Integrand size = 389, antiderivative size = 22 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {x}{\left (5-\frac {1}{5} x \left (-5+e^2+4 \log (19)\right )^2\right )^2} \] Output:
x/(5-1/5*x*(exp(2)-5+4*ln(19))^2)^2
Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {25 x}{\left (-25+x \left (-5+e^2+4 \log (19)\right )^2\right )^2} \] Input:
Integrate[(-625 - 625*x + 250*E^2*x - 25*E^4*x + (1000*x - 200*E^2*x)*Log[ 19] - 400*x*Log[19]^2)/(-15625 + 46875*x - 46875*x^2 + 15625*x^3 - 30*E^10 *x^3 + E^12*x^3 + E^2*(-18750*x + 37500*x^2 - 18750*x^3) + E^6*(1500*x^2 - 2500*x^3) + E^8*(-75*x^2 + 375*x^3) + E^4*(1875*x - 11250*x^2 + 9375*x^3) + (-75000*x + 150000*x^2 - 75000*x^3 - 600*E^8*x^3 + 24*E^10*x^3 + E^4*(1 8000*x^2 - 30000*x^3) + E^6*(-1200*x^2 + 6000*x^3) + E^2*(15000*x - 90000* x^2 + 75000*x^3))*Log[19] + (30000*x - 180000*x^2 + 150000*x^3 - 4800*E^6* x^3 + 240*E^8*x^3 + E^2*(72000*x^2 - 120000*x^3) + E^4*(-7200*x^2 + 36000* x^3))*Log[19]^2 + (96000*x^2 - 160000*x^3 - 19200*E^4*x^3 + 1280*E^6*x^3 + E^2*(-19200*x^2 + 96000*x^3))*Log[19]^3 + (-19200*x^2 + 96000*x^3 - 38400 *E^2*x^3 + 3840*E^4*x^3)*Log[19]^4 + (-30720*x^3 + 6144*E^2*x^3)*Log[19]^5 + 4096*x^3*Log[19]^6),x]
Output:
(25*x)/(-25 + x*(-5 + E^2 + 4*Log[19])^2)^2
Time = 0.29 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 9, number of rules used = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6, 6, 6, 6, 6, 6, 2007, 204, 38}
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.
| \(\displaystyle \int \frac {-25 e^4 x+250 e^2 x-625 x-400 x \log ^2(19)+\left (1000 x-200 e^2 x\right ) \log (19)-625}{e^{12} x^3-30 e^{10} x^3+15625 x^3+4096 x^3 \log ^6(19)+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (250 e^2-625\right ) x-25 e^4 x-400 x \log ^2(19)+\left (1000 x-200 e^2 x\right ) \log (19)-625}{e^{12} x^3-30 e^{10} x^3+15625 x^3+4096 x^3 \log ^6(19)+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (-625+250 e^2-25 e^4\right ) x-400 x \log ^2(19)+\left (1000 x-200 e^2 x\right ) \log (19)-625}{e^{12} x^3-30 e^{10} x^3+15625 x^3+4096 x^3 \log ^6(19)+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )+\left (1000 x-200 e^2 x\right ) \log (19)-625}{e^{12} x^3-30 e^{10} x^3+15625 x^3+4096 x^3 \log ^6(19)+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )+\left (1000 x-200 e^2 x\right ) \log (19)-625}{\left (15625-30 e^{10}\right ) x^3+e^{12} x^3+4096 x^3 \log ^6(19)+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )+\left (1000 x-200 e^2 x\right ) \log (19)-625}{\left (15625-30 e^{10}+e^{12}\right ) x^3+4096 x^3 \log ^6(19)+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )+\left (1000 x-200 e^2 x\right ) \log (19)-625}{x^3 \left (15625-30 e^{10}+e^{12}+4096 \log ^6(19)\right )+\left (6144 e^2 x^3-30720 x^3\right ) \log ^5(19)-46875 x^2+e^2 \left (-18750 x^3+37500 x^2-18750 x\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (375 x^3-75 x^2\right )+e^4 \left (9375 x^3-11250 x^2+1875 x\right )+\left (3840 e^4 x^3-38400 e^2 x^3+96000 x^3-19200 x^2\right ) \log ^4(19)+\left (1280 e^6 x^3-19200 e^4 x^3-160000 x^3+96000 x^2+e^2 \left (96000 x^3-19200 x^2\right )\right ) \log ^3(19)+\left (240 e^8 x^3-4800 e^6 x^3+150000 x^3-180000 x^2+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (36000 x^3-7200 x^2\right )+30000 x\right ) \log ^2(19)+\left (24 e^{10} x^3-600 e^8 x^3-75000 x^3+150000 x^2+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (6000 x^3-1200 x^2\right )+e^2 \left (75000 x^3-90000 x^2+15000 x\right )-75000 x\right ) \log (19)+46875 x-15625}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )+\left (1000 x-200 e^2 x\right ) \log (19)-625}{\left (x \left (-5+e^2+4 \log (19)\right )^2-25\right )^3}dx\) |
| \(\Big \downarrow \) 204 |
| \(\displaystyle \int \frac {-25 x \left (5-e^2-4 \log (19)\right )^2-625}{\left (x \left (5-e^2-4 \log (19)\right )^2-25\right )^3}dx\) |
| \(\Big \downarrow \) 38 |
| \(\displaystyle \frac {25 x}{\left (25-x \left (5-e^2-4 \log (19)\right )^2\right )^2}\) |
Input:
Int[(-625 - 625*x + 250*E^2*x - 25*E^4*x + (1000*x - 200*E^2*x)*Log[19] - 400*x*Log[19]^2)/(-15625 + 46875*x - 46875*x^2 + 15625*x^3 - 30*E^10*x^3 + E^12*x^3 + E^2*(-18750*x + 37500*x^2 - 18750*x^3) + E^6*(1500*x^2 - 2500* x^3) + E^8*(-75*x^2 + 375*x^3) + E^4*(1875*x - 11250*x^2 + 9375*x^3) + (-7 5000*x + 150000*x^2 - 75000*x^3 - 600*E^8*x^3 + 24*E^10*x^3 + E^4*(18000*x ^2 - 30000*x^3) + E^6*(-1200*x^2 + 6000*x^3) + E^2*(15000*x - 90000*x^2 + 75000*x^3))*Log[19] + (30000*x - 180000*x^2 + 150000*x^3 - 4800*E^6*x^3 + 240*E^8*x^3 + E^2*(72000*x^2 - 120000*x^3) + E^4*(-7200*x^2 + 36000*x^3))* Log[19]^2 + (96000*x^2 - 160000*x^3 - 19200*E^4*x^3 + 1280*E^6*x^3 + E^2*( -19200*x^2 + 96000*x^3))*Log[19]^3 + (-19200*x^2 + 96000*x^3 - 38400*E^2*x ^3 + 3840*E^4*x^3)*Log[19]^4 + (-30720*x^3 + 6144*E^2*x^3)*Log[19]^5 + 409 6*x^3*Log[19]^6),x]
Output:
(25*x)/(25 - x*(5 - E^2 - 4*Log[19])^2)^2
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[((a_) + (b_.)*(x_))^(m_.)*((c_) + (d_.)*(x_)), x_Symbol] :> Simp[d*x*(( a + b*x)^(m + 1)/(b*(m + 2))), x] /; FreeQ[{a, b, c, d, m}, x] && EqQ[a*d - b*c*(m + 2), 0]
Int[(u_)^(m_.)*(v_)^(n_.), x_Symbol] :> Int[ExpandToSum[u, x]^m*ExpandToSum [v, x]^n, x] /; FreeQ[{m, n}, x] && LinearQ[{u, v}, x] && !LinearMatchQ[{u , v}, 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]
Leaf count of result is larger than twice the leaf count of optimal. \(40\) vs. \(2(19)=38\).
Time = 1.28 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.86
| method | result | size |
| norman | \(\frac {25 x}{\left (16 x \ln \left (19\right )^{2}+8 \ln \left (19\right ) {\mathrm e}^{2} x +x \,{\mathrm e}^{4}-40 \ln \left (19\right ) x -10 \,{\mathrm e}^{2} x +25 x -25\right )^{2}}\) | \(41\) |
| risch | \(\frac {25 x}{256 \left (\ln \left (19\right )^{4} x^{2}+\ln \left (19\right )^{3} {\mathrm e}^{2} x^{2}+\frac {3 \ln \left (19\right )^{2} {\mathrm e}^{4} x^{2}}{8}+\frac {\ln \left (19\right ) {\mathrm e}^{6} x^{2}}{16}+\frac {x^{2} {\mathrm e}^{8}}{256}-5 \ln \left (19\right )^{3} x^{2}-\frac {15 \ln \left (19\right )^{2} {\mathrm e}^{2} x^{2}}{4}-\frac {15 \ln \left (19\right ) {\mathrm e}^{4} x^{2}}{16}-\frac {5 \,{\mathrm e}^{6} x^{2}}{64}+\frac {75 \ln \left (19\right )^{2} x^{2}}{8}+\frac {75 \ln \left (19\right ) {\mathrm e}^{2} x^{2}}{16}+\frac {75 x^{2} {\mathrm e}^{4}}{128}-\frac {25 x \ln \left (19\right )^{2}}{8}-\frac {25 \ln \left (19\right ) {\mathrm e}^{2} x}{16}-\frac {125 \ln \left (19\right ) x^{2}}{16}-\frac {25 x \,{\mathrm e}^{4}}{128}-\frac {125 x^{2} {\mathrm e}^{2}}{64}+\frac {125 \ln \left (19\right ) x}{16}+\frac {125 \,{\mathrm e}^{2} x}{64}+\frac {625 x^{2}}{256}-\frac {625 x}{128}+\frac {625}{256}\right )}\) | \(165\) |
| gosper | \(\frac {25 x}{256 \ln \left (19\right )^{4} x^{2}+256 \ln \left (19\right )^{3} {\mathrm e}^{2} x^{2}+96 \ln \left (19\right )^{2} {\mathrm e}^{4} x^{2}+16 \ln \left (19\right ) {\mathrm e}^{6} x^{2}+x^{2} {\mathrm e}^{8}-1280 \ln \left (19\right )^{3} x^{2}-960 \ln \left (19\right )^{2} {\mathrm e}^{2} x^{2}-240 \ln \left (19\right ) {\mathrm e}^{4} x^{2}-20 \,{\mathrm e}^{6} x^{2}+2400 \ln \left (19\right )^{2} x^{2}+1200 \ln \left (19\right ) {\mathrm e}^{2} x^{2}+150 x^{2} {\mathrm e}^{4}-800 x \ln \left (19\right )^{2}-400 \ln \left (19\right ) {\mathrm e}^{2} x -2000 \ln \left (19\right ) x^{2}-50 x \,{\mathrm e}^{4}-500 x^{2} {\mathrm e}^{2}+2000 \ln \left (19\right ) x +500 \,{\mathrm e}^{2} x +625 x^{2}-1250 x +625}\) | \(180\) |
| parallelrisch | \(\frac {25 x}{256 \ln \left (19\right )^{4} x^{2}+256 \ln \left (19\right )^{3} {\mathrm e}^{2} x^{2}+96 \ln \left (19\right )^{2} {\mathrm e}^{4} x^{2}+16 \ln \left (19\right ) {\mathrm e}^{6} x^{2}+x^{2} {\mathrm e}^{8}-1280 \ln \left (19\right )^{3} x^{2}-960 \ln \left (19\right )^{2} {\mathrm e}^{2} x^{2}-240 \ln \left (19\right ) {\mathrm e}^{4} x^{2}-20 \,{\mathrm e}^{6} x^{2}+2400 \ln \left (19\right )^{2} x^{2}+1200 \ln \left (19\right ) {\mathrm e}^{2} x^{2}+150 x^{2} {\mathrm e}^{4}-800 x \ln \left (19\right )^{2}-400 \ln \left (19\right ) {\mathrm e}^{2} x -2000 \ln \left (19\right ) x^{2}-50 x \,{\mathrm e}^{4}-500 x^{2} {\mathrm e}^{2}+2000 \ln \left (19\right ) x +500 \,{\mathrm e}^{2} x +625 x^{2}-1250 x +625}\) | \(180\) |
| default | \(\text {Expression too large to display}\) | \(714\) |
Input:
int((-400*x*ln(19)^2+(-200*exp(2)*x+1000*x)*ln(19)-25*x*exp(2)^2+250*exp(2 )*x-625*x-625)/(4096*x^3*ln(19)^6+(6144*x^3*exp(2)-30720*x^3)*ln(19)^5+(38 40*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*ln(19)^4+(1280*x^3*e xp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000*x^3+96000*x ^2)*ln(19)^3+(240*x^3*exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-7200*x^2)*exp( 2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+30000*x)*ln(19)^ 2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2)^3+(-30000*x ^3+18000*x^2)*exp(2)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-75000*x^3+1500 00*x^2-75000*x)*ln(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(375*x^3-75*x^2)*exp(2 )^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x)*exp(2)^2+(-1 8750*x^3+37500*x^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875*x-15625),x,me thod=_RETURNVERBOSE)
Output:
25*x/(16*x*ln(19)^2+8*ln(19)*exp(2)*x+x*exp(2)^2-40*ln(19)*x-10*exp(2)*x+2 5*x-25)^2
Leaf count of result is larger than twice the leaf count of optimal. 147 vs. \(2 (19) = 38\).
Time = 0.07 (sec) , antiderivative size = 147, normalized size of antiderivative = 6.68 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {25 \, x}{256 \, x^{2} \log \left (19\right )^{4} + 256 \, {\left (x^{2} e^{2} - 5 \, x^{2}\right )} \log \left (19\right )^{3} + x^{2} e^{8} - 20 \, x^{2} e^{6} + 32 \, {\left (3 \, x^{2} e^{4} - 30 \, x^{2} e^{2} + 75 \, x^{2} - 25 \, x\right )} \log \left (19\right )^{2} + 625 \, x^{2} + 50 \, {\left (3 \, x^{2} - x\right )} e^{4} - 500 \, {\left (x^{2} - x\right )} e^{2} + 16 \, {\left (x^{2} e^{6} - 15 \, x^{2} e^{4} - 125 \, x^{2} + 25 \, {\left (3 \, x^{2} - x\right )} e^{2} + 125 \, x\right )} \log \left (19\right ) - 1250 \, x + 625} \] Input:
integrate((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+2 50*exp(2)*x-625*x-625)/(4096*x^3*log(19)^6+(6144*x^3*exp(2)-30720*x^3)*log (19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^4+ (1280*x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000* x^3+96000*x^2)*log(19)^3+(240*x^3*exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-72 00*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+3000 0*x)*log(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2 )^3+(-30000*x^3+18000*x^2)*exp(2)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-7 5000*x^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(375*x^3 -75*x^2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x )*exp(2)^2+(-18750*x^3+37500*x^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875 *x-15625),x, algorithm="fricas")
Output:
25*x/(256*x^2*log(19)^4 + 256*(x^2*e^2 - 5*x^2)*log(19)^3 + x^2*e^8 - 20*x ^2*e^6 + 32*(3*x^2*e^4 - 30*x^2*e^2 + 75*x^2 - 25*x)*log(19)^2 + 625*x^2 + 50*(3*x^2 - x)*e^4 - 500*(x^2 - x)*e^2 + 16*(x^2*e^6 - 15*x^2*e^4 - 125*x ^2 + 25*(3*x^2 - x)*e^2 + 125*x)*log(19) - 1250*x + 625)
Leaf count of result is larger than twice the leaf count of optimal. 143 vs. \(2 (19) = 38\).
Time = 3.16 (sec) , antiderivative size = 143, normalized size of antiderivative = 6.50 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {25 x}{x^{2} \left (- 960 e^{2} \log {\left (19 \right )}^{2} - 240 e^{4} \log {\left (19 \right )} - 1280 \log {\left (19 \right )}^{3} - 20 e^{6} - 2000 \log {\left (19 \right )} - 500 e^{2} + 625 + e^{8} + 150 e^{4} + 16 e^{6} \log {\left (19 \right )} + 256 \log {\left (19 \right )}^{4} + 2400 \log {\left (19 \right )}^{2} + 1200 e^{2} \log {\left (19 \right )} + 96 e^{4} \log {\left (19 \right )}^{2} + 256 e^{2} \log {\left (19 \right )}^{3}\right ) + x \left (- 400 e^{2} \log {\left (19 \right )} - 800 \log {\left (19 \right )}^{2} - 50 e^{4} - 1250 + 500 e^{2} + 2000 \log {\left (19 \right )}\right ) + 625} \] Input:
integrate((-400*x*ln(19)**2+(-200*exp(2)*x+1000*x)*ln(19)-25*x*exp(2)**2+2 50*exp(2)*x-625*x-625)/(4096*x**3*ln(19)**6+(6144*x**3*exp(2)-30720*x**3)* ln(19)**5+(3840*x**3*exp(2)**2-38400*x**3*exp(2)+96000*x**3-19200*x**2)*ln (19)**4+(1280*x**3*exp(2)**3-19200*x**3*exp(2)**2+(96000*x**3-19200*x**2)* exp(2)-160000*x**3+96000*x**2)*ln(19)**3+(240*x**3*exp(2)**4-4800*x**3*exp (2)**3+(36000*x**3-7200*x**2)*exp(2)**2+(-120000*x**3+72000*x**2)*exp(2)+1 50000*x**3-180000*x**2+30000*x)*ln(19)**2+(24*x**3*exp(2)**5-600*x**3*exp( 2)**4+(6000*x**3-1200*x**2)*exp(2)**3+(-30000*x**3+18000*x**2)*exp(2)**2+( 75000*x**3-90000*x**2+15000*x)*exp(2)-75000*x**3+150000*x**2-75000*x)*ln(1 9)+x**3*exp(2)**6-30*x**3*exp(2)**5+(375*x**3-75*x**2)*exp(2)**4+(-2500*x* *3+1500*x**2)*exp(2)**3+(9375*x**3-11250*x**2+1875*x)*exp(2)**2+(-18750*x* *3+37500*x**2-18750*x)*exp(2)+15625*x**3-46875*x**2+46875*x-15625),x)
Output:
25*x/(x**2*(-960*exp(2)*log(19)**2 - 240*exp(4)*log(19) - 1280*log(19)**3 - 20*exp(6) - 2000*log(19) - 500*exp(2) + 625 + exp(8) + 150*exp(4) + 16*e xp(6)*log(19) + 256*log(19)**4 + 2400*log(19)**2 + 1200*exp(2)*log(19) + 9 6*exp(4)*log(19)**2 + 256*exp(2)*log(19)**3) + x*(-400*exp(2)*log(19) - 80 0*log(19)**2 - 50*exp(4) - 1250 + 500*exp(2) + 2000*log(19)) + 625)
Leaf count of result is larger than twice the leaf count of optimal. 98 vs. \(2 (19) = 38\).
Time = 0.04 (sec) , antiderivative size = 98, normalized size of antiderivative = 4.45 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {25 \, x}{{\left (256 \, {\left (e^{2} - 5\right )} \log \left (19\right )^{3} + 256 \, \log \left (19\right )^{4} + 96 \, {\left (e^{4} - 10 \, e^{2} + 25\right )} \log \left (19\right )^{2} + 16 \, {\left (e^{6} - 15 \, e^{4} + 75 \, e^{2} - 125\right )} \log \left (19\right ) + e^{8} - 20 \, e^{6} + 150 \, e^{4} - 500 \, e^{2} + 625\right )} x^{2} - 50 \, {\left (8 \, {\left (e^{2} - 5\right )} \log \left (19\right ) + 16 \, \log \left (19\right )^{2} + e^{4} - 10 \, e^{2} + 25\right )} x + 625} \] Input:
integrate((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+2 50*exp(2)*x-625*x-625)/(4096*x^3*log(19)^6+(6144*x^3*exp(2)-30720*x^3)*log (19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^4+ (1280*x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000* x^3+96000*x^2)*log(19)^3+(240*x^3*exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-72 00*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+3000 0*x)*log(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2 )^3+(-30000*x^3+18000*x^2)*exp(2)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-7 5000*x^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(375*x^3 -75*x^2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x )*exp(2)^2+(-18750*x^3+37500*x^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875 *x-15625),x, algorithm="maxima")
Output:
25*x/((256*(e^2 - 5)*log(19)^3 + 256*log(19)^4 + 96*(e^4 - 10*e^2 + 25)*lo g(19)^2 + 16*(e^6 - 15*e^4 + 75*e^2 - 125)*log(19) + e^8 - 20*e^6 + 150*e^ 4 - 500*e^2 + 625)*x^2 - 50*(8*(e^2 - 5)*log(19) + 16*log(19)^2 + e^4 - 10 *e^2 + 25)*x + 625)
Time = 0.13 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.73 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {25 \, x}{{\left (8 \, x e^{2} \log \left (19\right ) + 16 \, x \log \left (19\right )^{2} + x e^{4} - 10 \, x e^{2} - 40 \, x \log \left (19\right ) + 25 \, x - 25\right )}^{2}} \] Input:
integrate((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+2 50*exp(2)*x-625*x-625)/(4096*x^3*log(19)^6+(6144*x^3*exp(2)-30720*x^3)*log (19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^4+ (1280*x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000* x^3+96000*x^2)*log(19)^3+(240*x^3*exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-72 00*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+3000 0*x)*log(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2 )^3+(-30000*x^3+18000*x^2)*exp(2)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-7 5000*x^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(375*x^3 -75*x^2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x )*exp(2)^2+(-18750*x^3+37500*x^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875 *x-15625),x, algorithm="giac")
Output:
25*x/(8*x*e^2*log(19) + 16*x*log(19)^2 + x*e^4 - 10*x*e^2 - 40*x*log(19) + 25*x - 25)^2
Time = 2.96 (sec) , antiderivative size = 120, normalized size of antiderivative = 5.45 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx=\frac {25\,x}{\left (150\,{\mathrm {e}}^4-500\,{\mathrm {e}}^2-20\,{\mathrm {e}}^6+{\mathrm {e}}^8-2000\,\ln \left (19\right )+1200\,{\mathrm {e}}^2\,\ln \left (19\right )-240\,{\mathrm {e}}^4\,\ln \left (19\right )+16\,{\mathrm {e}}^6\,\ln \left (19\right )-960\,{\mathrm {e}}^2\,{\ln \left (19\right )}^2+256\,{\mathrm {e}}^2\,{\ln \left (19\right )}^3+96\,{\mathrm {e}}^4\,{\ln \left (19\right )}^2+2400\,{\ln \left (19\right )}^2-1280\,{\ln \left (19\right )}^3+256\,{\ln \left (19\right )}^4+625\right )\,x^2+\left (500\,{\mathrm {e}}^2-50\,{\mathrm {e}}^4+2000\,\ln \left (19\right )-400\,{\mathrm {e}}^2\,\ln \left (19\right )-800\,{\ln \left (19\right )}^2-1250\right )\,x+625} \] Input:
int(-(625*x - 250*x*exp(2) + 25*x*exp(4) - log(19)*(1000*x - 200*x*exp(2)) + 400*x*log(19)^2 + 625)/(46875*x + 4096*x^3*log(19)^6 + log(19)^2*(30000 *x - exp(4)*(7200*x^2 - 36000*x^3) + exp(2)*(72000*x^2 - 120000*x^3) - 480 0*x^3*exp(6) + 240*x^3*exp(8) - 180000*x^2 + 150000*x^3) - log(19)^4*(3840 0*x^3*exp(2) - 3840*x^3*exp(4) + 19200*x^2 - 96000*x^3) - log(19)*(75000*x - exp(2)*(15000*x - 90000*x^2 + 75000*x^3) + exp(6)*(1200*x^2 - 6000*x^3) - exp(4)*(18000*x^2 - 30000*x^3) + 600*x^3*exp(8) - 24*x^3*exp(10) - 1500 00*x^2 + 75000*x^3) + log(19)^5*(6144*x^3*exp(2) - 30720*x^3) + exp(4)*(18 75*x - 11250*x^2 + 9375*x^3) - exp(2)*(18750*x - 37500*x^2 + 18750*x^3) - exp(8)*(75*x^2 - 375*x^3) + exp(6)*(1500*x^2 - 2500*x^3) - 30*x^3*exp(10) + x^3*exp(12) - log(19)^3*(exp(2)*(19200*x^2 - 96000*x^3) + 19200*x^3*exp( 4) - 1280*x^3*exp(6) - 96000*x^2 + 160000*x^3) - 46875*x^2 + 15625*x^3 - 1 5625),x)
Output:
(25*x)/(x^2*(150*exp(4) - 500*exp(2) - 20*exp(6) + exp(8) - 2000*log(19) + 1200*exp(2)*log(19) - 240*exp(4)*log(19) + 16*exp(6)*log(19) - 960*exp(2) *log(19)^2 + 256*exp(2)*log(19)^3 + 96*exp(4)*log(19)^2 + 2400*log(19)^2 - 1280*log(19)^3 + 256*log(19)^4 + 625) - x*(50*exp(4) - 500*exp(2) - 2000* log(19) + 400*exp(2)*log(19) + 800*log(19)^2 + 1250) + 625)
Time = 0.29 (sec) , antiderivative size = 552, normalized size of antiderivative = 25.09 \[ \int \frac {-625-625 x+250 e^2 x-25 e^4 x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx =\text {Too large to display} \] Input:
int((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+250*exp (2)*x-625*x-625)/(4096*x^3*log(19)^6+(6144*x^3*exp(2)-30720*x^3)*log(19)^5 +(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^4+(1280* x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000*x^3+96 000*x^2)*log(19)^3+(240*x^3*exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-7200*x^2 )*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+30000*x)*l og(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2)^3+(- 30000*x^3+18000*x^2)*exp(2)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-75000*x ^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(375*x^3-75*x^ 2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x)*exp( 2)^2+(-18750*x^3+37500*x^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875*x-156 25),x)
Output:
(256*log(19)**4*x**2 + 256*log(19)**3*e**2*x**2 - 1280*log(19)**3*x**2 + 9 6*log(19)**2*e**4*x**2 - 960*log(19)**2*e**2*x**2 + 2400*log(19)**2*x**2 + 16*log(19)*e**6*x**2 - 240*log(19)*e**4*x**2 + 1200*log(19)*e**2*x**2 - 2 000*log(19)*x**2 + e**8*x**2 - 20*e**6*x**2 + 150*e**4*x**2 - 500*e**2*x** 2 + 625*x**2 + 625)/(2*(4096*log(19)**6*x**2 + 6144*log(19)**5*e**2*x**2 - 30720*log(19)**5*x**2 + 3840*log(19)**4*e**4*x**2 - 38400*log(19)**4*e**2 *x**2 + 96000*log(19)**4*x**2 - 12800*log(19)**4*x + 1280*log(19)**3*e**6* x**2 - 19200*log(19)**3*e**4*x**2 + 96000*log(19)**3*e**2*x**2 - 12800*log (19)**3*e**2*x - 160000*log(19)**3*x**2 + 64000*log(19)**3*x + 240*log(19) **2*e**8*x**2 - 4800*log(19)**2*e**6*x**2 + 36000*log(19)**2*e**4*x**2 - 4 800*log(19)**2*e**4*x - 120000*log(19)**2*e**2*x**2 + 48000*log(19)**2*e** 2*x + 150000*log(19)**2*x**2 - 120000*log(19)**2*x + 10000*log(19)**2 + 24 *log(19)*e**10*x**2 - 600*log(19)*e**8*x**2 + 6000*log(19)*e**6*x**2 - 800 *log(19)*e**6*x - 30000*log(19)*e**4*x**2 + 12000*log(19)*e**4*x + 75000*l og(19)*e**2*x**2 - 60000*log(19)*e**2*x + 5000*log(19)*e**2 - 75000*log(19 )*x**2 + 100000*log(19)*x - 25000*log(19) + e**12*x**2 - 30*e**10*x**2 + 3 75*e**8*x**2 - 50*e**8*x - 2500*e**6*x**2 + 1000*e**6*x + 9375*e**4*x**2 - 7500*e**4*x + 625*e**4 - 18750*e**2*x**2 + 25000*e**2*x - 6250*e**2 + 156 25*x**2 - 31250*x + 15625))