Integrand size = 127, antiderivative size = 25 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx=e^{\left (-2+\frac {2+x}{16+5 \left (-5-4 x+\log ^2(2)\right )}\right )^2} \]
Time = 0.95 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.96 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx=\frac {2 e^{\frac {\left (20+41 x-10 \log ^2(2)\right )^2}{\left (9+20 x-5 \log ^2(2)\right )^2}} \left (31+5 \log ^2(2)\right )}{62+10 \log ^2(2)} \]
Integrate[(E^((400 + 1640*x + 1681*x^2 + (-400 - 820*x)*Log[2]^2 + 100*Log [2]^4)/(81 + 360*x + 400*x^2 + (-90 - 200*x)*Log[2]^2 + 25*Log[2]^4))*(124 0 + 2542*x + (-420 + 410*x)*Log[2]^2 - 100*Log[2]^4))/(-729 - 4860*x - 108 00*x^2 - 8000*x^3 + (1215 + 5400*x + 6000*x^2)*Log[2]^2 + (-675 - 1500*x)* Log[2]^4 + 125*Log[2]^6),x]
(2*E^((20 + 41*x - 10*Log[2]^2)^2/(9 + 20*x - 5*Log[2]^2)^2)*(31 + 5*Log[2 ]^2))/(62 + 10*Log[2]^2)
Time = 3.05 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.28, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.047, Rules used = {2007, 2092, 7292, 7239, 27, 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.
| \(\displaystyle \int \frac {\left (2542 x+(410 x-420) \log ^2(2)+1240-100 \log ^4(2)\right ) \exp \left (\frac {1681 x^2+1640 x+(-820 x-400) \log ^2(2)+400+100 \log ^4(2)}{400 x^2+360 x+(-200 x-90) \log ^2(2)+81+25 \log ^4(2)}\right )}{-8000 x^3-10800 x^2+\left (6000 x^2+5400 x+1215\right ) \log ^2(2)-4860 x+(-1500 x-675) \log ^4(2)-729+125 \log ^6(2)} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {\left (2542 x+(410 x-420) \log ^2(2)+1240-100 \log ^4(2)\right ) \exp \left (\frac {1681 x^2+1640 x+(-820 x-400) \log ^2(2)+400+100 \log ^4(2)}{400 x^2+360 x+(-200 x-90) \log ^2(2)+81+25 \log ^4(2)}\right )}{\left (-20 x-9+5 \log ^2(2)\right )^3}dx\) |
| \(\Big \downarrow \) 2092 |
| \(\displaystyle \int \frac {\left (82 x \left (31+5 \log ^2(2)\right )+20 \left (62-5 \log ^4(2)-21 \log ^2(2)\right )\right ) \exp \left (\frac {1681 x^2+1640 x+(-820 x-400) \log ^2(2)+400+100 \log ^4(2)}{400 x^2+360 x+(-200 x-90) \log ^2(2)+81+25 \log ^4(2)}\right )}{\left (-20 x-9+5 \log ^2(2)\right )^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-82 x \left (31+5 \log ^2(2)\right )-20 \left (62-5 \log ^4(2)-21 \log ^2(2)\right )\right ) \exp \left (\frac {1681 x^2+820 x \left (2-\log ^2(2)\right )+100 \left (2-\log ^2(2)\right )^2}{400 x^2+40 x \left (9-5 \log ^2(2)\right )+\left (9-5 \log ^2(2)\right )^2}\right )}{\left (20 x+9-5 \log ^2(2)\right )^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (-31-5 \log ^2(2)\right ) \left (41 x+20-10 \log ^2(2)\right ) \exp \left (\frac {\left (41 x+20-10 \log ^2(2)\right )^2}{\left (20 x+9-5 \log ^2(2)\right )^2}\right )}{\left (20 x+9-5 \log ^2(2)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -2 \left (31+5 \log ^2(2)\right ) \int \frac {\exp \left (\frac {\left (41 x+10 \left (2-\log ^2(2)\right )\right )^2}{\left (20 x-5 \log ^2(2)+9\right )^2}\right ) \left (41 x+10 \left (2-\log ^2(2)\right )\right )}{\left (20 x-5 \log ^2(2)+9\right )^3}dx\) |
| \(\Big \downarrow \) 7257 |
| \(\displaystyle \exp \left (\frac {\left (41 x+10 \left (2-\log ^2(2)\right )\right )^2}{\left (20 x+9-5 \log ^2(2)\right )^2}\right )\) |
Int[(E^((400 + 1640*x + 1681*x^2 + (-400 - 820*x)*Log[2]^2 + 100*Log[2]^4) /(81 + 360*x + 400*x^2 + (-90 - 200*x)*Log[2]^2 + 25*Log[2]^4))*(1240 + 25 42*x + (-420 + 410*x)*Log[2]^2 - 100*Log[2]^4))/(-729 - 4860*x - 10800*x^2 - 8000*x^3 + (1215 + 5400*x + 6000*x^2)*Log[2]^2 + (-675 - 1500*x)*Log[2] ^4 + 125*Log[2]^6),x]
3.29.23.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Px_)*(u_)^(p_.)*(z_)^(q_.), x_Symbol] :> Int[Px*ExpandToSum[z, x]^q*Ex pandToSum[u, x]^p, x] /; FreeQ[{p, q}, x] && BinomialQ[z, x] && BinomialQ[u , x] && !(BinomialMatchQ[z, x] && BinomialMatchQ[u, 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 = 0.43 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16
| method | result | size |
| risch | \({\mathrm e}^{\frac {\left (10 \ln \left (2\right )^{2}-41 x -20\right )^{2}}{\left (5 \ln \left (2\right )^{2}-20 x -9\right )^{2}}}\) | \(29\) |
| parallelrisch | \({\mathrm e}^{\frac {100 \ln \left (2\right )^{4}+\left (-820 x -400\right ) \ln \left (2\right )^{2}+1681 x^{2}+1640 x +400}{25 \ln \left (2\right )^{4}-200 x \ln \left (2\right )^{2}-90 \ln \left (2\right )^{2}+400 x^{2}+360 x +81}}\) | \(60\) |
| gosper | \({\mathrm e}^{\frac {100 \ln \left (2\right )^{4}-820 x \ln \left (2\right )^{2}-400 \ln \left (2\right )^{2}+1681 x^{2}+1640 x +400}{25 \ln \left (2\right )^{4}-200 x \ln \left (2\right )^{2}-90 \ln \left (2\right )^{2}+400 x^{2}+360 x +81}}\) | \(63\) |
| norman | \(\frac {\left (25 \ln \left (2\right )^{4}-90 \ln \left (2\right )^{2}+81\right ) {\mathrm e}^{\frac {100 \ln \left (2\right )^{4}+\left (-820 x -400\right ) \ln \left (2\right )^{2}+1681 x^{2}+1640 x +400}{25 \ln \left (2\right )^{4}+\left (-200 x -90\right ) \ln \left (2\right )^{2}+400 x^{2}+360 x +81}}+\left (-200 \ln \left (2\right )^{2}+360\right ) x \,{\mathrm e}^{\frac {100 \ln \left (2\right )^{4}+\left (-820 x -400\right ) \ln \left (2\right )^{2}+1681 x^{2}+1640 x +400}{25 \ln \left (2\right )^{4}+\left (-200 x -90\right ) \ln \left (2\right )^{2}+400 x^{2}+360 x +81}}+400 x^{2} {\mathrm e}^{\frac {100 \ln \left (2\right )^{4}+\left (-820 x -400\right ) \ln \left (2\right )^{2}+1681 x^{2}+1640 x +400}{25 \ln \left (2\right )^{4}+\left (-200 x -90\right ) \ln \left (2\right )^{2}+400 x^{2}+360 x +81}}}{\left (5 \ln \left (2\right )^{2}-20 x -9\right )^{2}}\) | \(214\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(875\) |
| default | \(\text {Expression too large to display}\) | \(875\) |
int((-100*ln(2)^4+(410*x-420)*ln(2)^2+2542*x+1240)*exp((100*ln(2)^4+(-820* x-400)*ln(2)^2+1681*x^2+1640*x+400)/(25*ln(2)^4+(-200*x-90)*ln(2)^2+400*x^ 2+360*x+81))/(125*ln(2)^6+(-1500*x-675)*ln(2)^4+(6000*x^2+5400*x+1215)*ln( 2)^2-8000*x^3-10800*x^2-4860*x-729),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (22) = 44\).
Time = 0.25 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx=e^{\left (\frac {100 \, \log \left (2\right )^{4} - 20 \, {\left (41 \, x + 20\right )} \log \left (2\right )^{2} + 1681 \, x^{2} + 1640 \, x + 400}{25 \, \log \left (2\right )^{4} - 10 \, {\left (20 \, x + 9\right )} \log \left (2\right )^{2} + 400 \, x^{2} + 360 \, x + 81}\right )} \]
integrate((-100*log(2)^4+(410*x-420)*log(2)^2+2542*x+1240)*exp((100*log(2) ^4+(-820*x-400)*log(2)^2+1681*x^2+1640*x+400)/(25*log(2)^4+(-200*x-90)*log (2)^2+400*x^2+360*x+81))/(125*log(2)^6+(-1500*x-675)*log(2)^4+(6000*x^2+54 00*x+1215)*log(2)^2-8000*x^3-10800*x^2-4860*x-729),x, algorithm=\
e^((100*log(2)^4 - 20*(41*x + 20)*log(2)^2 + 1681*x^2 + 1640*x + 400)/(25* log(2)^4 - 10*(20*x + 9)*log(2)^2 + 400*x^2 + 360*x + 81))
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (19) = 38\).
Time = 0.46 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx=e^{\frac {1681 x^{2} + 1640 x + \left (- 820 x - 400\right ) \log {\left (2 \right )}^{2} + 100 \log {\left (2 \right )}^{4} + 400}{400 x^{2} + 360 x + \left (- 200 x - 90\right ) \log {\left (2 \right )}^{2} + 25 \log {\left (2 \right )}^{4} + 81}} \]
integrate((-100*ln(2)**4+(410*x-420)*ln(2)**2+2542*x+1240)*exp((100*ln(2)* *4+(-820*x-400)*ln(2)**2+1681*x**2+1640*x+400)/(25*ln(2)**4+(-200*x-90)*ln (2)**2+400*x**2+360*x+81))/(125*ln(2)**6+(-1500*x-675)*ln(2)**4+(6000*x**2 +5400*x+1215)*ln(2)**2-8000*x**3-10800*x**2-4860*x-729),x)
exp((1681*x**2 + 1640*x + (-820*x - 400)*log(2)**2 + 100*log(2)**4 + 400)/ (400*x**2 + 360*x + (-200*x - 90)*log(2)**2 + 25*log(2)**4 + 81))
Leaf count of result is larger than twice the leaf count of optimal. 147 vs. \(2 (22) = 44\).
Time = 46.61 (sec) , antiderivative size = 147, normalized size of antiderivative = 5.88 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx=e^{\left (\frac {\log \left (2\right )^{4}}{16 \, {\left (25 \, \log \left (2\right )^{4} - 40 \, {\left (5 \, \log \left (2\right )^{2} - 9\right )} x + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 81\right )}} + \frac {31 \, \log \left (2\right )^{2}}{40 \, {\left (25 \, \log \left (2\right )^{4} - 40 \, {\left (5 \, \log \left (2\right )^{2} - 9\right )} x + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 81\right )}} - \frac {41 \, \log \left (2\right )^{2}}{40 \, {\left (5 \, \log \left (2\right )^{2} - 20 \, x - 9\right )}} + \frac {961}{400 \, {\left (25 \, \log \left (2\right )^{4} - 40 \, {\left (5 \, \log \left (2\right )^{2} - 9\right )} x + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 81\right )}} - \frac {1271}{200 \, {\left (5 \, \log \left (2\right )^{2} - 20 \, x - 9\right )}} + \frac {1681}{400}\right )} \]
integrate((-100*log(2)^4+(410*x-420)*log(2)^2+2542*x+1240)*exp((100*log(2) ^4+(-820*x-400)*log(2)^2+1681*x^2+1640*x+400)/(25*log(2)^4+(-200*x-90)*log (2)^2+400*x^2+360*x+81))/(125*log(2)^6+(-1500*x-675)*log(2)^4+(6000*x^2+54 00*x+1215)*log(2)^2-8000*x^3-10800*x^2-4860*x-729),x, algorithm=\
e^(1/16*log(2)^4/(25*log(2)^4 - 40*(5*log(2)^2 - 9)*x + 400*x^2 - 90*log(2 )^2 + 81) + 31/40*log(2)^2/(25*log(2)^4 - 40*(5*log(2)^2 - 9)*x + 400*x^2 - 90*log(2)^2 + 81) - 41/40*log(2)^2/(5*log(2)^2 - 20*x - 9) + 961/400/(25 *log(2)^4 - 40*(5*log(2)^2 - 9)*x + 400*x^2 - 90*log(2)^2 + 81) - 1271/200 /(5*log(2)^2 - 20*x - 9) + 1681/400)
Leaf count of result is larger than twice the leaf count of optimal. 217 vs. \(2 (22) = 44\).
Time = 0.30 (sec) , antiderivative size = 217, normalized size of antiderivative = 8.68 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx=e^{\left (\frac {100 \, \log \left (2\right )^{4}}{25 \, \log \left (2\right )^{4} - 200 \, x \log \left (2\right )^{2} + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 360 \, x + 81} - \frac {820 \, x \log \left (2\right )^{2}}{25 \, \log \left (2\right )^{4} - 200 \, x \log \left (2\right )^{2} + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 360 \, x + 81} + \frac {1681 \, x^{2}}{25 \, \log \left (2\right )^{4} - 200 \, x \log \left (2\right )^{2} + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 360 \, x + 81} - \frac {400 \, \log \left (2\right )^{2}}{25 \, \log \left (2\right )^{4} - 200 \, x \log \left (2\right )^{2} + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 360 \, x + 81} + \frac {1640 \, x}{25 \, \log \left (2\right )^{4} - 200 \, x \log \left (2\right )^{2} + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 360 \, x + 81} + \frac {400}{25 \, \log \left (2\right )^{4} - 200 \, x \log \left (2\right )^{2} + 400 \, x^{2} - 90 \, \log \left (2\right )^{2} + 360 \, x + 81}\right )} \]
integrate((-100*log(2)^4+(410*x-420)*log(2)^2+2542*x+1240)*exp((100*log(2) ^4+(-820*x-400)*log(2)^2+1681*x^2+1640*x+400)/(25*log(2)^4+(-200*x-90)*log (2)^2+400*x^2+360*x+81))/(125*log(2)^6+(-1500*x-675)*log(2)^4+(6000*x^2+54 00*x+1215)*log(2)^2-8000*x^3-10800*x^2-4860*x-729),x, algorithm=\
e^(100*log(2)^4/(25*log(2)^4 - 200*x*log(2)^2 + 400*x^2 - 90*log(2)^2 + 36 0*x + 81) - 820*x*log(2)^2/(25*log(2)^4 - 200*x*log(2)^2 + 400*x^2 - 90*lo g(2)^2 + 360*x + 81) + 1681*x^2/(25*log(2)^4 - 200*x*log(2)^2 + 400*x^2 - 90*log(2)^2 + 360*x + 81) - 400*log(2)^2/(25*log(2)^4 - 200*x*log(2)^2 + 4 00*x^2 - 90*log(2)^2 + 360*x + 81) + 1640*x/(25*log(2)^4 - 200*x*log(2)^2 + 400*x^2 - 90*log(2)^2 + 360*x + 81) + 400/(25*log(2)^4 - 200*x*log(2)^2 + 400*x^2 - 90*log(2)^2 + 360*x + 81))
Time = 13.34 (sec) , antiderivative size = 222, normalized size of antiderivative = 8.88 \[ \int \frac {e^{\frac {400+1640 x+1681 x^2+(-400-820 x) \log ^2(2)+100 \log ^4(2)}{81+360 x+400 x^2+(-90-200 x) \log ^2(2)+25 \log ^4(2)}} \left (1240+2542 x+(-420+410 x) \log ^2(2)-100 \log ^4(2)\right )}{-729-4860 x-10800 x^2-8000 x^3+\left (1215+5400 x+6000 x^2\right ) \log ^2(2)+(-675-1500 x) \log ^4(2)+125 \log ^6(2)} \, dx={\mathrm {e}}^{\frac {1640\,x}{360\,x-200\,x\,{\ln \left (2\right )}^2-90\,{\ln \left (2\right )}^2+25\,{\ln \left (2\right )}^4+400\,x^2+81}}\,{\mathrm {e}}^{\frac {100\,{\ln \left (2\right )}^4}{360\,x-200\,x\,{\ln \left (2\right )}^2-90\,{\ln \left (2\right )}^2+25\,{\ln \left (2\right )}^4+400\,x^2+81}}\,{\mathrm {e}}^{-\frac {400\,{\ln \left (2\right )}^2}{360\,x-200\,x\,{\ln \left (2\right )}^2-90\,{\ln \left (2\right )}^2+25\,{\ln \left (2\right )}^4+400\,x^2+81}}\,{\mathrm {e}}^{\frac {1681\,x^2}{360\,x-200\,x\,{\ln \left (2\right )}^2-90\,{\ln \left (2\right )}^2+25\,{\ln \left (2\right )}^4+400\,x^2+81}}\,{\mathrm {e}}^{\frac {400}{360\,x-200\,x\,{\ln \left (2\right )}^2-90\,{\ln \left (2\right )}^2+25\,{\ln \left (2\right )}^4+400\,x^2+81}}\,{\mathrm {e}}^{-\frac {820\,x\,{\ln \left (2\right )}^2}{360\,x-200\,x\,{\ln \left (2\right )}^2-90\,{\ln \left (2\right )}^2+25\,{\ln \left (2\right )}^4+400\,x^2+81}} \]
int(-(exp((1640*x - log(2)^2*(820*x + 400) + 100*log(2)^4 + 1681*x^2 + 400 )/(360*x - log(2)^2*(200*x + 90) + 25*log(2)^4 + 400*x^2 + 81))*(2542*x + log(2)^2*(410*x - 420) - 100*log(2)^4 + 1240))/(4860*x + log(2)^4*(1500*x + 675) - log(2)^2*(5400*x + 6000*x^2 + 1215) - 125*log(2)^6 + 10800*x^2 + 8000*x^3 + 729),x)
exp((1640*x)/(360*x - 200*x*log(2)^2 - 90*log(2)^2 + 25*log(2)^4 + 400*x^2 + 81))*exp((100*log(2)^4)/(360*x - 200*x*log(2)^2 - 90*log(2)^2 + 25*log( 2)^4 + 400*x^2 + 81))*exp(-(400*log(2)^2)/(360*x - 200*x*log(2)^2 - 90*log (2)^2 + 25*log(2)^4 + 400*x^2 + 81))*exp((1681*x^2)/(360*x - 200*x*log(2)^ 2 - 90*log(2)^2 + 25*log(2)^4 + 400*x^2 + 81))*exp(400/(360*x - 200*x*log( 2)^2 - 90*log(2)^2 + 25*log(2)^4 + 400*x^2 + 81))*exp(-(820*x*log(2)^2)/(3 60*x - 200*x*log(2)^2 - 90*log(2)^2 + 25*log(2)^4 + 400*x^2 + 81))