3.33.90 \(\int \frac {4-x-x^2+\log (3)+e^x (4-6 x+x^2+(1-x) \log (3))+(-4+2 x-\log (3)) \log (x)}{32 x^2-16 x^3+2 x^4+(16 x^2-4 x^3) \log (3)+2 x^2 \log ^2(3)} \, dx\)

Optimal. Leaf size=25 \[ \frac {e^x+x-\log (x)}{2 x (-4+x-\log (3))} \]

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Rubi [B]  time = 1.48, antiderivative size = 101, normalized size of antiderivative = 4.04, number of steps used = 23, number of rules used = 12, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.140, Rules used = {6, 6741, 27, 12, 6742, 44, 2177, 2178, 2357, 2304, 2314, 31} \begin {gather*} \frac {x \log (x)}{2 (4+\log (3))^2 (-x+4+\log (3))}+\frac {\log (x)}{2 x (4+\log (3))}+\frac {\log (x)}{2 (4+\log (3))^2}-\frac {e^x}{2 (4+\log (3)) (-x+4+\log (3))}-\frac {1}{2 (-x+4+\log (3))}-\frac {e^x}{2 x (4+\log (3))} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4 - x - x^2 + Log[3] + E^x*(4 - 6*x + x^2 + (1 - x)*Log[3]) + (-4 + 2*x - Log[3])*Log[x])/(32*x^2 - 16*x^
3 + 2*x^4 + (16*x^2 - 4*x^3)*Log[3] + 2*x^2*Log[3]^2),x]

[Out]

-1/2*E^x/(x*(4 + Log[3])) - 1/(2*(4 - x + Log[3])) - E^x/(2*(4 + Log[3])*(4 - x + Log[3])) + Log[x]/(2*(4 + Lo
g[3])^2) + Log[x]/(2*x*(4 + Log[3])) + (x*Log[x])/(2*(4 + Log[3])^2*(4 - x + Log[3]))

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

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

Rule 27

Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 44

Int[((a_) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*
x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] &&  !(IGtQ[n, 0] && L
tQ[m + n + 2, 0])

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 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2314

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_), x_Symbol] :> Simp[(x*(d + e*x^r)^(q
+ 1)*(a + b*Log[c*x^n]))/d, x] - Dist[(b*n)/d, Int[(d + e*x^r)^(q + 1), x], x] /; FreeQ[{a, b, c, d, e, n, q,
r}, x] && EqQ[r*(q + 1) + 1, 0]

Rule 2357

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

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 {4-x-x^2+\log (3)+e^x \left (4-6 x+x^2+(1-x) \log (3)\right )+(-4+2 x-\log (3)) \log (x)}{-16 x^3+2 x^4+\left (16 x^2-4 x^3\right ) \log (3)+x^2 \left (32+2 \log ^2(3)\right )} \, dx\\ &=\int \frac {-x-x^2+4 \left (1+\frac {\log (3)}{4}\right )+e^x \left (4-6 x+x^2+(1-x) \log (3)\right )+(-4+2 x-\log (3)) \log (x)}{x^2 \left (2 x^2-4 x (4+\log (3))+2 (4+\log (3))^2\right )} \, dx\\ &=\int \frac {-x-x^2+4 \left (1+\frac {\log (3)}{4}\right )+e^x \left (4-6 x+x^2+(1-x) \log (3)\right )+(-4+2 x-\log (3)) \log (x)}{2 x^2 (-4+x-\log (3))^2} \, dx\\ &=\frac {1}{2} \int \frac {-x-x^2+4 \left (1+\frac {\log (3)}{4}\right )+e^x \left (4-6 x+x^2+(1-x) \log (3)\right )+(-4+2 x-\log (3)) \log (x)}{x^2 (-4+x-\log (3))^2} \, dx\\ &=\frac {1}{2} \int \left (-\frac {1}{(-4+x-\log (3))^2}-\frac {1}{x (-4+x-\log (3))^2}+\frac {4+\log (3)}{x^2 (-4+x-\log (3))^2}+\frac {e^x \left (4+x^2+\log (3)-x (6+\log (3))\right )}{x^2 (4-x+\log (3))^2}+\frac {(-4+2 x-\log (3)) \log (x)}{x^2 (-4+x-\log (3))^2}\right ) \, dx\\ &=-\frac {1}{2 (4-x+\log (3))}-\frac {1}{2} \int \frac {1}{x (-4+x-\log (3))^2} \, dx+\frac {1}{2} \int \frac {e^x \left (4+x^2+\log (3)-x (6+\log (3))\right )}{x^2 (4-x+\log (3))^2} \, dx+\frac {1}{2} \int \frac {(-4+2 x-\log (3)) \log (x)}{x^2 (-4+x-\log (3))^2} \, dx+\frac {1}{2} (4+\log (3)) \int \frac {1}{x^2 (-4+x-\log (3))^2} \, dx\\ &=-\frac {1}{2 (4-x+\log (3))}-\frac {1}{2} \int \left (\frac {1}{x (4+\log (3))^2}-\frac {1}{(-4+x-\log (3)) (4+\log (3))^2}+\frac {1}{(4+\log (3)) (4-x+\log (3))^2}\right ) \, dx+\frac {1}{2} \int \left (\frac {e^x}{x^2 (4+\log (3))}-\frac {e^x}{x (4+\log (3))}+\frac {e^x}{(-4+x-\log (3)) (4+\log (3))}-\frac {e^x}{(4+\log (3)) (4-x+\log (3))^2}\right ) \, dx+\frac {1}{2} \int \left (-\frac {\log (x)}{x^2 (4+\log (3))}+\frac {\log (x)}{(4+\log (3)) (4-x+\log (3))^2}\right ) \, dx+\frac {1}{2} (4+\log (3)) \int \left (\frac {2}{x (4+\log (3))^3}-\frac {2}{(-4+x-\log (3)) (4+\log (3))^3}+\frac {1}{x^2 (4+\log (3))^2}+\frac {1}{(4+\log (3))^2 (4-x+\log (3))^2}\right ) \, dx\\ &=-\frac {1}{2 x (4+\log (3))}-\frac {1}{2 (4-x+\log (3))}+\frac {\log (x)}{2 (4+\log (3))^2}-\frac {\log (4-x+\log (3))}{2 (4+\log (3))^2}+\frac {\int \frac {e^x}{x^2} \, dx}{2 (4+\log (3))}-\frac {\int \frac {e^x}{x} \, dx}{2 (4+\log (3))}+\frac {\int \frac {e^x}{-4+x-\log (3)} \, dx}{2 (4+\log (3))}-\frac {\int \frac {e^x}{(4-x+\log (3))^2} \, dx}{2 (4+\log (3))}-\frac {\int \frac {\log (x)}{x^2} \, dx}{2 (4+\log (3))}+\frac {\int \frac {\log (x)}{(4-x+\log (3))^2} \, dx}{2 (4+\log (3))}\\ &=-\frac {e^x}{2 x (4+\log (3))}-\frac {\text {Ei}(x)}{2 (4+\log (3))}+\frac {3 e^4 \text {Ei}(-4+x-\log (3))}{2 (4+\log (3))}-\frac {1}{2 (4-x+\log (3))}-\frac {e^x}{2 (4+\log (3)) (4-x+\log (3))}+\frac {\log (x)}{2 (4+\log (3))^2}+\frac {\log (x)}{2 x (4+\log (3))}+\frac {x \log (x)}{2 (4+\log (3))^2 (4-x+\log (3))}-\frac {\log (4-x+\log (3))}{2 (4+\log (3))^2}-\frac {\int \frac {1}{4-x+\log (3)} \, dx}{2 (4+\log (3))^2}+\frac {\int \frac {e^x}{x} \, dx}{2 (4+\log (3))}+\frac {\int \frac {e^x}{4-x+\log (3)} \, dx}{2 (4+\log (3))}\\ &=-\frac {e^x}{2 x (4+\log (3))}-\frac {1}{2 (4-x+\log (3))}-\frac {e^x}{2 (4+\log (3)) (4-x+\log (3))}+\frac {\log (x)}{2 (4+\log (3))^2}+\frac {\log (x)}{2 x (4+\log (3))}+\frac {x \log (x)}{2 (4+\log (3))^2 (4-x+\log (3))}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.46, size = 25, normalized size = 1.00 \begin {gather*} \frac {e^x+x-\log (x)}{2 x (-4+x-\log (3))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 - x - x^2 + Log[3] + E^x*(4 - 6*x + x^2 + (1 - x)*Log[3]) + (-4 + 2*x - Log[3])*Log[x])/(32*x^2 -
16*x^3 + 2*x^4 + (16*x^2 - 4*x^3)*Log[3] + 2*x^2*Log[3]^2),x]

[Out]

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

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fricas [A]  time = 0.53, size = 24, normalized size = 0.96 \begin {gather*} \frac {x + e^{x} - \log \relax (x)}{2 \, {\left (x^{2} - x \log \relax (3) - 4 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(3)+2*x-4)*log(x)+((-x+1)*log(3)+x^2-6*x+4)*exp(x)+log(3)-x^2-x+4)/(2*x^2*log(3)^2+(-4*x^3+16*
x^2)*log(3)+2*x^4-16*x^3+32*x^2),x, algorithm="fricas")

[Out]

1/2*(x + e^x - log(x))/(x^2 - x*log(3) - 4*x)

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giac [A]  time = 0.34, size = 24, normalized size = 0.96 \begin {gather*} \frac {x + e^{x} - \log \relax (x)}{2 \, {\left (x^{2} - x \log \relax (3) - 4 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(3)+2*x-4)*log(x)+((-x+1)*log(3)+x^2-6*x+4)*exp(x)+log(3)-x^2-x+4)/(2*x^2*log(3)^2+(-4*x^3+16*
x^2)*log(3)+2*x^4-16*x^3+32*x^2),x, algorithm="giac")

[Out]

1/2*(x + e^x - log(x))/(x^2 - x*log(3) - 4*x)

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maple [A]  time = 0.22, size = 26, normalized size = 1.04

method	result	size
norman	\(\frac {-\frac {x}{2}-\frac {{\mathrm e}^{x}}{2}+\frac {\ln \relax (x )}{2}}{x \left (4+\ln \relax (3)-x \right )}\)	\(26\)
default	\(\frac {\ln \relax (x )}{2 \left (\ln \relax (3)+4\right )^{2}}+\frac {1}{2 x -8-2 \ln \relax (3)}-\frac {\ln \left (x -4-\ln \relax (3)\right )}{2 \left (\ln \relax (3)+4\right )^{2}}+\frac {\ln \left (4+\ln \relax (3)-x \right )}{2 \left (\ln \relax (3)+4\right )^{2}}+\frac {\ln \relax (x ) x}{2 \left (\ln \relax (3)+4\right )^{2} \left (4+\ln \relax (3)-x \right )}+\frac {\ln \relax (x )}{2 \left (\ln \relax (3)+4\right ) x}-\frac {\ln \relax (3) {\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{\left (\ln \relax (3)+4\right )^{2}}+\frac {\ln \relax (3) {\mathrm e}^{x}}{2 \left (\ln \relax (3)+4\right ) \left (x -4-\ln \relax (3)\right )}+\frac {\ln \relax (3) {\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{2 \ln \relax (3)+8}-\frac {{\mathrm e}^{x}}{2 \left (x -4-\ln \relax (3)\right )}-\frac {{\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{2}-\frac {4 \expIntegralEi \left (1, -x \right )}{\left (\ln \relax (3)+4\right )^{3}}+\frac {4 \,{\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{\left (\ln \relax (3)+4\right )^{3}}-\frac {2 \,{\mathrm e}^{x}}{\left (\ln \relax (3)+4\right )^{2} \left (x -4-\ln \relax (3)\right )}-\frac {5 \,{\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{\left (\ln \relax (3)+4\right )^{2}}-\frac {2 \,{\mathrm e}^{x}}{\left (\ln \relax (3)+4\right )^{2} x}+\frac {\expIntegralEi \left (1, -x \right )}{\left (\ln \relax (3)+4\right )^{2}}+\frac {3 \,{\mathrm e}^{x}}{\left (\ln \relax (3)+4\right ) \left (x -4-\ln \relax (3)\right )}+\frac {3 \,{\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{\ln \relax (3)+4}-\frac {\ln \relax (3) \expIntegralEi \left (1, -x \right )}{\left (\ln \relax (3)+4\right )^{3}}+\frac {\ln \relax (3) {\mathrm e}^{\ln \relax (3)+4} \expIntegralEi \left (1, 4+\ln \relax (3)-x \right )}{\left (\ln \relax (3)+4\right )^{3}}-\frac {\ln \relax (3) {\mathrm e}^{x}}{2 \left (\ln \relax (3)+4\right )^{2} \left (x -4-\ln \relax (3)\right )}-\frac {\ln \relax (3) {\mathrm e}^{x}}{2 \left (\ln \relax (3)+4\right )^{2} x}\)	\(402\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-ln(3)+2*x-4)*ln(x)+((1-x)*ln(3)+x^2-6*x+4)*exp(x)+ln(3)-x^2-x+4)/(2*x^2*ln(3)^2+(-4*x^3+16*x^2)*ln(3)+2
*x^4-16*x^3+32*x^2),x,method=_RETURNVERBOSE)

[Out]

(-1/2*x-1/2*exp(x)+1/2*ln(x))/x/(4+ln(3)-x)

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maxima [B]  time = 0.61, size = 362, normalized size = 14.48 \begin {gather*} -\frac {1}{2} \, {\left (\frac {2 \, x - \log \relax (3) - 4}{{\left (\log \relax (3)^{2} + 8 \, \log \relax (3) + 16\right )} x^{2} - {\left (\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64\right )} x} + \frac {2 \, \log \left (x - \log \relax (3) - 4\right )}{\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64} - \frac {2 \, \log \relax (x)}{\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64}\right )} \log \relax (3) + \frac {x {\left (\log \relax (3) + 4\right )} + {\left (\log \relax (3)^{2} + 8 \, \log \relax (3) + 16\right )} e^{x} - \log \relax (3)^{2} - {\left (x^{2} - x {\left (\log \relax (3) + 4\right )} + \log \relax (3)^{2} + 8 \, \log \relax (3) + 16\right )} \log \relax (x) - 8 \, \log \relax (3) - 16}{2 \, {\left ({\left (\log \relax (3)^{2} + 8 \, \log \relax (3) + 16\right )} x^{2} - {\left (\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64\right )} x\right )}} - \frac {2 \, {\left (2 \, x - \log \relax (3) - 4\right )}}{{\left (\log \relax (3)^{2} + 8 \, \log \relax (3) + 16\right )} x^{2} - {\left (\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64\right )} x} - \frac {4 \, \log \left (x - \log \relax (3) - 4\right )}{\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64} + \frac {\log \left (x - \log \relax (3) - 4\right )}{\log \relax (3)^{2} + 8 \, \log \relax (3) + 16} + \frac {4 \, \log \relax (x)}{\log \relax (3)^{3} + 12 \, \log \relax (3)^{2} + 48 \, \log \relax (3) + 64} - \frac {\log \relax (x)}{2 \, {\left (\log \relax (3)^{2} + 8 \, \log \relax (3) + 16\right )}} + \frac {1}{2 \, {\left (x {\left (\log \relax (3) + 4\right )} - \log \relax (3)^{2} - 8 \, \log \relax (3) - 16\right )}} + \frac {1}{2 \, {\left (x - \log \relax (3) - 4\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(3)+2*x-4)*log(x)+((-x+1)*log(3)+x^2-6*x+4)*exp(x)+log(3)-x^2-x+4)/(2*x^2*log(3)^2+(-4*x^3+16*
x^2)*log(3)+2*x^4-16*x^3+32*x^2),x, algorithm="maxima")

[Out]

-1/2*((2*x - log(3) - 4)/((log(3)^2 + 8*log(3) + 16)*x^2 - (log(3)^3 + 12*log(3)^2 + 48*log(3) + 64)*x) + 2*lo
g(x - log(3) - 4)/(log(3)^3 + 12*log(3)^2 + 48*log(3) + 64) - 2*log(x)/(log(3)^3 + 12*log(3)^2 + 48*log(3) + 6
4))*log(3) + 1/2*(x*(log(3) + 4) + (log(3)^2 + 8*log(3) + 16)*e^x - log(3)^2 - (x^2 - x*(log(3) + 4) + log(3)^
2 + 8*log(3) + 16)*log(x) - 8*log(3) - 16)/((log(3)^2 + 8*log(3) + 16)*x^2 - (log(3)^3 + 12*log(3)^2 + 48*log(
3) + 64)*x) - 2*(2*x - log(3) - 4)/((log(3)^2 + 8*log(3) + 16)*x^2 - (log(3)^3 + 12*log(3)^2 + 48*log(3) + 64)
*x) - 4*log(x - log(3) - 4)/(log(3)^3 + 12*log(3)^2 + 48*log(3) + 64) + log(x - log(3) - 4)/(log(3)^2 + 8*log(
3) + 16) + 4*log(x)/(log(3)^3 + 12*log(3)^2 + 48*log(3) + 64) - 1/2*log(x)/(log(3)^2 + 8*log(3) + 16) + 1/2/(x
*(log(3) + 4) - log(3)^2 - 8*log(3) - 16) + 1/2/(x - log(3) - 4)

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mupad [B]  time = 7.25, size = 7592, normalized size = 303.68 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x - log(3) + exp(x)*(6*x + log(3)*(x - 1) - x^2 - 4) + x^2 + log(x)*(log(3) - 2*x + 4) - 4)/(2*x^2*log(3
)^2 + log(3)*(16*x^2 - 4*x^3) + 32*x^2 - 16*x^3 + 2*x^4),x)

[Out]

exp(x)/(log(9) - 2*x + 8) - log((12*x - 2*log(81) + (512*log(3) + 64*log(81) - x*(128*log(81) - 384*log(3) - 4
8*log(3)^2 + 4*log(81)^2 + 256) + 32*log(3)*log(81) + 4*log(3)^2*log(81) + 64*log(3)^2 + 1024)/(2*(log(3) + 4)
^2) - 32)/(2*(log(3) + 4)^2))/(2*(log(3) + 4)^2) - ((2*exp(x))/(log(3) + 4) - (4*x*exp(x))/(8*log(3) + log(3)^
2 + 16))/(4*x + x*log(3) - x^2) - (3*ei(x))/(8*log(3) + log(3)^2 + 16) - 2/(x*(8*log(3) + log(3)^2 + 16)) + lo
g(x - log(3) - 4)/(2*(log(3) + 4)^2) - ((exp(x)*log(3))/(log(3) + 4) + (x*exp(x)*(2*log(3) + log(3)^2))/(8*log
(3) + log(3)^2 + 16))/(8*x + 2*x*log(3) - 2*x^2) + (3*exp(4)*ei(x - log(3) - 4))/2 + (x - x^3/(log(3) + 4)^2 +
x*log(x) - (x^2*log(x))/(log(3) + 4) + (x^3*log(x))/(log(3) + 4)^2)/(2*x^2*log(3) + 8*x^2 - 2*x^3) - (3*exp(x
))/((log(3) + 4)*(log(3) - x + 4)) - (2*atanh((log(81) - 4*x + 16)/((log(81) - 4*log(3))^(1/2)*(4*log(3) + log
(81) + 32)^(1/2))))/((log(81) - 4*log(3))^(1/2)*(4*log(3) + log(81) + 32)^(1/2)) + (log((2*x*log(3)^2)/(256*lo
g(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (log(3)^2*log(81) + 16*log(3)^2)/(256*log(3) + 96*log(3)^
2 + 16*log(3)^3 + log(3)^4 + 256) + ((log(3)^2*(16*log(81) + 8*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32
))^(1/2) + 256) - log(3)*(64*log(81) + 4*log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*
(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + (log(81)^2*(-(4*log(3) - log(81))*(4*log(3) + log(81
) + 32))^(1/2))/8 + 6*log(81)^2 + log(81)^3/8) + log(3)^3*(2*log(81) + (-(4*log(3) - log(81))*(4*log(3) + log(
81) + 32))^(1/2) + 32))*((((393216*log(3) + 16384*log(81) + 24576*log(3)*log(81) + 15360*log(3)^2*log(81) + 51
20*log(3)^3*log(81) + 960*log(3)^4*log(81) + 96*log(3)^5*log(81) + 4*log(3)^6*log(81) + 245760*log(3)^2 + 8192
0*log(3)^3 + 15360*log(3)^4 + 1536*log(3)^5 + 64*log(3)^6 + 262144)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 +
log(3)^4 + 256) - (2*x*(16384*log(81) - 16384*log(3) + 16384*log(3)*log(81) + 512*log(3)*log(81)^2 + 6144*log(
3)^2*log(81) + 1024*log(3)^3*log(81) + 64*log(3)^4*log(81) - 43008*log(3)^2 - 22528*log(3)^3 - 5248*log(3)^4 -
576*log(3)^5 - 24*log(3)^6 + 512*log(81)^2 + 192*log(3)^2*log(81)^2 + 32*log(3)^3*log(81)^2 + 2*log(3)^4*log(
81)^2 + 32768))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256))*(log(3)^2*(16*log(81) + 8*(-(4*log(
3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 256) - log(3)*(64*log(81) + 4*log(81)*(-(4*log(3) - log(81))*
(4*log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + (log(81)^2*(-(
4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2))/8 + 6*log(81)^2 + log(81)^3/8) + log(3)^3*(2*log(81) + (
-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 32)))/(8192*log(81) - 32768*log(3) + 8192*log(3)*log(
81) + 256*log(3)*log(81)^2 + 3072*log(3)^2*log(81) + 512*log(3)^3*log(81) + 32*log(3)^4*log(81) - 36864*log(3)
^2 - 16384*log(3)^3 - 3584*log(3)^4 - 384*log(3)^5 - 16*log(3)^6 + 256*log(81)^2 + 96*log(3)^2*log(81)^2 + 16*
log(3)^3*log(81)^2 + log(3)^4*log(81)^2) - (3072*log(3) + 512*log(3)*log(81) + 16*log(3)*log(81)^2 + 256*log(3
)^2*log(81) + 32*log(3)^3*log(81) + 1024*log(3)^2 - 128*log(3)^3 - 64*log(3)^4 - 4*log(3)^5 + 8*log(3)^2*log(8
1)^2 + log(3)^3*log(81)^2)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (2*x*(512*log(3) + 32*l
og(3)*log(81) + 16*log(3)^2*log(81) + 2*log(3)^3*log(81) + 256*log(3)^2 + 32*log(3)^3))/(256*log(3) + 96*log(3
)^2 + 16*log(3)^3 + log(3)^4 + 256)))/(8192*log(81) - 32768*log(3) + 8192*log(3)*log(81) + 256*log(3)*log(81)^
2 + 3072*log(3)^2*log(81) + 512*log(3)^3*log(81) + 32*log(3)^4*log(81) - 36864*log(3)^2 - 16384*log(3)^3 - 358
4*log(3)^4 - 384*log(3)^5 - 16*log(3)^6 + 256*log(81)^2 + 96*log(3)^2*log(81)^2 + 16*log(3)^3*log(81)^2 + log(
3)^4*log(81)^2))*(log(3)^2*(16*log(81) + 8*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 256) - lo
g(3)*(64*log(81) + 4*log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81
))*(4*log(3) + log(81) + 32))^(1/2) + (log(81)^2*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2))/8 +
6*log(81)^2 + log(81)^3/8) + log(3)^3*(2*log(81) + (-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 3
2)))/(8192*log(81) - 32768*log(3) + 8192*log(3)*log(81) + 256*log(3)*log(81)^2 + 3072*log(3)^2*log(81) + 512*l
og(3)^3*log(81) + 32*log(3)^4*log(81) - 36864*log(3)^2 - 16384*log(3)^3 - 3584*log(3)^4 - 384*log(3)^5 - 16*lo
g(3)^6 + 256*log(81)^2 + 96*log(3)^2*log(81)^2 + 16*log(3)^3*log(81)^2 + log(3)^4*log(81)^2) + (log((2*x*log(3
)^2)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (log(3)^2*log(81) + 16*log(3)^2)/(256*log(3)
+ 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (((2*x*(512*log(3) + 32*log(3)*log(81) + 16*log(3)^2*log(81) +
2*log(3)^3*log(81) + 256*log(3)^2 + 32*log(3)^3))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) -
(3072*log(3) + 512*log(3)*log(81) + 16*log(3)*log(81)^2 + 256*log(3)^2*log(81) + 32*log(3)^3*log(81) + 1024*l
og(3)^2 - 128*log(3)^3 - 64*log(3)^4 - 4*log(3)^5 + 8*log(3)^2*log(81)^2 + log(3)^3*log(81)^2)/(256*log(3) + 9
6*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (((393216*log(3) + 16384*log(81) + 24576*log(3)*log(81) + 15360*l
og(3)^2*log(81) + 5120*log(3)^3*log(81) + 960*log(3)^4*log(81) + 96*log(3)^5*log(81) + 4*log(3)^6*log(81) + 24
5760*log(3)^2 + 81920*log(3)^3 + 15360*log(3)^4 + 1536*log(3)^5 + 64*log(3)^6 + 262144)/(256*log(3) + 96*log(3
)^2 + 16*log(3)^3 + log(3)^4 + 256) - (2*x*(16384*log(81) - 16384*log(3) + 16384*log(3)*log(81) + 512*log(3)*l
og(81)^2 + 6144*log(3)^2*log(81) + 1024*log(3)^3*log(81) + 64*log(3)^4*log(81) - 43008*log(3)^2 - 22528*log(3)
^3 - 5248*log(3)^4 - 576*log(3)^5 - 24*log(3)^6 + 512*log(81)^2 + 192*log(3)^2*log(81)^2 + 32*log(3)^3*log(81)
^2 + 2*log(3)^4*log(81)^2 + 32768))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256))*(log(3)^3*(2*lo
g(81) - (-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 32) + log(3)^2*(16*log(81) - 8*(-(4*log(3) -
log(81))*(4*log(3) + log(81) + 32))^(1/2) + 256) - log(3)*(64*log(81) - 4*log(81)*(-(4*log(3) - log(81))*(4*l
og(3) + log(81) + 32))^(1/2) - 16*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) - (log(81)^2*(-(4*lo
g(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2))/8 + 6*log(81)^2 + log(81)^3/8)))/(8192*log(81) - 32768*log(3
) + 8192*log(3)*log(81) + 256*log(3)*log(81)^2 + 3072*log(3)^2*log(81) + 512*log(3)^3*log(81) + 32*log(3)^4*lo
g(81) - 36864*log(3)^2 - 16384*log(3)^3 - 3584*log(3)^4 - 384*log(3)^5 - 16*log(3)^6 + 256*log(81)^2 + 96*log(
3)^2*log(81)^2 + 16*log(3)^3*log(81)^2 + log(3)^4*log(81)^2))*(log(3)^3*(2*log(81) - (-(4*log(3) - log(81))*(4
*log(3) + log(81) + 32))^(1/2) + 32) + log(3)^2*(16*log(81) - 8*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 3
2))^(1/2) + 256) - log(3)*(64*log(81) - 4*log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) - 16
*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) - (log(81)^2*(-(4*log(3) - log(81))*(4*log(3) + log(8
1) + 32))^(1/2))/8 + 6*log(81)^2 + log(81)^3/8)))/(8192*log(81) - 32768*log(3) + 8192*log(3)*log(81) + 256*log
(3)*log(81)^2 + 3072*log(3)^2*log(81) + 512*log(3)^3*log(81) + 32*log(3)^4*log(81) - 36864*log(3)^2 - 16384*lo
g(3)^3 - 3584*log(3)^4 - 384*log(3)^5 - 16*log(3)^6 + 256*log(81)^2 + 96*log(3)^2*log(81)^2 + 16*log(3)^3*log(
81)^2 + log(3)^4*log(81)^2))*(log(3)^3*(2*log(81) - (-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) +
32) + log(3)^2*(16*log(81) - 8*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 256) - log(3)*(64*log
(81) - 4*log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) - 16*(-(4*log(3) - log(81))*(4*log(3)
+ log(81) + 32))^(1/2) - (log(81)^2*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2))/8 + 6*log(81)^2
+ log(81)^3/8)))/(8192*log(81) - 32768*log(3) + 8192*log(3)*log(81) + 256*log(3)*log(81)^2 + 3072*log(3)^2*log
(81) + 512*log(3)^3*log(81) + 32*log(3)^4*log(81) - 36864*log(3)^2 - 16384*log(3)^3 - 3584*log(3)^4 - 384*log(
3)^5 - 16*log(3)^6 + 256*log(81)^2 + 96*log(3)^2*log(81)^2 + 16*log(3)^3*log(81)^2 + log(3)^4*log(81)^2) + (lo
g((4*x)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (4*log(9) + 32)/(256*log(3) + 96*log(3)^2
+ 16*log(3)^3 + log(3)^4 + 256) + ((2*log(9) + 16)*(((2*log(9) + 16)*((49152*log(3) + 4096*log(9) + 6144*log(3
)*log(9) + 3840*log(3)^2*log(9) + 1280*log(3)^3*log(9) + 240*log(3)^4*log(9) + 24*log(3)^5*log(9) + log(3)^6*l
og(9) + 30720*log(3)^2 + 10240*log(3)^3 + 1920*log(3)^4 + 192*log(3)^5 + 8*log(3)^6 + 32768)/(256*log(3) + 96*
log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (2*x*(4096*log(9) - 2048*log(3) + 4096*log(3)*log(9) + 256*log(3)*l
og(9)^2 + 1536*log(3)^2*log(9) + 256*log(3)^3*log(9) + 16*log(3)^4*log(9) - 5376*log(3)^2 - 2816*log(3)^3 - 65
6*log(3)^4 - 72*log(3)^5 - 3*log(3)^6 + 256*log(9)^2 + 96*log(3)^2*log(9)^2 + 16*log(3)^3*log(9)^2 + log(3)^4*
log(9)^2 + 4096))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256)))/(log(3) + 4)^4 - (512*log(3) + 5
12*log(9) + 256*log(3)*log(9) + 16*log(3)*log(9)^2 + 32*log(3)^2*log(9) - 64*log(3)^2 - 32*log(3)^3 - 2*log(3)
^4 + 32*log(9)^2 + 2*log(3)^2*log(9)^2 + 1536)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (2*
x*(128*log(3) + 32*log(9) + 16*log(3)*log(9) + 2*log(3)^2*log(9) + 16*log(3)^2 + 256))/(256*log(3) + 96*log(3)
^2 + 16*log(3)^3 + log(3)^4 + 256)))/(log(3) + 4)^4)*(2*log(9) + 16))/(log(3) + 4)^4 - log(3)/(2*x*(8*log(3) +
log(3)^2 + 16)) + (log(3)*ei(x))/((log(3) + 4)*(8*log(3) + log(3)^2 + 16)) + (log(3)*log((2*x*log(3)^2)/(256*
log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (log(3)^2*log(81) + 16*log(3)^2)/(256*log(3) + 96*log(3
)^2 + 16*log(3)^3 + log(3)^4 + 256) + (log(3)*(log(81) + 16)*((2*x*(512*log(3) + 32*log(3)*log(81) + 16*log(3)
^2*log(81) + 2*log(3)^3*log(81) + 256*log(3)^2 + 32*log(3)^3))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3
)^4 + 256) - (3072*log(3) + 512*log(3)*log(81) + 16*log(3)*log(81)^2 + 256*log(3)^2*log(81) + 32*log(3)^3*log(
81) + 1024*log(3)^2 - 128*log(3)^3 - 64*log(3)^4 - 4*log(3)^5 + 8*log(3)^2*log(81)^2 + log(3)^3*log(81)^2)/(25
6*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (log(3)*((393216*log(3) + 16384*log(81) + 24576*log(3
)*log(81) + 15360*log(3)^2*log(81) + 5120*log(3)^3*log(81) + 960*log(3)^4*log(81) + 96*log(3)^5*log(81) + 4*lo
g(3)^6*log(81) + 245760*log(3)^2 + 81920*log(3)^3 + 15360*log(3)^4 + 1536*log(3)^5 + 64*log(3)^6 + 262144)/(25
6*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (2*x*(16384*log(81) - 16384*log(3) + 16384*log(3)*log
(81) + 512*log(3)*log(81)^2 + 6144*log(3)^2*log(81) + 1024*log(3)^3*log(81) + 64*log(3)^4*log(81) - 43008*log(
3)^2 - 22528*log(3)^3 - 5248*log(3)^4 - 576*log(3)^5 - 24*log(3)^6 + 512*log(81)^2 + 192*log(3)^2*log(81)^2 +
32*log(3)^3*log(81)^2 + 2*log(3)^4*log(81)^2 + 32768))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 25
6))*(log(81) + 16))/(1024*log(3) + 384*log(3)^2 + 64*log(3)^3 + 4*log(3)^4 + 1024)))/(1024*log(3) + 384*log(3)
^2 + 64*log(3)^3 + 4*log(3)^4 + 1024))*(log(81) + 16))/(1024*log(3) + 384*log(3)^2 + 64*log(3)^3 + 4*log(3)^4
+ 1024) - (3*exp(4)*ei(x - log(3) - 4)*(10*log(3) + 6*log(3)^2 + log(3)^3))/(2*(48*log(3) + 12*log(3)^2 + log(
3)^3 + 64)) + (ei(x)*(2*log(3) + 12))/((log(3) + 4)*(8*log(3) + log(3)^2 + 16)) - (9*exp(4)*ei(x - log(3) - 4)
*(log(3) + 3))/(8*log(3) + log(3)^2 + 16) + (6*exp(4)*ei(x - log(3) - 4)*(log(3) + 2))/(48*log(3) + 12*log(3)^
2 + log(3)^3 + 64) + (log(((2*log(81) - 12*x + ((128*log(3) - 32*log(81) + log(81)*(-(4*log(3) - log(81))*(4*l
og(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*log(3)^2 - log(
81)^2)*(512*log(3) + 64*log(81) - x*(128*log(81) - 384*log(3) - 48*log(3)^2 + 4*log(81)^2 + 256) + 32*log(3)*l
og(81) + 4*log(3)^2*log(81) + 64*log(3)^2 + 1024))/((4*log(3) - log(81))*(4*log(3) + log(81) + 32)*((log(81)*(
log(81) + 32))/4 + ((4*log(3) - log(81))*(4*log(3) + log(81) + 32))/4 + 64)) + 32)*(128*log(3) - 32*log(81) +
log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4*log(3) + log(81
) + 32))^(1/2) + 16*log(3)^2 - log(81)^2))/((4*log(3) + log(81) + 32)*((log(81)*(log(81) + 32))/4 + ((4*log(3)
- log(81))*(4*log(3) + log(81) + 32))/4 + 64)))*(128*log(3) - 32*log(81) + log(81)*(-(4*log(3) - log(81))*(4*
log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*log(3)^2 - log
(81)^2))/((4*log(3) - log(81))*(4*log(3) + log(81) + 32)*((log(81)*(log(81) + 32))/4 + ((4*log(3) - log(81))*(
4*log(3) + log(81) + 32))/4 + 64)) - (log(((12*x - 2*log(81) + ((32*log(81) - 128*log(3) + log(81)*(-(4*log(3)
- log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) - 16
*log(3)^2 + log(81)^2)*(512*log(3) + 64*log(81) - x*(128*log(81) - 384*log(3) - 48*log(3)^2 + 4*log(81)^2 + 25
6) + 32*log(3)*log(81) + 4*log(3)^2*log(81) + 64*log(3)^2 + 1024))/((4*log(3) - log(81))*(4*log(3) + log(81) +
32)*((log(81)*(log(81) + 32))/4 + ((4*log(3) - log(81))*(4*log(3) + log(81) + 32))/4 + 64)) - 32)*(32*log(81)
- 128*log(3) + log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4
*log(3) + log(81) + 32))^(1/2) - 16*log(3)^2 + log(81)^2))/((4*log(3) - log(81))*(4*log(3) + log(81) + 32)*((l
og(81)*(log(81) + 32))/4 + ((4*log(3) - log(81))*(4*log(3) + log(81) + 32))/4 + 64)))*(32*log(81) - 128*log(3)
+ log(81)*(-(4*log(3) - log(81))*(4*log(3) + log(81) + 32))^(1/2) + 16*(-(4*log(3) - log(81))*(4*log(3) + log
(81) + 32))^(1/2) - 16*log(3)^2 + log(81)^2))/((4*log(3) - log(81))*(4*log(3) + log(81) + 32)*((log(81)*(log(8
1) + 32))/4 + ((4*log(3) - log(81))*(4*log(3) + log(81) + 32))/4 + 64)) - (log((4*x)/(256*log(3) + 96*log(3)^2
+ 16*log(3)^3 + log(3)^4 + 256) - (4*log(9) + 32)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) +
(((512*log(3) + 512*log(9) + 256*log(3)*log(9) + 16*log(3)*log(9)^2 + 32*log(3)^2*log(9) - 64*log(3)^2 - 32*l
og(3)^3 - 2*log(3)^4 + 32*log(9)^2 + 2*log(3)^2*log(9)^2 + 1536)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log
(3)^4 + 256) - (2*x*(128*log(3) + 32*log(9) + 16*log(3)*log(9) + 2*log(3)^2*log(9) + 16*log(3)^2 + 256))/(256*
log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (((49152*log(3) + 4096*log(9) + 6144*log(3)*log(9) + 38
40*log(3)^2*log(9) + 1280*log(3)^3*log(9) + 240*log(3)^4*log(9) + 24*log(3)^5*log(9) + log(3)^6*log(9) + 30720
*log(3)^2 + 10240*log(3)^3 + 1920*log(3)^4 + 192*log(3)^5 + 8*log(3)^6 + 32768)/(256*log(3) + 96*log(3)^2 + 16
*log(3)^3 + log(3)^4 + 256) - (2*x*(4096*log(9) - 2048*log(3) + 4096*log(3)*log(9) + 256*log(3)*log(9)^2 + 153
6*log(3)^2*log(9) + 256*log(3)^3*log(9) + 16*log(3)^4*log(9) - 5376*log(3)^2 - 2816*log(3)^3 - 656*log(3)^4 -
72*log(3)^5 - 3*log(3)^6 + 256*log(9)^2 + 96*log(3)^2*log(9)^2 + 16*log(3)^3*log(9)^2 + log(3)^4*log(9)^2 + 40
96))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256))*(256*log(3) - 16*log(3)*(-(2*log(3) - log(9))*
(2*log(3) + log(9) + 16))^(1/2) + 32*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) - 2*log(3)^2*(-(2*l
og(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 32*log(3)^2 - log(9)^3 + log(9)*(32*log(3) + 16*(-(2*log(3)
- log(9))*(2*log(3) + log(9) + 16))^(1/2) + 4*log(3)^2 - 128) + log(9)^2*((-(2*log(3) - log(9))*(2*log(3) + lo
g(9) + 16))^(1/2) - 24)))/((2*log(3) - log(9))*(2*log(3) + log(9) + 16)*(log(9)*(log(9) + 16)*((log(9)*(log(9)
+ 16))/16 + 8) + (2*log(3) - log(9))*(2*log(3) + log(9) + 16)*((log(9)*(log(9) + 16))/8 + ((2*log(3) - log(9)
)*(2*log(3) + log(9) + 16))/16 + 8) + 256)))*(256*log(3) - 16*log(3)*(-(2*log(3) - log(9))*(2*log(3) + log(9)
+ 16))^(1/2) + 32*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) - 2*log(3)^2*(-(2*log(3) - log(9))*(2*
log(3) + log(9) + 16))^(1/2) + 32*log(3)^2 - log(9)^3 + log(9)*(32*log(3) + 16*(-(2*log(3) - log(9))*(2*log(3)
+ log(9) + 16))^(1/2) + 4*log(3)^2 - 128) + log(9)^2*((-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) -
24)))/((2*log(3) - log(9))*(2*log(3) + log(9) + 16)*(log(9)*(log(9) + 16)*((log(9)*(log(9) + 16))/16 + 8) + (
2*log(3) - log(9))*(2*log(3) + log(9) + 16)*((log(9)*(log(9) + 16))/8 + ((2*log(3) - log(9))*(2*log(3) + log(9
) + 16))/16 + 8) + 256)))*(256*log(3) - 16*log(3)*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 32*(
-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) - 2*log(3)^2*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 1
6))^(1/2) + 32*log(3)^2 - log(9)^3 + log(9)*(32*log(3) + 16*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1
/2) + 4*log(3)^2 - 128) + log(9)^2*((-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) - 24)))/((2*log(3) -
log(9))*(2*log(3) + log(9) + 16)*(log(9)*(log(9) + 16)*((log(9)*(log(9) + 16))/16 + 8) + (2*log(3) - log(9))*
(2*log(3) + log(9) + 16)*((log(9)*(log(9) + 16))/8 + ((2*log(3) - log(9))*(2*log(3) + log(9) + 16))/16 + 8) +
256)) - (log((4*x)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (4*log(9) + 32)/(256*log(3) + 9
6*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (((512*log(3) + 512*log(9) + 256*log(3)*log(9) + 16*log(3)*log(9)
^2 + 32*log(3)^2*log(9) - 64*log(3)^2 - 32*log(3)^3 - 2*log(3)^4 + 32*log(9)^2 + 2*log(3)^2*log(9)^2 + 1536)/(
256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (2*x*(128*log(3) + 32*log(9) + 16*log(3)*log(9) + 2
*log(3)^2*log(9) + 16*log(3)^2 + 256))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) + (((49152*lo
g(3) + 4096*log(9) + 6144*log(3)*log(9) + 3840*log(3)^2*log(9) + 1280*log(3)^3*log(9) + 240*log(3)^4*log(9) +
24*log(3)^5*log(9) + log(3)^6*log(9) + 30720*log(3)^2 + 10240*log(3)^3 + 1920*log(3)^4 + 192*log(3)^5 + 8*log(
3)^6 + 32768)/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256) - (2*x*(4096*log(9) - 2048*log(3) + 40
96*log(3)*log(9) + 256*log(3)*log(9)^2 + 1536*log(3)^2*log(9) + 256*log(3)^3*log(9) + 16*log(3)^4*log(9) - 537
6*log(3)^2 - 2816*log(3)^3 - 656*log(3)^4 - 72*log(3)^5 - 3*log(3)^6 + 256*log(9)^2 + 96*log(3)^2*log(9)^2 + 1
6*log(3)^3*log(9)^2 + log(3)^4*log(9)^2 + 4096))/(256*log(3) + 96*log(3)^2 + 16*log(3)^3 + log(3)^4 + 256))*(2
56*log(3) + 16*log(3)*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) - 32*(-(2*log(3) - log(9))*(2*log(
3) + log(9) + 16))^(1/2) + 2*log(3)^2*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 32*log(3)^2 - lo
g(9)^3 + log(9)*(32*log(3) - 16*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 4*log(3)^2 - 128) - lo
g(9)^2*((-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 24)))/((2*log(3) - log(9))*(2*log(3) + log(9)
+ 16)*(log(9)*(log(9) + 16)*((log(9)*(log(9) + 16))/16 + 8) + (2*log(3) - log(9))*(2*log(3) + log(9) + 16)*((l
og(9)*(log(9) + 16))/8 + ((2*log(3) - log(9))*(2*log(3) + log(9) + 16))/16 + 8) + 256)))*(256*log(3) + 16*log(
3)*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) - 32*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^
(1/2) + 2*log(3)^2*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 32*log(3)^2 - log(9)^3 + log(9)*(32
*log(3) - 16*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 4*log(3)^2 - 128) - log(9)^2*((-(2*log(3)
- log(9))*(2*log(3) + log(9) + 16))^(1/2) + 24)))/((2*log(3) - log(9))*(2*log(3) + log(9) + 16)*(log(9)*(log(
9) + 16)*((log(9)*(log(9) + 16))/16 + 8) + (2*log(3) - log(9))*(2*log(3) + log(9) + 16)*((log(9)*(log(9) + 16)
)/8 + ((2*log(3) - log(9))*(2*log(3) + log(9) + 16))/16 + 8) + 256)))*(256*log(3) + 16*log(3)*(-(2*log(3) - lo
g(9))*(2*log(3) + log(9) + 16))^(1/2) - 32*(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 2*log(3)^2*
(-(2*log(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 32*log(3)^2 - log(9)^3 + log(9)*(32*log(3) - 16*(-(2*l
og(3) - log(9))*(2*log(3) + log(9) + 16))^(1/2) + 4*log(3)^2 - 128) - log(9)^2*((-(2*log(3) - log(9))*(2*log(3
) + log(9) + 16))^(1/2) + 24)))/((2*log(3) - log(9))*(2*log(3) + log(9) + 16)*(log(9)*(log(9) + 16)*((log(9)*(
log(9) + 16))/16 + 8) + (2*log(3) - log(9))*(2*log(3) + log(9) + 16)*((log(9)*(log(9) + 16))/8 + ((2*log(3) -
log(9))*(2*log(3) + log(9) + 16))/16 + 8) + 256))

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sympy [B]  time = 0.69, size = 48, normalized size = 1.92 \begin {gather*} \frac {e^{x}}{2 x^{2} - 8 x - 2 x \log {\relax (3 )}} - \frac {\log {\relax (x )}}{2 x^{2} - 8 x - 2 x \log {\relax (3 )}} + \frac {1}{2 x - 8 - 2 \log {\relax (3 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-ln(3)+2*x-4)*ln(x)+((-x+1)*ln(3)+x**2-6*x+4)*exp(x)+ln(3)-x**2-x+4)/(2*x**2*ln(3)**2+(-4*x**3+16*
x**2)*ln(3)+2*x**4-16*x**3+32*x**2),x)

[Out]

exp(x)/(2*x**2 - 8*x - 2*x*log(3)) - log(x)/(2*x**2 - 8*x - 2*x*log(3)) + 1/(2*x - 8 - 2*log(3))

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