Integrand size = 481, antiderivative size = 25 \[ \int \frac {e^{\frac {1}{4+4 x-3 x^2-2 x^3+x^4+\left (-8 x-4 x^2+4 x^3\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-4-2 x+6 x^2\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+4 x \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )}} \left (-16+40 x+16 x^2+(2-4 x) \log (3)+(48+16 x-4 \log (3)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{64+128 x-112 x^3-20 x^4+36 x^5+4 x^6-4 x^7+\left (-8-12 x+6 x^2+11 x^3-3 x^4-3 x^5+x^6\right ) \log (3)+\left (-192 x-288 x^2+48 x^3+168 x^4-24 x^6+\left (24 x+24 x^2-18 x^3-12 x^4+6 x^5\right ) \log (3)\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-96-144 x+216 x^2+276 x^3-48 x^4-60 x^5+\left (12+12 x-33 x^2-18 x^3+15 x^4\right ) \log (3)\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (192 x+192 x^2-112 x^3-80 x^4+\left (-24 x-12 x^2+20 x^3\right ) \log (3)\right ) \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (48+48 x-108 x^2-60 x^3+\left (-6-3 x+15 x^2\right ) \log (3)\right ) \log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-48 x-24 x^2+6 x \log (3)\right ) \log ^5\left (\frac {1}{4} (-8-4 x+\log (3))\right )+(-8-4 x+\log (3)) \log ^6\left (\frac {1}{4} (-8-4 x+\log (3))\right )} \, dx=e^{\frac {1}{\left (-2-x+\left (x+\log \left (-2-x+\frac {\log (3)}{4}\right )\right )^2\right )^2}} \] Output:
exp(1/((ln(1/4*ln(3)-x-2)+x)^2-2-x)^2)
\[ \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=\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 \] Input:
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]
Output:
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]
Time = 2.67 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.64, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {7239, 27, 25, 7257}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (16 x^2+40 x+(16 x+48-4 \log (3)) \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )+(2-4 x) \log (3)-16\right ) \exp \left (\frac {1}{x^4-2 x^3-3 x^2+\left (6 x^2-2 x-4\right ) \log ^2\left (\frac {1}{4} (-4 x-8+\log (3))\right )+\left (4 x^3-4 x^2-8 x\right ) \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )+4 x+\log ^4\left (\frac {1}{4} (-4 x-8+\log (3))\right )+4 x \log ^3\left (\frac {1}{4} (-4 x-8+\log (3))\right )+4}\right )}{-4 x^7+4 x^6+36 x^5-20 x^4-112 x^3+\left (-24 x^2-48 x+6 x \log (3)\right ) \log ^5\left (\frac {1}{4} (-4 x-8+\log (3))\right )+\left (-60 x^3-108 x^2+\left (15 x^2-3 x-6\right ) \log (3)+48 x+48\right ) \log ^4\left (\frac {1}{4} (-4 x-8+\log (3))\right )+\left (-80 x^4-112 x^3+192 x^2+\left (20 x^3-12 x^2-24 x\right ) \log (3)+192 x\right ) \log ^3\left (\frac {1}{4} (-4 x-8+\log (3))\right )+\left (-60 x^5-48 x^4+276 x^3+216 x^2+\left (15 x^4-18 x^3-33 x^2+12 x+12\right ) \log (3)-144 x-96\right ) \log ^2\left (\frac {1}{4} (-4 x-8+\log (3))\right )+\left (-24 x^6+168 x^4+48 x^3-288 x^2+\left (6 x^5-12 x^4-18 x^3+24 x^2+24 x\right ) \log (3)-192 x\right ) \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )+\left (x^6-3 x^5-3 x^4+11 x^3+6 x^2-12 x-8\right ) \log (3)+128 x+(-4 x-8+\log (3)) \log ^6\left (\frac {1}{4} (-4 x-8+\log (3))\right )+64} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (8 x^2-2 x (\log (3)-10)+(8 x+24-\log (9)) \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )-8 \left (1-\frac {\log (3)}{8}\right )\right ) \exp \left (\frac {1}{\left (x^2-x+\log ^2\left (\frac {1}{4} (-4 x-8+\log (3))\right )+2 x \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )-2\right )^2}\right )}{(4 x+8-\log (3)) \left (-x^2+x-\log ^2\left (\frac {1}{4} (-4 x-8+\log (3))\right )-2 x \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )+2\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\exp \left (\frac {1}{\left (x^2+2 \log \left (\frac {1}{4} (-4 x+\log (3)-8)\right ) x-x+\log ^2\left (\frac {1}{4} (-4 x+\log (3)-8)\right )-2\right )^2}\right ) \left (-8 x^2-2 (10-\log (3)) x-(8 x-\log (9)+24) \log \left (\frac {1}{4} (-4 x+\log (3)-8)\right )-\log (3)+8\right )}{(4 x-\log (3)+8) \left (-x^2-2 \log \left (\frac {1}{4} (-4 x+\log (3)-8)\right ) x+x-\log ^2\left (\frac {1}{4} (-4 x+\log (3)-8)\right )+2\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\exp \left (\frac {1}{\left (x^2+2 \log \left (\frac {1}{4} (-4 x+\log (3)-8)\right ) x-x+\log ^2\left (\frac {1}{4} (-4 x+\log (3)-8)\right )-2\right )^2}\right ) \left (-8 x^2-2 (10-\log (3)) x-(8 x-\log (9)+24) \log \left (\frac {1}{4} (-4 x+\log (3)-8)\right )-\log (3)+8\right )}{(4 x-\log (3)+8) \left (-x^2-2 \log \left (\frac {1}{4} (-4 x+\log (3)-8)\right ) x+x-\log ^2\left (\frac {1}{4} (-4 x+\log (3)-8)\right )+2\right )^3}dx\) |
| \(\Big \downarrow \) 7257 |
| \(\displaystyle \exp \left (\frac {1}{\left (x^2-x+\log ^2\left (\frac {1}{4} (-4 x-8+\log (3))\right )+2 x \log \left (\frac {1}{4} (-4 x-8+\log (3))\right )-2\right )^2}\right )\) |
Input:
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*Lo g[(-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]
Output:
E^(-2 - x + x^2 + 2*x*Log[(-8 - 4*x + Log[3])/4] + Log[(-8 - 4*x + Log[3]) /4]^2)^(-2)
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Sim p[q*(F^v/Log[F]), x] /; !FalseQ[q]] /; FreeQ[F, x]
Time = 53.86 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.48
| method | result | size |
| risch | \({\mathrm e}^{\frac {1}{\left (\ln \left (\frac {\ln \left (3\right )}{4}-x -2\right )^{2}+2 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right ) x +x^{2}-x -2\right )^{2}}}\) | \(37\) |
| parallelrisch | \({\mathrm e}^{\frac {1}{\ln \left (\frac {\ln \left (3\right )}{4}-x -2\right )^{4}+4 x \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right )^{3}+6 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right )^{2} x^{2}+4 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right ) x^{3}+x^{4}-2 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right )^{2} x -4 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right ) x^{2}-2 x^{3}-4 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right )^{2}-8 \ln \left (\frac {\ln \left (3\right )}{4}-x -2\right ) x -3 x^{2}+4 x +4}}\) | \(138\) |
Input:
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)*e xp(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+((1 5*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^2-1 2*x-8)*ln(3)-4*x^7+4*x^6+36*x^5-20*x^4-112*x^3+128*x+64),x,method=_RETURNV ERBOSE)
Output:
exp(1/(ln(1/4*ln(3)-x-2)^2+2*ln(1/4*ln(3)-x-2)*x+x^2-x-2)^2)
Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (22) = 44\).
Time = 0.13 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.84 \[ \int \frac {e^{\frac {1}{4+4 x-3 x^2-2 x^3+x^4+\left (-8 x-4 x^2+4 x^3\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-4-2 x+6 x^2\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+4 x \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )}} \left (-16+40 x+16 x^2+(2-4 x) \log (3)+(48+16 x-4 \log (3)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{64+128 x-112 x^3-20 x^4+36 x^5+4 x^6-4 x^7+\left (-8-12 x+6 x^2+11 x^3-3 x^4-3 x^5+x^6\right ) \log (3)+\left (-192 x-288 x^2+48 x^3+168 x^4-24 x^6+\left (24 x+24 x^2-18 x^3-12 x^4+6 x^5\right ) \log (3)\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-96-144 x+216 x^2+276 x^3-48 x^4-60 x^5+\left (12+12 x-33 x^2-18 x^3+15 x^4\right ) \log (3)\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (192 x+192 x^2-112 x^3-80 x^4+\left (-24 x-12 x^2+20 x^3\right ) \log (3)\right ) \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (48+48 x-108 x^2-60 x^3+\left (-6-3 x+15 x^2\right ) \log (3)\right ) \log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-48 x-24 x^2+6 x \log (3)\right ) \log ^5\left (\frac {1}{4} (-8-4 x+\log (3))\right )+(-8-4 x+\log (3)) \log ^6\left (\frac {1}{4} (-8-4 x+\log (3))\right )} \, dx=e^{\left (\frac {1}{x^{4} + 4 \, x \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{3} + \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{4} - 2 \, x^{3} + 2 \, {\left (3 \, x^{2} - x - 2\right )} \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{2} - 3 \, x^{2} + 4 \, {\left (x^{3} - x^{2} - 2 \, x\right )} \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right ) + 4 \, x + 4}\right )} \] Input:
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)*lo g(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+19 2*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^5-4 8*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*log(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, algorithm="fricas")
Output:
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))
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (20) = 40\).
Time = 1.54 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.76 \[ \int \frac {e^{\frac {1}{4+4 x-3 x^2-2 x^3+x^4+\left (-8 x-4 x^2+4 x^3\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-4-2 x+6 x^2\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+4 x \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )}} \left (-16+40 x+16 x^2+(2-4 x) \log (3)+(48+16 x-4 \log (3)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{64+128 x-112 x^3-20 x^4+36 x^5+4 x^6-4 x^7+\left (-8-12 x+6 x^2+11 x^3-3 x^4-3 x^5+x^6\right ) \log (3)+\left (-192 x-288 x^2+48 x^3+168 x^4-24 x^6+\left (24 x+24 x^2-18 x^3-12 x^4+6 x^5\right ) \log (3)\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-96-144 x+216 x^2+276 x^3-48 x^4-60 x^5+\left (12+12 x-33 x^2-18 x^3+15 x^4\right ) \log (3)\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (192 x+192 x^2-112 x^3-80 x^4+\left (-24 x-12 x^2+20 x^3\right ) \log (3)\right ) \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (48+48 x-108 x^2-60 x^3+\left (-6-3 x+15 x^2\right ) \log (3)\right ) \log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-48 x-24 x^2+6 x \log (3)\right ) \log ^5\left (\frac {1}{4} (-8-4 x+\log (3))\right )+(-8-4 x+\log (3)) \log ^6\left (\frac {1}{4} (-8-4 x+\log (3))\right )} \, dx=e^{\frac {1}{x^{4} - 2 x^{3} - 3 x^{2} + 4 x \log {\left (- x - 2 + \frac {\log {\left (3 \right )}}{4} \right )}^{3} + 4 x + \left (6 x^{2} - 2 x - 4\right ) \log {\left (- x - 2 + \frac {\log {\left (3 \right )}}{4} \right )}^{2} + \left (4 x^{3} - 4 x^{2} - 8 x\right ) \log {\left (- x - 2 + \frac {\log {\left (3 \right )}}{4} \right )} + \log {\left (- x - 2 + \frac {\log {\left (3 \right )}}{4} \right )}^{4} + 4}} \] Input:
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)*l n(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+19 2*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)
Output:
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))
Leaf count of result is larger than twice the leaf count of optimal. 220 vs. \(2 (22) = 44\).
Time = 0.39 (sec) , antiderivative size = 220, normalized size of antiderivative = 8.80 \[ \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=e^{\left (\frac {1}{x^{4} - 2 \, x^{3} {\left (4 \, \log \left (2\right ) - 2 \, \log \left (-4 \, x + \log \left (3\right ) - 8\right ) + 1\right )} + 16 \, \log \left (2\right )^{4} - 8 \, \log \left (2\right ) \log \left (-4 \, x + \log \left (3\right ) - 8\right )^{3} + \log \left (-4 \, x + \log \left (3\right ) - 8\right )^{4} + {\left (24 \, \log \left (2\right )^{2} - 4 \, {\left (6 \, \log \left (2\right ) + 1\right )} \log \left (-4 \, x + \log \left (3\right ) - 8\right ) + 6 \, \log \left (-4 \, x + \log \left (3\right ) - 8\right )^{2} + 8 \, \log \left (2\right ) - 3\right )} x^{2} + 4 \, {\left (6 \, \log \left (2\right )^{2} - 1\right )} \log \left (-4 \, x + \log \left (3\right ) - 8\right )^{2} - 2 \, {\left (16 \, \log \left (2\right )^{3} + {\left (12 \, \log \left (2\right ) + 1\right )} \log \left (-4 \, x + \log \left (3\right ) - 8\right )^{2} - 2 \, \log \left (-4 \, x + \log \left (3\right ) - 8\right )^{3} + 4 \, \log \left (2\right )^{2} - 4 \, {\left (6 \, \log \left (2\right )^{2} + \log \left (2\right ) - 1\right )} \log \left (-4 \, x + \log \left (3\right ) - 8\right ) - 8 \, \log \left (2\right ) - 2\right )} x - 16 \, \log \left (2\right )^{2} - 16 \, {\left (2 \, \log \left (2\right )^{3} - \log \left (2\right )\right )} \log \left (-4 \, x + \log \left (3\right ) - 8\right ) + 4}\right )} \] Input:
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)*lo g(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+19 2*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^5-4 8*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*log(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, algorithm="maxima")
Output:
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))
Leaf count of result is larger than twice the leaf count of optimal. 137 vs. \(2 (22) = 44\).
Time = 1.88 (sec) , antiderivative size = 137, normalized size of antiderivative = 5.48 \[ \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=e^{\left (\frac {1}{x^{4} + 4 \, x^{3} \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right ) + 6 \, x^{2} \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{2} + 4 \, x \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{3} + \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{4} - 2 \, x^{3} - 4 \, x^{2} \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right ) - 2 \, x \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{2} - 3 \, x^{2} - 8 \, x \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right ) - 4 \, \log \left (-x + \frac {1}{4} \, \log \left (3\right ) - 2\right )^{2} + 4 \, x + 4}\right )} \] Input:
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)*lo g(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+19 2*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^5-4 8*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*log(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, algorithm="giac")
Output:
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))
Timed out. \[ \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=\int -\frac {{\mathrm {e}}^{\frac {1}{4\,x-\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )\,\left (-4\,x^3+4\,x^2+8\,x\right )-{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^2\,\left (-6\,x^2+2\,x+4\right )+4\,x\,{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^3+{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^4-3\,x^2-2\,x^3+x^4+4}}\,\left (40\,x-\ln \left (3\right )\,\left (4\,x-2\right )+\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )\,\left (16\,x-4\,\ln \left (3\right )+48\right )+16\,x^2-16\right )}{{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^4\,\left (\ln \left (3\right )\,\left (-15\,x^2+3\,x+6\right )-48\,x+108\,x^2+60\,x^3-48\right )-128\,x+\ln \left (3\right )\,\left (-x^6+3\,x^5+3\,x^4-11\,x^3-6\,x^2+12\,x+8\right )+{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^6\,\left (4\,x-\ln \left (3\right )+8\right )+{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^3\,\left (\ln \left (3\right )\,\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 \left (3\right )}{4}-x-2\right )\,\left (192\,x+288\,x^2-48\,x^3-168\,x^4+24\,x^6-\ln \left (3\right )\,\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 \left (3\right )}{4}-x-2\right )}^5\,\left (48\,x-6\,x\,\ln \left (3\right )+24\,x^2\right )+{\ln \left (\frac {\ln \left (3\right )}{4}-x-2\right )}^2\,\left (144\,x-\ln \left (3\right )\,\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 \] Input:
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) + log( 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 + 1 2*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 + l og(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)
Output:
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) + log( 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 + 1 2*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 + l og(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)
\[ \int \frac {e^{\frac {1}{4+4 x-3 x^2-2 x^3+x^4+\left (-8 x-4 x^2+4 x^3\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-4-2 x+6 x^2\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+4 x \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )}} \left (-16+40 x+16 x^2+(2-4 x) \log (3)+(48+16 x-4 \log (3)) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )\right )}{64+128 x-112 x^3-20 x^4+36 x^5+4 x^6-4 x^7+\left (-8-12 x+6 x^2+11 x^3-3 x^4-3 x^5+x^6\right ) \log (3)+\left (-192 x-288 x^2+48 x^3+168 x^4-24 x^6+\left (24 x+24 x^2-18 x^3-12 x^4+6 x^5\right ) \log (3)\right ) \log \left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-96-144 x+216 x^2+276 x^3-48 x^4-60 x^5+\left (12+12 x-33 x^2-18 x^3+15 x^4\right ) \log (3)\right ) \log ^2\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (192 x+192 x^2-112 x^3-80 x^4+\left (-24 x-12 x^2+20 x^3\right ) \log (3)\right ) \log ^3\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (48+48 x-108 x^2-60 x^3+\left (-6-3 x+15 x^2\right ) \log (3)\right ) \log ^4\left (\frac {1}{4} (-8-4 x+\log (3))\right )+\left (-48 x-24 x^2+6 x \log (3)\right ) \log ^5\left (\frac {1}{4} (-8-4 x+\log (3))\right )+(-8-4 x+\log (3)) \log ^6\left (\frac {1}{4} (-8-4 x+\log (3))\right )} \, dx=\text {too large to display} \] Input:
int(((-4*log(3)+16*x+48)*log(1/4*log(3)-x-2)+(-4*x+2)*log(3)+16*x^2+40*x-1 6)*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)*lo g(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)*l og(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*log(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)
Output:
2*(int(e**(1/(log((log(3) - 4*x - 8)/4)**4 + 4*log((log(3) - 4*x - 8)/4)** 3*x + 6*log((log(3) - 4*x - 8)/4)**2*x**2 - 2*log((log(3) - 4*x - 8)/4)**2 *x - 4*log((log(3) - 4*x - 8)/4)**2 + 4*log((log(3) - 4*x - 8)/4)*x**3 - 4 *log((log(3) - 4*x - 8)/4)*x**2 - 8*log((log(3) - 4*x - 8)/4)*x + x**4 - 2 *x**3 - 3*x**2 + 4*x + 4))/(log((log(3) - 4*x - 8)/4)**6*log(3) - 4*log((l og(3) - 4*x - 8)/4)**6*x - 8*log((log(3) - 4*x - 8)/4)**6 + 6*log((log(3) - 4*x - 8)/4)**5*log(3)*x - 24*log((log(3) - 4*x - 8)/4)**5*x**2 - 48*log( (log(3) - 4*x - 8)/4)**5*x + 15*log((log(3) - 4*x - 8)/4)**4*log(3)*x**2 - 3*log((log(3) - 4*x - 8)/4)**4*log(3)*x - 6*log((log(3) - 4*x - 8)/4)**4* log(3) - 60*log((log(3) - 4*x - 8)/4)**4*x**3 - 108*log((log(3) - 4*x - 8) /4)**4*x**2 + 48*log((log(3) - 4*x - 8)/4)**4*x + 48*log((log(3) - 4*x - 8 )/4)**4 + 20*log((log(3) - 4*x - 8)/4)**3*log(3)*x**3 - 12*log((log(3) - 4 *x - 8)/4)**3*log(3)*x**2 - 24*log((log(3) - 4*x - 8)/4)**3*log(3)*x - 80* log((log(3) - 4*x - 8)/4)**3*x**4 - 112*log((log(3) - 4*x - 8)/4)**3*x**3 + 192*log((log(3) - 4*x - 8)/4)**3*x**2 + 192*log((log(3) - 4*x - 8)/4)**3 *x + 15*log((log(3) - 4*x - 8)/4)**2*log(3)*x**4 - 18*log((log(3) - 4*x - 8)/4)**2*log(3)*x**3 - 33*log((log(3) - 4*x - 8)/4)**2*log(3)*x**2 + 12*lo g((log(3) - 4*x - 8)/4)**2*log(3)*x + 12*log((log(3) - 4*x - 8)/4)**2*log( 3) - 60*log((log(3) - 4*x - 8)/4)**2*x**5 - 48*log((log(3) - 4*x - 8)/4)** 2*x**4 + 276*log((log(3) - 4*x - 8)/4)**2*x**3 + 216*log((log(3) - 4*x ...