3.84.7 \(\int \frac {e^{\frac {1}{4+4 x-3 x^2-2 x^3+x^4+(-8 x-4 x^2+4 x^3) \log (\frac {1}{4} (-8-4 x+\log (3)))+(-4-2 x+6 x^2) \log ^2(\frac {1}{4} (-8-4 x+\log (3)))+4 x \log ^3(\frac {1}{4} (-8-4 x+\log (3)))+\log ^4(\frac {1}{4} (-8-4 x+\log (3)))}} (-16+40 x+16 x^2+(2-4 x) \log (3)+(48+16 x-4 \log (3)) \log (\frac {1}{4} (-8-4 x+\log (3))))}{64+128 x-112 x^3-20 x^4+36 x^5+4 x^6-4 x^7+(-8-12 x+6 x^2+11 x^3-3 x^4-3 x^5+x^6) \log (3)+(-192 x-288 x^2+48 x^3+168 x^4-24 x^6+(24 x+24 x^2-18 x^3-12 x^4+6 x^5) \log (3)) \log (\frac {1}{4} (-8-4 x+\log (3)))+(-96-144 x+216 x^2+276 x^3-48 x^4-60 x^5+(12+12 x-33 x^2-18 x^3+15 x^4) \log (3)) \log ^2(\frac {1}{4} (-8-4 x+\log (3)))+(192 x+192 x^2-112 x^3-80 x^4+(-24 x-12 x^2+20 x^3) \log (3)) \log ^3(\frac {1}{4} (-8-4 x+\log (3)))+(48+48 x-108 x^2-60 x^3+(-6-3 x+15 x^2) \log (3)) \log ^4(\frac {1}{4} (-8-4 x+\log (3)))+(-48 x-24 x^2+6 x \log (3)) \log ^5(\frac {1}{4} (-8-4 x+\log (3)))+(-8-4 x+\log (3)) \log ^6(\frac {1}{4} (-8-4 x+\log (3)))} \, dx\)

Optimal. Leaf size=25 \[ e^{\frac {1}{\left (-2-x+\left (x+\log \left (-2-x+\frac {\log (3)}{4}\right )\right )^2\right )^2}} \]

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Rubi [A]  time = 2.24, antiderivative size = 41, normalized size of antiderivative = 1.64, number of steps used = 3, number of rules used = 3, integrand size = 481, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {6688, 12, 6706} \begin {gather*} \exp \left (\frac {1}{\left (x^2-x+\log ^2\left (\frac {1}{4} (-4 x-8+\log (3))\right )+2 x \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )-2\right )^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(4 + 4*x - 3*x^2 - 2*x^3 + x^4 + (-8*x - 4*x^2 + 4*x^3)*Log[(-8 - 4*x + Log[3])/4] + (-4 - 2*x + 6*x^2)
*Log[(-8 - 4*x + Log[3])/4]^2 + 4*x*Log[(-8 - 4*x + Log[3])/4]^3 + Log[(-8 - 4*x + Log[3])/4]^4)^(-1)*(-16 + 4
0*x + 16*x^2 + (2 - 4*x)*Log[3] + (48 + 16*x - 4*Log[3])*Log[(-8 - 4*x + Log[3])/4]))/(64 + 128*x - 112*x^3 -
20*x^4 + 36*x^5 + 4*x^6 - 4*x^7 + (-8 - 12*x + 6*x^2 + 11*x^3 - 3*x^4 - 3*x^5 + x^6)*Log[3] + (-192*x - 288*x^
2 + 48*x^3 + 168*x^4 - 24*x^6 + (24*x + 24*x^2 - 18*x^3 - 12*x^4 + 6*x^5)*Log[3])*Log[(-8 - 4*x + Log[3])/4] +
(-96 - 144*x + 216*x^2 + 276*x^3 - 48*x^4 - 60*x^5 + (12 + 12*x - 33*x^2 - 18*x^3 + 15*x^4)*Log[3])*Log[(-8 -
4*x + Log[3])/4]^2 + (192*x + 192*x^2 - 112*x^3 - 80*x^4 + (-24*x - 12*x^2 + 20*x^3)*Log[3])*Log[(-8 - 4*x +
Log[3])/4]^3 + (48 + 48*x - 108*x^2 - 60*x^3 + (-6 - 3*x + 15*x^2)*Log[3])*Log[(-8 - 4*x + Log[3])/4]^4 + (-48
*x - 24*x^2 + 6*x*Log[3])*Log[(-8 - 4*x + Log[3])/4]^5 + (-8 - 4*x + Log[3])*Log[(-8 - 4*x + Log[3])/4]^6),x]

[Out]

E^(-2 - x + x^2 + 2*x*Log[(-8 - 4*x + Log[3])/4] + Log[(-8 - 4*x + Log[3])/4]^2)^(-2)

Rule 12

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

Rule 6688

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

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \exp \left (\frac {1}{\left (-2-x+x^2+2 x \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )^2}\right ) \left (8 x^2-8 \left (1-\frac {\log (3)}{8}\right )-2 x (-10+\log (3))+(24+8 x-\log (9)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{(8+4 x-\log (3)) \left (2+x-x^2-2 x \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )-\log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )^3} \, dx\\ &=2 \int \frac {\exp \left (\frac {1}{\left (-2-x+x^2+2 x \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )^2}\right ) \left (8 x^2-8 \left (1-\frac {\log (3)}{8}\right )-2 x (-10+\log (3))+(24+8 x-\log (9)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{(8+4 x-\log (3)) \left (2+x-x^2-2 x \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )-\log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )^3} \, dx\\ &=\exp \left (\frac {1}{\left (-2-x+x^2+2 x \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )^2}\right )\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.42, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {1}{4+4 x-3 x^2-2 x^3+x^4+\left (-8 x-4 x^2+4 x^3\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-4-2 x+6 x^2\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+4 x \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )}} \left (-16+40 x+16 x^2+(2-4 x) \log (3)+(48+16 x-4 \log (3)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{64+128 x-112 x^3-20 x^4+36 x^5+4 x^6-4 x^7+\left (-8-12 x+6 x^2+11 x^3-3 x^4-3 x^5+x^6\right ) \log (3)+\left (-192 x-288 x^2+48 x^3+168 x^4-24 x^6+\left (24 x+24 x^2-18 x^3-12 x^4+6 x^5\right ) \log (3)\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-96-144 x+216 x^2+276 x^3-48 x^4-60 x^5+\left (12+12 x-33 x^2-18 x^3+15 x^4\right ) \log (3)\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (192 x+192 x^2-112 x^3-80 x^4+\left (-24 x-12 x^2+20 x^3\right ) \log (3)\right ) \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (48+48 x-108 x^2-60 x^3+\left (-6-3 x+15 x^2\right ) \log (3)\right ) \log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-48 x-24 x^2+6 x \log (3)\right ) \log ^5\left (\frac {1}{4} (-8-4 x+\log (3))\right )+(-8-4 x+\log (3)) \log ^6\left (\frac {1}{4} (-8-4 x+\log (3))\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^(4 + 4*x - 3*x^2 - 2*x^3 + x^4 + (-8*x - 4*x^2 + 4*x^3)*Log[(-8 - 4*x + Log[3])/4] + (-4 - 2*x +
6*x^2)*Log[(-8 - 4*x + Log[3])/4]^2 + 4*x*Log[(-8 - 4*x + Log[3])/4]^3 + Log[(-8 - 4*x + Log[3])/4]^4)^(-1)*(-
16 + 40*x + 16*x^2 + (2 - 4*x)*Log[3] + (48 + 16*x - 4*Log[3])*Log[(-8 - 4*x + Log[3])/4]))/(64 + 128*x - 112*
x^3 - 20*x^4 + 36*x^5 + 4*x^6 - 4*x^7 + (-8 - 12*x + 6*x^2 + 11*x^3 - 3*x^4 - 3*x^5 + x^6)*Log[3] + (-192*x -
288*x^2 + 48*x^3 + 168*x^4 - 24*x^6 + (24*x + 24*x^2 - 18*x^3 - 12*x^4 + 6*x^5)*Log[3])*Log[(-8 - 4*x + Log[3]
)/4] + (-96 - 144*x + 216*x^2 + 276*x^3 - 48*x^4 - 60*x^5 + (12 + 12*x - 33*x^2 - 18*x^3 + 15*x^4)*Log[3])*Log
[(-8 - 4*x + Log[3])/4]^2 + (192*x + 192*x^2 - 112*x^3 - 80*x^4 + (-24*x - 12*x^2 + 20*x^3)*Log[3])*Log[(-8 -
4*x + Log[3])/4]^3 + (48 + 48*x - 108*x^2 - 60*x^3 + (-6 - 3*x + 15*x^2)*Log[3])*Log[(-8 - 4*x + Log[3])/4]^4
+ (-48*x - 24*x^2 + 6*x*Log[3])*Log[(-8 - 4*x + Log[3])/4]^5 + (-8 - 4*x + Log[3])*Log[(-8 - 4*x + Log[3])/4]^
6),x]

[Out]

Integrate[(E^(4 + 4*x - 3*x^2 - 2*x^3 + x^4 + (-8*x - 4*x^2 + 4*x^3)*Log[(-8 - 4*x + Log[3])/4] + (-4 - 2*x +
6*x^2)*Log[(-8 - 4*x + Log[3])/4]^2 + 4*x*Log[(-8 - 4*x + Log[3])/4]^3 + Log[(-8 - 4*x + Log[3])/4]^4)^(-1)*(-
16 + 40*x + 16*x^2 + (2 - 4*x)*Log[3] + (48 + 16*x - 4*Log[3])*Log[(-8 - 4*x + Log[3])/4]))/(64 + 128*x - 112*
x^3 - 20*x^4 + 36*x^5 + 4*x^6 - 4*x^7 + (-8 - 12*x + 6*x^2 + 11*x^3 - 3*x^4 - 3*x^5 + x^6)*Log[3] + (-192*x -
288*x^2 + 48*x^3 + 168*x^4 - 24*x^6 + (24*x + 24*x^2 - 18*x^3 - 12*x^4 + 6*x^5)*Log[3])*Log[(-8 - 4*x + Log[3]
)/4] + (-96 - 144*x + 216*x^2 + 276*x^3 - 48*x^4 - 60*x^5 + (12 + 12*x - 33*x^2 - 18*x^3 + 15*x^4)*Log[3])*Log
[(-8 - 4*x + Log[3])/4]^2 + (192*x + 192*x^2 - 112*x^3 - 80*x^4 + (-24*x - 12*x^2 + 20*x^3)*Log[3])*Log[(-8 -
4*x + Log[3])/4]^3 + (48 + 48*x - 108*x^2 - 60*x^3 + (-6 - 3*x + 15*x^2)*Log[3])*Log[(-8 - 4*x + Log[3])/4]^4
+ (-48*x - 24*x^2 + 6*x*Log[3])*Log[(-8 - 4*x + Log[3])/4]^5 + (-8 - 4*x + Log[3])*Log[(-8 - 4*x + Log[3])/4]^
6), x]

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fricas [B]  time = 1.01, size = 96, normalized size = 3.84 \begin {gather*} e^{\left (\frac {1}{x^{4} + 4 \, x \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{3} + \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{4} - 2 \, x^{3} + 2 \, {\left (3 \, x^{2} - x - 2\right )} \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{2} - 3 \, x^{2} + 4 \, {\left (x^{3} - x^{2} - 2 \, x\right )} \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right ) + 4 \, x + 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*log(3)+16*x+48)*log(1/4*log(3)-x-2)+(-4*x+2)*log(3)+16*x^2+40*x-16)*exp(1/(log(1/4*log(3)-x-2)^
4+4*x*log(1/4*log(3)-x-2)^3+(6*x^2-2*x-4)*log(1/4*log(3)-x-2)^2+(4*x^3-4*x^2-8*x)*log(1/4*log(3)-x-2)+x^4-2*x^
3-3*x^2+4*x+4))/((log(3)-4*x-8)*log(1/4*log(3)-x-2)^6+(6*x*log(3)-24*x^2-48*x)*log(1/4*log(3)-x-2)^5+((15*x^2-
3*x-6)*log(3)-60*x^3-108*x^2+48*x+48)*log(1/4*log(3)-x-2)^4+((20*x^3-12*x^2-24*x)*log(3)-80*x^4-112*x^3+192*x^
2+192*x)*log(1/4*log(3)-x-2)^3+((15*x^4-18*x^3-33*x^2+12*x+12)*log(3)-60*x^5-48*x^4+276*x^3+216*x^2-144*x-96)*
log(1/4*log(3)-x-2)^2+((6*x^5-12*x^4-18*x^3+24*x^2+24*x)*log(3)-24*x^6+168*x^4+48*x^3-288*x^2-192*x)*log(1/4*l
og(3)-x-2)+(x^6-3*x^5-3*x^4+11*x^3+6*x^2-12*x-8)*log(3)-4*x^7+4*x^6+36*x^5-20*x^4-112*x^3+128*x+64),x, algorit
hm="fricas")

[Out]

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

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giac [B]  time = 157.50, size = 137, normalized size = 5.48 \begin {gather*} e^{\left (\frac {1}{x^{4} + 4 \, x^{3} \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right ) + 6 \, x^{2} \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{2} + 4 \, x \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{3} + \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{4} - 2 \, x^{3} - 4 \, x^{2} \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right ) - 2 \, x \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{2} - 3 \, x^{2} - 8 \, x \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right ) - 4 \, \log \left (-x + \frac {1}{4} \, \log \relax (3) - 2\right )^{2} + 4 \, x + 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*log(3)+16*x+48)*log(1/4*log(3)-x-2)+(-4*x+2)*log(3)+16*x^2+40*x-16)*exp(1/(log(1/4*log(3)-x-2)^
4+4*x*log(1/4*log(3)-x-2)^3+(6*x^2-2*x-4)*log(1/4*log(3)-x-2)^2+(4*x^3-4*x^2-8*x)*log(1/4*log(3)-x-2)+x^4-2*x^
3-3*x^2+4*x+4))/((log(3)-4*x-8)*log(1/4*log(3)-x-2)^6+(6*x*log(3)-24*x^2-48*x)*log(1/4*log(3)-x-2)^5+((15*x^2-
3*x-6)*log(3)-60*x^3-108*x^2+48*x+48)*log(1/4*log(3)-x-2)^4+((20*x^3-12*x^2-24*x)*log(3)-80*x^4-112*x^3+192*x^
2+192*x)*log(1/4*log(3)-x-2)^3+((15*x^4-18*x^3-33*x^2+12*x+12)*log(3)-60*x^5-48*x^4+276*x^3+216*x^2-144*x-96)*
log(1/4*log(3)-x-2)^2+((6*x^5-12*x^4-18*x^3+24*x^2+24*x)*log(3)-24*x^6+168*x^4+48*x^3-288*x^2-192*x)*log(1/4*l
og(3)-x-2)+(x^6-3*x^5-3*x^4+11*x^3+6*x^2-12*x-8)*log(3)-4*x^7+4*x^6+36*x^5-20*x^4-112*x^3+128*x+64),x, algorit
hm="giac")

[Out]

e^(1/(x^4 + 4*x^3*log(-x + 1/4*log(3) - 2) + 6*x^2*log(-x + 1/4*log(3) - 2)^2 + 4*x*log(-x + 1/4*log(3) - 2)^3
+ log(-x + 1/4*log(3) - 2)^4 - 2*x^3 - 4*x^2*log(-x + 1/4*log(3) - 2) - 2*x*log(-x + 1/4*log(3) - 2)^2 - 3*x^
2 - 8*x*log(-x + 1/4*log(3) - 2) - 4*log(-x + 1/4*log(3) - 2)^2 + 4*x + 4))

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maple [A]  time = 0.08, size = 37, normalized size = 1.48

method	result	size
risch	\({\mathrm e}^{\frac {1}{\left (\ln \left (\frac {\ln \relax (3)}{4}-x -2\right )^{2}+2 \ln \left (\frac {\ln \relax (3)}{4}-x -2\right ) x +x^{2}-x -2\right )^{2}}}\)	\(37\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*ln(3)+16*x+48)*ln(1/4*ln(3)-x-2)+(-4*x+2)*ln(3)+16*x^2+40*x-16)*exp(1/(ln(1/4*ln(3)-x-2)^4+4*x*ln(1/4
*ln(3)-x-2)^3+(6*x^2-2*x-4)*ln(1/4*ln(3)-x-2)^2+(4*x^3-4*x^2-8*x)*ln(1/4*ln(3)-x-2)+x^4-2*x^3-3*x^2+4*x+4))/((
ln(3)-4*x-8)*ln(1/4*ln(3)-x-2)^6+(6*x*ln(3)-24*x^2-48*x)*ln(1/4*ln(3)-x-2)^5+((15*x^2-3*x-6)*ln(3)-60*x^3-108*
x^2+48*x+48)*ln(1/4*ln(3)-x-2)^4+((20*x^3-12*x^2-24*x)*ln(3)-80*x^4-112*x^3+192*x^2+192*x)*ln(1/4*ln(3)-x-2)^3
+((15*x^4-18*x^3-33*x^2+12*x+12)*ln(3)-60*x^5-48*x^4+276*x^3+216*x^2-144*x-96)*ln(1/4*ln(3)-x-2)^2+((6*x^5-12*
x^4-18*x^3+24*x^2+24*x)*ln(3)-24*x^6+168*x^4+48*x^3-288*x^2-192*x)*ln(1/4*ln(3)-x-2)+(x^6-3*x^5-3*x^4+11*x^3+6
*x^2-12*x-8)*ln(3)-4*x^7+4*x^6+36*x^5-20*x^4-112*x^3+128*x+64),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.81, size = 220, normalized size = 8.80 \begin {gather*} e^{\left (\frac {1}{x^{4} - 2 \, x^{3} {\left (4 \, \log \relax (2) - 2 \, \log \left (-4 \, x + \log \relax (3) - 8\right ) + 1\right )} + 16 \, \log \relax (2)^{4} - 8 \, \log \relax (2) \log \left (-4 \, x + \log \relax (3) - 8\right )^{3} + \log \left (-4 \, x + \log \relax (3) - 8\right )^{4} + {\left (24 \, \log \relax (2)^{2} - 4 \, {\left (6 \, \log \relax (2) + 1\right )} \log \left (-4 \, x + \log \relax (3) - 8\right ) + 6 \, \log \left (-4 \, x + \log \relax (3) - 8\right )^{2} + 8 \, \log \relax (2) - 3\right )} x^{2} + 4 \, {\left (6 \, \log \relax (2)^{2} - 1\right )} \log \left (-4 \, x + \log \relax (3) - 8\right )^{2} - 2 \, {\left (16 \, \log \relax (2)^{3} + {\left (12 \, \log \relax (2) + 1\right )} \log \left (-4 \, x + \log \relax (3) - 8\right )^{2} - 2 \, \log \left (-4 \, x + \log \relax (3) - 8\right )^{3} + 4 \, \log \relax (2)^{2} - 4 \, {\left (6 \, \log \relax (2)^{2} + \log \relax (2) - 1\right )} \log \left (-4 \, x + \log \relax (3) - 8\right ) - 8 \, \log \relax (2) - 2\right )} x - 16 \, \log \relax (2)^{2} - 16 \, {\left (2 \, \log \relax (2)^{3} - \log \relax (2)\right )} \log \left (-4 \, x + \log \relax (3) - 8\right ) + 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*log(3)+16*x+48)*log(1/4*log(3)-x-2)+(-4*x+2)*log(3)+16*x^2+40*x-16)*exp(1/(log(1/4*log(3)-x-2)^
4+4*x*log(1/4*log(3)-x-2)^3+(6*x^2-2*x-4)*log(1/4*log(3)-x-2)^2+(4*x^3-4*x^2-8*x)*log(1/4*log(3)-x-2)+x^4-2*x^
3-3*x^2+4*x+4))/((log(3)-4*x-8)*log(1/4*log(3)-x-2)^6+(6*x*log(3)-24*x^2-48*x)*log(1/4*log(3)-x-2)^5+((15*x^2-
3*x-6)*log(3)-60*x^3-108*x^2+48*x+48)*log(1/4*log(3)-x-2)^4+((20*x^3-12*x^2-24*x)*log(3)-80*x^4-112*x^3+192*x^
2+192*x)*log(1/4*log(3)-x-2)^3+((15*x^4-18*x^3-33*x^2+12*x+12)*log(3)-60*x^5-48*x^4+276*x^3+216*x^2-144*x-96)*
log(1/4*log(3)-x-2)^2+((6*x^5-12*x^4-18*x^3+24*x^2+24*x)*log(3)-24*x^6+168*x^4+48*x^3-288*x^2-192*x)*log(1/4*l
og(3)-x-2)+(x^6-3*x^5-3*x^4+11*x^3+6*x^2-12*x-8)*log(3)-4*x^7+4*x^6+36*x^5-20*x^4-112*x^3+128*x+64),x, algorit
hm="maxima")

[Out]

e^(1/(x^4 - 2*x^3*(4*log(2) - 2*log(-4*x + log(3) - 8) + 1) + 16*log(2)^4 - 8*log(2)*log(-4*x + log(3) - 8)^3
+ log(-4*x + log(3) - 8)^4 + (24*log(2)^2 - 4*(6*log(2) + 1)*log(-4*x + log(3) - 8) + 6*log(-4*x + log(3) - 8)
^2 + 8*log(2) - 3)*x^2 + 4*(6*log(2)^2 - 1)*log(-4*x + log(3) - 8)^2 - 2*(16*log(2)^3 + (12*log(2) + 1)*log(-4
*x + log(3) - 8)^2 - 2*log(-4*x + log(3) - 8)^3 + 4*log(2)^2 - 4*(6*log(2)^2 + log(2) - 1)*log(-4*x + log(3) -
8) - 8*log(2) - 2)*x - 16*log(2)^2 - 16*(2*log(2)^3 - log(2))*log(-4*x + log(3) - 8) + 4))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{\frac {1}{4\,x-\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )\,\left (-4\,x^3+4\,x^2+8\,x\right )-{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^2\,\left (-6\,x^2+2\,x+4\right )+4\,x\,{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^3+{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^4-3\,x^2-2\,x^3+x^4+4}}\,\left (40\,x-\ln \relax (3)\,\left (4\,x-2\right )+\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )\,\left (16\,x-4\,\ln \relax (3)+48\right )+16\,x^2-16\right )}{{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^4\,\left (\ln \relax (3)\,\left (-15\,x^2+3\,x+6\right )-48\,x+108\,x^2+60\,x^3-48\right )-128\,x+\ln \relax (3)\,\left (-x^6+3\,x^5+3\,x^4-11\,x^3-6\,x^2+12\,x+8\right )+{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^6\,\left (4\,x-\ln \relax (3)+8\right )+{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^3\,\left (\ln \relax (3)\,\left (-20\,x^3+12\,x^2+24\,x\right )-192\,x-192\,x^2+112\,x^3+80\,x^4\right )+\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )\,\left (192\,x+288\,x^2-48\,x^3-168\,x^4+24\,x^6-\ln \relax (3)\,\left (6\,x^5-12\,x^4-18\,x^3+24\,x^2+24\,x\right )\right )+112\,x^3+20\,x^4-36\,x^5-4\,x^6+4\,x^7+{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^5\,\left (48\,x-6\,x\,\ln \relax (3)+24\,x^2\right )+{\ln \left (\frac {\ln \relax (3)}{4}-x-2\right )}^2\,\left (144\,x-\ln \relax (3)\,\left (15\,x^4-18\,x^3-33\,x^2+12\,x+12\right )-216\,x^2-276\,x^3+48\,x^4+60\,x^5+96\right )-64} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(1/(4*x - log(log(3)/4 - x - 2)*(8*x + 4*x^2 - 4*x^3) - log(log(3)/4 - x - 2)^2*(2*x - 6*x^2 + 4) + 4
*x*log(log(3)/4 - x - 2)^3 + log(log(3)/4 - x - 2)^4 - 3*x^2 - 2*x^3 + x^4 + 4))*(40*x - log(3)*(4*x - 2) + lo
g(log(3)/4 - x - 2)*(16*x - 4*log(3) + 48) + 16*x^2 - 16))/(log(log(3)/4 - x - 2)^4*(log(3)*(3*x - 15*x^2 + 6)
- 48*x + 108*x^2 + 60*x^3 - 48) - 128*x + log(3)*(12*x - 6*x^2 - 11*x^3 + 3*x^4 + 3*x^5 - x^6 + 8) + log(log(
3)/4 - x - 2)^6*(4*x - log(3) + 8) + log(log(3)/4 - x - 2)^3*(log(3)*(24*x + 12*x^2 - 20*x^3) - 192*x - 192*x^
2 + 112*x^3 + 80*x^4) + log(log(3)/4 - x - 2)*(192*x + 288*x^2 - 48*x^3 - 168*x^4 + 24*x^6 - log(3)*(24*x + 24
*x^2 - 18*x^3 - 12*x^4 + 6*x^5)) + 112*x^3 + 20*x^4 - 36*x^5 - 4*x^6 + 4*x^7 + log(log(3)/4 - x - 2)^5*(48*x -
6*x*log(3) + 24*x^2) + log(log(3)/4 - x - 2)^2*(144*x - log(3)*(12*x - 33*x^2 - 18*x^3 + 15*x^4 + 12) - 216*x
^2 - 276*x^3 + 48*x^4 + 60*x^5 + 96) - 64),x)

[Out]

int(-(exp(1/(4*x - log(log(3)/4 - x - 2)*(8*x + 4*x^2 - 4*x^3) - log(log(3)/4 - x - 2)^2*(2*x - 6*x^2 + 4) + 4
*x*log(log(3)/4 - x - 2)^3 + log(log(3)/4 - x - 2)^4 - 3*x^2 - 2*x^3 + x^4 + 4))*(40*x - log(3)*(4*x - 2) + lo
g(log(3)/4 - x - 2)*(16*x - 4*log(3) + 48) + 16*x^2 - 16))/(log(log(3)/4 - x - 2)^4*(log(3)*(3*x - 15*x^2 + 6)
- 48*x + 108*x^2 + 60*x^3 - 48) - 128*x + log(3)*(12*x - 6*x^2 - 11*x^3 + 3*x^4 + 3*x^5 - x^6 + 8) + log(log(
3)/4 - x - 2)^6*(4*x - log(3) + 8) + log(log(3)/4 - x - 2)^3*(log(3)*(24*x + 12*x^2 - 20*x^3) - 192*x - 192*x^
2 + 112*x^3 + 80*x^4) + log(log(3)/4 - x - 2)*(192*x + 288*x^2 - 48*x^3 - 168*x^4 + 24*x^6 - log(3)*(24*x + 24
*x^2 - 18*x^3 - 12*x^4 + 6*x^5)) + 112*x^3 + 20*x^4 - 36*x^5 - 4*x^6 + 4*x^7 + log(log(3)/4 - x - 2)^5*(48*x -
6*x*log(3) + 24*x^2) + log(log(3)/4 - x - 2)^2*(144*x - log(3)*(12*x - 33*x^2 - 18*x^3 + 15*x^4 + 12) - 216*x
^2 - 276*x^3 + 48*x^4 + 60*x^5 + 96) - 64), x)

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sympy [B]  time = 3.57, size = 94, normalized size = 3.76 \begin {gather*} e^{\frac {1}{x^{4} - 2 x^{3} - 3 x^{2} + 4 x \log {\left (- x - 2 + \frac {\log {\relax (3 )}}{4} \right )}^{3} + 4 x + \left (6 x^{2} - 2 x - 4\right ) \log {\left (- x - 2 + \frac {\log {\relax (3 )}}{4} \right )}^{2} + \left (4 x^{3} - 4 x^{2} - 8 x\right ) \log {\left (- x - 2 + \frac {\log {\relax (3 )}}{4} \right )} + \log {\left (- x - 2 + \frac {\log {\relax (3 )}}{4} \right )}^{4} + 4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*ln(3)+16*x+48)*ln(1/4*ln(3)-x-2)+(-4*x+2)*ln(3)+16*x**2+40*x-16)*exp(1/(ln(1/4*ln(3)-x-2)**4+4*
x*ln(1/4*ln(3)-x-2)**3+(6*x**2-2*x-4)*ln(1/4*ln(3)-x-2)**2+(4*x**3-4*x**2-8*x)*ln(1/4*ln(3)-x-2)+x**4-2*x**3-3
*x**2+4*x+4))/((ln(3)-4*x-8)*ln(1/4*ln(3)-x-2)**6+(6*x*ln(3)-24*x**2-48*x)*ln(1/4*ln(3)-x-2)**5+((15*x**2-3*x-
6)*ln(3)-60*x**3-108*x**2+48*x+48)*ln(1/4*ln(3)-x-2)**4+((20*x**3-12*x**2-24*x)*ln(3)-80*x**4-112*x**3+192*x**
2+192*x)*ln(1/4*ln(3)-x-2)**3+((15*x**4-18*x**3-33*x**2+12*x+12)*ln(3)-60*x**5-48*x**4+276*x**3+216*x**2-144*x
-96)*ln(1/4*ln(3)-x-2)**2+((6*x**5-12*x**4-18*x**3+24*x**2+24*x)*ln(3)-24*x**6+168*x**4+48*x**3-288*x**2-192*x
)*ln(1/4*ln(3)-x-2)+(x**6-3*x**5-3*x**4+11*x**3+6*x**2-12*x-8)*ln(3)-4*x**7+4*x**6+36*x**5-20*x**4-112*x**3+12
8*x+64),x)

[Out]

exp(1/(x**4 - 2*x**3 - 3*x**2 + 4*x*log(-x - 2 + log(3)/4)**3 + 4*x + (6*x**2 - 2*x - 4)*log(-x - 2 + log(3)/4
)**2 + (4*x**3 - 4*x**2 - 8*x)*log(-x - 2 + log(3)/4) + log(-x - 2 + log(3)/4)**4 + 4))

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