log (\log (x)))^3} \, dx-9 \int \left (\frac {e^{3 x}}{(-1+\log (\log (x)))^3}+\frac {e^{3 x}}{(-1+\log (\log (x)))^2}\right ) \, dx+9 \int \left (\frac {e^{3 x}}{(-1+\log (\log (x)))^3}+\frac {2 e^{3 x}}{(-1+\log (\log (x)))^2}+\frac {e^{3 x}}{-1+\log (\log (x))}\right ) \, dx+\int \left (\frac {1}{(-1+\log (\log (x)))^3}+\frac {1}{(-1+\log (\log (x)))^2}\right ) \, dx-\int \left (\frac {1}{(-1+\log (\log (x)))^3}+\frac {2}{(-1+\log (\log (x)))^2}+\frac {1}{-1+\log (\log (x))}\right ) \, dx\\ &=\frac {x}{3}-\frac {e^{\frac {2 x}{\log (2) (1-\log (\log (x)))^2}} (2 x+x \log (x)-x \log (x) \log (\log (x)))}{\log (x) \left (\frac {2}{\log (x) (1-\log (\log (x)))^3}+\frac {1}{(1-\log (\log (x)))^2}\right ) (1-\log (\log (x)))^3}-2 \int \frac {1}{(-1+\log (\log (x)))^2} \, dx-3 \int e^{3 x} \, dx-2 \left (9 \int \frac {e^{3 x}}{(-1+\log (\log (x)))^2} \, dx\right )+18 \int \frac {e^{3 x}}{(-1+\log (\log (x)))^2} \, dx+2 \int \frac {1}{(-1+\log (\log (x)))^2} \, dx\\ &=-e^{3 x}+\frac {x}{3}-\frac {e^{\frac {2 x}{\log (2) (1-\log (\log (x)))^2}} (2 x+x \log (x)-x \log (x) \log (\log (x)))}{\log (x) \left (\frac {2}{\log (x) (1-\log (\log (x)))^3}+\frac {1}{(1-\log (\log (x)))^2}\right ) (1-\log (\log (x)))^3}-2 \int \frac {1}{(-1+\log (\log (x)))^2} \, dx-2 \left (9 \int \frac {e^{3 x}}{(-1+\log (\log (x)))^2} \, dx\right )+18 \int \frac {e^{3 x}}{(-1+\log (\log (x)))^2} \, dx+2 \int \frac {1}{(-1+\log (\log (x)))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.45, size = 43, normalized size = 1.34 \begin {gather*} \frac {-3 e^{3 x} \log (2)+x \log (2)-3 e^{\frac {2 x}{\log (2) (-1+\log (\log (x)))^2}} x \log (2)}{3 \log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-Log[2] + 9*E^(3*x)*Log[2])*Log[x] + (3*Log[2] - 27*E^(3*x)*Log[2])*Log[x]*Log[Log[x]] + (-3*Log[2
] + 27*E^(3*x)*Log[2])*Log[x]*Log[Log[x]]^2 + (Log[2] - 9*E^(3*x)*Log[2])*Log[x]*Log[Log[x]]^3 + E^((2*x)/(Log
[2] - 2*Log[2]*Log[Log[x]] + Log[2]*Log[Log[x]]^2))*(12*x + (6*x + 3*Log[2])*Log[x] + (-6*x - 9*Log[2])*Log[x]
*Log[Log[x]] + 9*Log[2]*Log[x]*Log[Log[x]]^2 - 3*Log[2]*Log[x]*Log[Log[x]]^3))/(-3*Log[2]*Log[x] + 9*Log[2]*Lo
g[x]*Log[Log[x]] - 9*Log[2]*Log[x]*Log[Log[x]]^2 + 3*Log[2]*Log[x]*Log[Log[x]]^3),x]

[Out]

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

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fricas [A]  time = 0.62, size = 37, normalized size = 1.16 \begin {gather*} -x e^{\left (\frac {2 \, x}{\log \relax (2) \log \left (\log \relax (x)\right )^{2} - 2 \, \log \relax (2) \log \left (\log \relax (x)\right ) + \log \relax (2)}\right )} + \frac {1}{3} \, x - e^{\left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*log(2)*log(x)*log(log(x))^3+9*log(2)*log(x)*log(log(x))^2+(-9*log(2)-6*x)*log(x)*log(log(x))+(3
*log(2)+6*x)*log(x)+12*x)*exp(x/(log(2)*log(log(x))^2-2*log(2)*log(log(x))+log(2)))^2+(-9*log(2)*exp(3*x)+log(
2))*log(x)*log(log(x))^3+(27*log(2)*exp(3*x)-3*log(2))*log(x)*log(log(x))^2+(-27*log(2)*exp(3*x)+3*log(2))*log
(x)*log(log(x))+(9*log(2)*exp(3*x)-log(2))*log(x))/(3*log(2)*log(x)*log(log(x))^3-9*log(2)*log(x)*log(log(x))^
2+9*log(2)*log(x)*log(log(x))-3*log(2)*log(x)),x, algorithm="fricas")

[Out]

-x*e^(2*x/(log(2)*log(log(x))^2 - 2*log(2)*log(log(x)) + log(2))) + 1/3*x - e^(3*x)

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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(((-3*log(2)*log(x)*log(log(x))^3+9*log(2)*log(x)*log(log(x))^2+(-9*log(2)-6*x)*log(x)*log(log(x))+(3
*log(2)+6*x)*log(x)+12*x)*exp(x/(log(2)*log(log(x))^2-2*log(2)*log(log(x))+log(2)))^2+(-9*log(2)*exp(3*x)+log(
2))*log(x)*log(log(x))^3+(27*log(2)*exp(3*x)-3*log(2))*log(x)*log(log(x))^2+(-27*log(2)*exp(3*x)+3*log(2))*log
(x)*log(log(x))+(9*log(2)*exp(3*x)-log(2))*log(x))/(3*log(2)*log(x)*log(log(x))^3-9*log(2)*log(x)*log(log(x))^
2+9*log(2)*log(x)*log(log(x))-3*log(2)*log(x)),x, algorithm="giac")

[Out]

undef

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maple [A]  time = 0.17, size = 29, normalized size = 0.91

method	result	size
risch	\(\frac {x}{3}-{\mathrm e}^{3 x}-{\mathrm e}^{\frac {2 x}{\ln \relax (2) \left (\ln \left (\ln \relax (x )\right )-1\right )^{2}}} x\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-3*ln(2)*ln(x)*ln(ln(x))^3+9*ln(2)*ln(x)*ln(ln(x))^2+(-9*ln(2)-6*x)*ln(x)*ln(ln(x))+(3*ln(2)+6*x)*ln(x)+
12*x)*exp(x/(ln(2)*ln(ln(x))^2-2*ln(2)*ln(ln(x))+ln(2)))^2+(-9*ln(2)*exp(3*x)+ln(2))*ln(x)*ln(ln(x))^3+(27*ln(
2)*exp(3*x)-3*ln(2))*ln(x)*ln(ln(x))^2+(-27*ln(2)*exp(3*x)+3*ln(2))*ln(x)*ln(ln(x))+(9*ln(2)*exp(3*x)-ln(2))*l
n(x))/(3*ln(2)*ln(x)*ln(ln(x))^3-9*ln(2)*ln(x)*ln(ln(x))^2+9*ln(2)*ln(x)*ln(ln(x))-3*ln(2)*ln(x)),x,method=_RE
TURNVERBOSE)

[Out]

1/3*x-exp(3*x)-exp(2*x/ln(2)/(ln(ln(x))-1)^2)*x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{3} \, x - e^{\left (3 \, x\right )} - \frac {1}{3} \, \int \frac {3 \, {\left (\log \relax (2) \log \relax (x) \log \left (\log \relax (x)\right )^{3} - 3 \, \log \relax (2) \log \relax (x) \log \left (\log \relax (x)\right )^{2} + {\left (2 \, x + 3 \, \log \relax (2)\right )} \log \relax (x) \log \left (\log \relax (x)\right ) - {\left (2 \, x + \log \relax (2)\right )} \log \relax (x) - 4 \, x\right )} e^{\left (\frac {2 \, x}{\log \relax (2) \log \left (\log \relax (x)\right )^{2} - 2 \, \log \relax (2) \log \left (\log \relax (x)\right ) + \log \relax (2)}\right )}}{\log \relax (2) \log \relax (x) \log \left (\log \relax (x)\right )^{3} - 3 \, \log \relax (2) \log \relax (x) \log \left (\log \relax (x)\right )^{2} + 3 \, \log \relax (2) \log \relax (x) \log \left (\log \relax (x)\right ) - \log \relax (2) \log \relax (x)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*log(2)*log(x)*log(log(x))^3+9*log(2)*log(x)*log(log(x))^2+(-9*log(2)-6*x)*log(x)*log(log(x))+(3
*log(2)+6*x)*log(x)+12*x)*exp(x/(log(2)*log(log(x))^2-2*log(2)*log(log(x))+log(2)))^2+(-9*log(2)*exp(3*x)+log(
2))*log(x)*log(log(x))^3+(27*log(2)*exp(3*x)-3*log(2))*log(x)*log(log(x))^2+(-27*log(2)*exp(3*x)+3*log(2))*log
(x)*log(log(x))+(9*log(2)*exp(3*x)-log(2))*log(x))/(3*log(2)*log(x)*log(log(x))^3-9*log(2)*log(x)*log(log(x))^
2+9*log(2)*log(x)*log(log(x))-3*log(2)*log(x)),x, algorithm="maxima")

[Out]

1/3*x - e^(3*x) - 1/3*integrate(3*(log(2)*log(x)*log(log(x))^3 - 3*log(2)*log(x)*log(log(x))^2 + (2*x + 3*log(
2))*log(x)*log(log(x)) - (2*x + log(2))*log(x) - 4*x)*e^(2*x/(log(2)*log(log(x))^2 - 2*log(2)*log(log(x)) + lo
g(2)))/(log(2)*log(x)*log(log(x))^3 - 3*log(2)*log(x)*log(log(x))^2 + 3*log(2)*log(x)*log(log(x)) - log(2)*log
(x)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{\frac {2\,x}{\ln \relax (2)\,{\ln \left (\ln \relax (x)\right )}^2-2\,\ln \relax (2)\,\ln \left (\ln \relax (x)\right )+\ln \relax (2)}}\,\left (-3\,\ln \relax (2)\,\ln \relax (x)\,{\ln \left (\ln \relax (x)\right )}^3+9\,\ln \relax (2)\,\ln \relax (x)\,{\ln \left (\ln \relax (x)\right )}^2-\ln \relax (x)\,\left (6\,x+9\,\ln \relax (2)\right )\,\ln \left (\ln \relax (x)\right )+12\,x+\ln \relax (x)\,\left (6\,x+3\,\ln \relax (2)\right )\right )-\ln \relax (x)\,\left (\ln \relax (2)-9\,{\mathrm {e}}^{3\,x}\,\ln \relax (2)\right )-{\ln \left (\ln \relax (x)\right )}^2\,\ln \relax (x)\,\left (3\,\ln \relax (2)-27\,{\mathrm {e}}^{3\,x}\,\ln \relax (2)\right )+\ln \left (\ln \relax (x)\right )\,\ln \relax (x)\,\left (3\,\ln \relax (2)-27\,{\mathrm {e}}^{3\,x}\,\ln \relax (2)\right )+{\ln \left (\ln \relax (x)\right )}^3\,\ln \relax (x)\,\left (\ln \relax (2)-9\,{\mathrm {e}}^{3\,x}\,\ln \relax (2)\right )}{-3\,\ln \relax (2)\,\ln \relax (x)\,{\ln \left (\ln \relax (x)\right )}^3+9\,\ln \relax (2)\,\ln \relax (x)\,{\ln \left (\ln \relax (x)\right )}^2-9\,\ln \relax (2)\,\ln \relax (x)\,\ln \left (\ln \relax (x)\right )+3\,\ln \relax (2)\,\ln \relax (x)} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((2*x)/(log(2) - 2*log(log(x))*log(2) + log(log(x))^2*log(2)))*(12*x + log(x)*(6*x + 3*log(2)) + 9*lo
g(log(x))^2*log(2)*log(x) - 3*log(log(x))^3*log(2)*log(x) - log(log(x))*log(x)*(6*x + 9*log(2))) - log(x)*(log
(2) - 9*exp(3*x)*log(2)) - log(log(x))^2*log(x)*(3*log(2) - 27*exp(3*x)*log(2)) + log(log(x))*log(x)*(3*log(2)
- 27*exp(3*x)*log(2)) + log(log(x))^3*log(x)*(log(2) - 9*exp(3*x)*log(2)))/(3*log(2)*log(x) - 9*log(log(x))*l
og(2)*log(x) + 9*log(log(x))^2*log(2)*log(x) - 3*log(log(x))^3*log(2)*log(x)),x)

[Out]

int(-(exp((2*x)/(log(2) - 2*log(log(x))*log(2) + log(log(x))^2*log(2)))*(12*x + log(x)*(6*x + 3*log(2)) + 9*lo
g(log(x))^2*log(2)*log(x) - 3*log(log(x))^3*log(2)*log(x) - log(log(x))*log(x)*(6*x + 9*log(2))) - log(x)*(log
(2) - 9*exp(3*x)*log(2)) - log(log(x))^2*log(x)*(3*log(2) - 27*exp(3*x)*log(2)) + log(log(x))*log(x)*(3*log(2)
- 27*exp(3*x)*log(2)) + log(log(x))^3*log(x)*(log(2) - 9*exp(3*x)*log(2)))/(3*log(2)*log(x) - 9*log(log(x))*l
og(2)*log(x) + 9*log(log(x))^2*log(2)*log(x) - 3*log(log(x))^3*log(2)*log(x)), x)

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sympy [A]  time = 8.53, size = 37, normalized size = 1.16 \begin {gather*} - x e^{\frac {2 x}{\log {\relax (2 )} \log {\left (\log {\relax (x )} \right )}^{2} - 2 \log {\relax (2 )} \log {\left (\log {\relax (x )} \right )} + \log {\relax (2 )}}} + \frac {x}{3} - e^{3 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*ln(2)*ln(x)*ln(ln(x))**3+9*ln(2)*ln(x)*ln(ln(x))**2+(-9*ln(2)-6*x)*ln(x)*ln(ln(x))+(3*ln(2)+6*x
)*ln(x)+12*x)*exp(x/(ln(2)*ln(ln(x))**2-2*ln(2)*ln(ln(x))+ln(2)))**2+(-9*ln(2)*exp(3*x)+ln(2))*ln(x)*ln(ln(x))
**3+(27*ln(2)*exp(3*x)-3*ln(2))*ln(x)*ln(ln(x))**2+(-27*ln(2)*exp(3*x)+3*ln(2))*ln(x)*ln(ln(x))+(9*ln(2)*exp(3
*x)-ln(2))*ln(x))/(3*ln(2)*ln(x)*ln(ln(x))**3-9*ln(2)*ln(x)*ln(ln(x))**2+9*ln(2)*ln(x)*ln(ln(x))-3*ln(2)*ln(x)
),x)

[Out]

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

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