Integrand size = 259, antiderivative size = 29 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=\left (e^8+\frac {16}{x^4}-x+\frac {e^2+x}{5+x}-\log (x)\right )^2 \] Output:
((x+exp(2))/(5+x)+16/x^4-ln(x)+exp(4)^2-x)^2
Leaf count is larger than twice the leaf count of optimal. \(169\) vs. \(2(29)=58\).
Time = 0.09 (sec) , antiderivative size = 169, normalized size of antiderivative = 5.83 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=2 \left (\frac {128}{x^8}+\frac {16 e^2 \left (1+5 e^6\right )}{5 x^4}-\frac {16 \left (20+e^2\right )}{25 x^3}+\frac {16 \left (-5+e^2\right )}{125 x^2}-\frac {16 \left (-5+e^2\right )}{625 x}-\left (1+e^8\right ) x+\frac {x^2}{2}+\frac {\left (-5+e^2\right )^2}{2 (5+x)^2}+\frac {-18830+3766 e^2-3125 e^8+625 e^{10}}{625 (5+x)}-\left (1+e^8\right ) \log (x)+\frac {\left (-80-16 x-\left (-5+e^2\right ) x^4+5 x^5+x^6\right ) \log (x)}{x^4 (5+x)}+\frac {\log ^2(x)}{2}\right ) \] Input:
Integrate[(-256000 - 153600*x - 30720*x^2 - 2048*x^3 - 4000*x^4 + 7200*x^5 + 5600*x^6 + 1280*x^7 + 96*x^8 + 200*x^9 - 2*E^4*x^9 + 290*x^10 + 148*x^1 1 + 30*x^12 + 2*x^13 + E^2*(-3200*x^4 - 1440*x^5 - 160*x^6 - 50*x^8 - 60*x ^9 - 14*x^10) + E^8*(-16000*x^4 - 9600*x^5 - 1920*x^6 - 128*x^7 - 250*x^8 - 350*x^9 - 170*x^10 - 32*x^11 - 2*x^12 + E^2*(-10*x^9 - 2*x^10)) + (16000 *x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^10 + 32*x ^11 + 2*x^12 + E^2*(10*x^9 + 2*x^10))*Log[x])/(125*x^9 + 75*x^10 + 15*x^11 + x^12),x]
Output:
2*(128/x^8 + (16*E^2*(1 + 5*E^6))/(5*x^4) - (16*(20 + E^2))/(25*x^3) + (16 *(-5 + E^2))/(125*x^2) - (16*(-5 + E^2))/(625*x) - (1 + E^8)*x + x^2/2 + ( -5 + E^2)^2/(2*(5 + x)^2) + (-18830 + 3766*E^2 - 3125*E^8 + 625*E^10)/(625 *(5 + x)) - (1 + E^8)*Log[x] + ((-80 - 16*x - (-5 + E^2)*x^4 + 5*x^5 + x^6 )*Log[x])/(x^4*(5 + x)) + Log[x]^2/2)
Leaf count is larger than twice the leaf count of optimal. \(534\) vs. \(2(29)=58\).
Time = 3.24 (sec) , antiderivative size = 534, normalized size of antiderivative = 18.41, number of steps used = 8, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6, 2026, 2007, 7239, 27, 25, 7293, 2009}
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.
| \(\displaystyle \int \frac {2 x^{13}+30 x^{12}+148 x^{11}+290 x^{10}-2 e^4 x^9+200 x^9+96 x^8+1280 x^7+5600 x^6+7200 x^5-4000 x^4-2048 x^3-30720 x^2+e^2 \left (-14 x^{10}-60 x^9-50 x^8-160 x^6-1440 x^5-3200 x^4\right )+e^8 \left (-2 x^{12}-32 x^{11}-170 x^{10}-350 x^9-250 x^8-128 x^7-1920 x^6-9600 x^5-16000 x^4+e^2 \left (-2 x^{10}-10 x^9\right )\right )+\left (2 x^{12}+32 x^{11}+170 x^{10}+350 x^9+250 x^8+128 x^7+1920 x^6+9600 x^5+16000 x^4+e^2 \left (2 x^{10}+10 x^9\right )\right ) \log (x)-153600 x-256000}{x^{12}+15 x^{11}+75 x^{10}+125 x^9} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {2 x^{13}+30 x^{12}+148 x^{11}+290 x^{10}+\left (200-2 e^4\right ) x^9+96 x^8+1280 x^7+5600 x^6+7200 x^5-4000 x^4-2048 x^3-30720 x^2+e^2 \left (-14 x^{10}-60 x^9-50 x^8-160 x^6-1440 x^5-3200 x^4\right )+e^8 \left (-2 x^{12}-32 x^{11}-170 x^{10}-350 x^9-250 x^8-128 x^7-1920 x^6-9600 x^5-16000 x^4+e^2 \left (-2 x^{10}-10 x^9\right )\right )+\left (2 x^{12}+32 x^{11}+170 x^{10}+350 x^9+250 x^8+128 x^7+1920 x^6+9600 x^5+16000 x^4+e^2 \left (2 x^{10}+10 x^9\right )\right ) \log (x)-153600 x-256000}{x^{12}+15 x^{11}+75 x^{10}+125 x^9}dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {2 x^{13}+30 x^{12}+148 x^{11}+290 x^{10}+\left (200-2 e^4\right ) x^9+96 x^8+1280 x^7+5600 x^6+7200 x^5-4000 x^4-2048 x^3-30720 x^2+e^2 \left (-14 x^{10}-60 x^9-50 x^8-160 x^6-1440 x^5-3200 x^4\right )+e^8 \left (-2 x^{12}-32 x^{11}-170 x^{10}-350 x^9-250 x^8-128 x^7-1920 x^6-9600 x^5-16000 x^4+e^2 \left (-2 x^{10}-10 x^9\right )\right )+\left (2 x^{12}+32 x^{11}+170 x^{10}+350 x^9+250 x^8+128 x^7+1920 x^6+9600 x^5+16000 x^4+e^2 \left (2 x^{10}+10 x^9\right )\right ) \log (x)-153600 x-256000}{x^9 \left (x^3+15 x^2+75 x+125\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {2 x^{13}+30 x^{12}+148 x^{11}+290 x^{10}+\left (200-2 e^4\right ) x^9+96 x^8+1280 x^7+5600 x^6+7200 x^5-4000 x^4-2048 x^3-30720 x^2+e^2 \left (-14 x^{10}-60 x^9-50 x^8-160 x^6-1440 x^5-3200 x^4\right )+e^8 \left (-2 x^{12}-32 x^{11}-170 x^{10}-350 x^9-250 x^8-128 x^7-1920 x^6-9600 x^5-16000 x^4+e^2 \left (-2 x^{10}-10 x^9\right )\right )+\left (2 x^{12}+32 x^{11}+170 x^{10}+350 x^9+250 x^8+128 x^7+1920 x^6+9600 x^5+16000 x^4+e^2 \left (2 x^{10}+10 x^9\right )\right ) \log (x)-153600 x-256000}{x^9 (x+5)^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (x^7+11 x^6+\left (30+e^2\right ) x^5+25 x^4+64 x^2+640 x+1600\right ) \left (x^6-\left (e^8-4\right ) x^5-\left (e^2+5 e^8\right ) x^4+(x+5) x^4 \log (x)-16 x-80\right )}{x^9 (x+5)^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (x^7+11 x^6+\left (30+e^2\right ) x^5+25 x^4+64 x^2+640 x+1600\right ) \left (-x^6-\left (4-e^8\right ) x^5-(x+5) \log (x) x^4+e^2 \left (1+5 e^6\right ) x^4+16 x+80\right )}{x^9 (x+5)^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (x^7+11 x^6+\left (30+e^2\right ) x^5+25 x^4+64 x^2+640 x+1600\right ) \left (-x^6-\left (4-e^8\right ) x^5-(x+5) \log (x) x^4+e^2 \left (1+5 e^6\right ) x^4+16 x+80\right )}{x^9 (x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\log (x) \left (-x^7-11 x^6-30 \left (1+\frac {e^2}{30}\right ) x^5-25 x^4-64 x^2-640 x-1600\right )}{x^5 (x+5)^2}+\frac {-x^7-11 x^6-30 \left (1+\frac {e^2}{30}\right ) x^5-25 x^4-64 x^2-640 x-1600}{x^3 (x+5)^3}+\frac {\left (2-e^4\right ) \left (2+e^4\right ) \left (-x^7-11 x^6-30 \left (1+\frac {e^2}{30}\right ) x^5-25 x^4-64 x^2-640 x-1600\right )}{x^4 (x+5)^3}+\frac {e^2 \left (1+5 e^6\right ) \left (x^7+11 x^6+30 \left (1+\frac {e^2}{30}\right ) x^5+25 x^4+64 x^2+640 x+1600\right )}{x^5 (x+5)^3}+\frac {16 \left (x^7+11 x^6+30 \left (1+\frac {e^2}{30}\right ) x^5+25 x^4+64 x^2+640 x+1600\right )}{x^8 (x+5)^3}+\frac {80 \left (x^7+11 x^6+30 \left (1+\frac {e^2}{30}\right ) x^5+25 x^4+64 x^2+640 x+1600\right )}{x^9 (x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (-\frac {128}{x^8}-\frac {16 e^2 \left (1+5 e^6\right )}{5 x^4}+\frac {16 \log (x)}{x^4}+\frac {64 \left (4-e^8\right )}{15 x^3}+\frac {64 e^2 \left (1+5 e^6\right )}{75 x^3}-\frac {16 \left (1811+125 e^2\right )}{9375 x^3}-\frac {11024}{9375 x^3}-\frac {x^2}{2}-\frac {32 \left (4-e^8\right )}{25 x^2}-\frac {32 e^2 \left (1+5 e^6\right )}{125 x^2}-\frac {8 \left (1811+125 e^2\right )}{15625 x^2}+\frac {24 \left (187+125 e^2\right )}{15625 x^2}+\frac {32}{5 x^2}-\left (4-e^8\right ) x+5 x-\frac {\left (5-e^2\right ) \left (2-e^4\right ) \left (2+e^4\right )}{x+5}+\frac {6266 \left (5-e^2\right )}{625 (x+5)}+\frac {e^2 \left (5-e^2\right ) \left (1+5 e^6\right )}{2 (x+5)^2}+\frac {5 \left (5-e^2\right ) \left (2-e^4\right ) \left (2+e^4\right )}{2 (x+5)^2}-\frac {25 \left (5-e^2\right )}{2 (x+5)^2}+\frac {64 \left (4-e^8\right )}{125 x}+\frac {64 e^2 \left (1+5 e^6\right )}{625 x}+\frac {48 \left (187+125 e^2\right )}{78125 x}+\frac {96 \left (219-125 e^2\right )}{78125 x}-\frac {64}{25 x}-\frac {\log ^2(x)}{2}+\frac {\left (5-e^2\right ) x \log (x)}{5 (x+5)}-x \log (x)+\frac {64}{625} \left (4-e^8\right ) \log (x)+\frac {689 e^2 \left (1+5 e^6\right ) \log (x)}{3125}-\frac {96 \left (219-125 e^2\right ) \log (x)}{390625}+\frac {32 \left (1907-625 e^2\right ) \log (x)}{390625}-\frac {64 \log (x)}{125}+\frac {2436}{625} \left (4-e^8\right ) \log (x+5)+\frac {2436 e^2 \left (1+5 e^6\right ) \log (x+5)}{3125}-\frac {1}{125} \left (1811+125 e^2\right ) \log (x+5)-\frac {1}{5} \left (5-e^2\right ) \log (x+5)+\frac {96 \left (219-125 e^2\right ) \log (x+5)}{390625}-\frac {32 \left (1907-625 e^2\right ) \log (x+5)}{390625}\right )\) |
Input:
Int[(-256000 - 153600*x - 30720*x^2 - 2048*x^3 - 4000*x^4 + 7200*x^5 + 560 0*x^6 + 1280*x^7 + 96*x^8 + 200*x^9 - 2*E^4*x^9 + 290*x^10 + 148*x^11 + 30 *x^12 + 2*x^13 + E^2*(-3200*x^4 - 1440*x^5 - 160*x^6 - 50*x^8 - 60*x^9 - 1 4*x^10) + E^8*(-16000*x^4 - 9600*x^5 - 1920*x^6 - 128*x^7 - 250*x^8 - 350* x^9 - 170*x^10 - 32*x^11 - 2*x^12 + E^2*(-10*x^9 - 2*x^10)) + (16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^10 + 32*x^11 + 2*x^12 + E^2*(10*x^9 + 2*x^10))*Log[x])/(125*x^9 + 75*x^10 + 15*x^11 + x^1 2),x]
Output:
-2*(-128/x^8 - (16*E^2*(1 + 5*E^6))/(5*x^4) - 11024/(9375*x^3) - (16*(1811 + 125*E^2))/(9375*x^3) + (64*E^2*(1 + 5*E^6))/(75*x^3) + (64*(4 - E^8))/( 15*x^3) + 32/(5*x^2) + (24*(187 + 125*E^2))/(15625*x^2) - (8*(1811 + 125*E ^2))/(15625*x^2) - (32*E^2*(1 + 5*E^6))/(125*x^2) - (32*(4 - E^8))/(25*x^2 ) - 64/(25*x) + (96*(219 - 125*E^2))/(78125*x) + (48*(187 + 125*E^2))/(781 25*x) + (64*E^2*(1 + 5*E^6))/(625*x) + (64*(4 - E^8))/(125*x) + 5*x - (4 - E^8)*x - x^2/2 - (25*(5 - E^2))/(2*(5 + x)^2) + (5*(5 - E^2)*(2 - E^4)*(2 + E^4))/(2*(5 + x)^2) + (E^2*(5 - E^2)*(1 + 5*E^6))/(2*(5 + x)^2) + (6266 *(5 - E^2))/(625*(5 + x)) - ((5 - E^2)*(2 - E^4)*(2 + E^4))/(5 + x) - (64* Log[x])/125 + (32*(1907 - 625*E^2)*Log[x])/390625 - (96*(219 - 125*E^2)*Lo g[x])/390625 + (689*E^2*(1 + 5*E^6)*Log[x])/3125 + (64*(4 - E^8)*Log[x])/6 25 + (16*Log[x])/x^4 - x*Log[x] + ((5 - E^2)*x*Log[x])/(5*(5 + x)) - Log[x ]^2/2 - (32*(1907 - 625*E^2)*Log[5 + x])/390625 + (96*(219 - 125*E^2)*Log[ 5 + x])/390625 - ((5 - E^2)*Log[5 + x])/5 - ((1811 + 125*E^2)*Log[5 + x])/ 125 + (2436*E^2*(1 + 5*E^6)*Log[5 + x])/3125 + (2436*(4 - E^8)*Log[5 + x]) /625)
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_)*(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[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(164\) vs. \(2(29)=58\).
Time = 80.00 (sec) , antiderivative size = 165, normalized size of antiderivative = 5.69
| method | result | size |
| default | \(x^{2}-2 \,{\mathrm e}^{8} x +\frac {256}{x^{8}}+\frac {-\frac {128}{5}-\frac {32 \,{\mathrm e}^{2}}{25}}{x^{3}}+\frac {-\frac {32}{25}+\frac {32 \,{\mathrm e}^{2}}{125}}{x^{2}}+\frac {\frac {32}{125}-\frac {32 \,{\mathrm e}^{2}}{625}}{x}-2 \left ({\mathrm e}^{8}+\frac {{\mathrm e}^{2}}{5}\right ) \ln \left (x \right )+\frac {16+64 \,{\mathrm e}^{8}+\frac {64 \,{\mathrm e}^{2}}{5}}{2 x^{4}}+\frac {25+{\mathrm e}^{4}-10 \,{\mathrm e}^{2}}{\left (5+x \right )^{2}}-2 \left (1-\frac {{\mathrm e}^{2}}{5}\right ) \ln \left (5+x \right )+\frac {-\frac {7532}{125}+\frac {7532 \,{\mathrm e}^{2}}{625}+2 \,{\mathrm e}^{10}-10 \,{\mathrm e}^{8}}{5+x}+2 x \ln \left (x \right )-2 x +\ln \left (x \right )^{2}-\frac {32 \ln \left (x \right )}{x^{4}}-\frac {8}{x^{4}}+2 \left ({\mathrm e}^{2}-5\right ) \left (-\frac {\ln \left (5+x \right )}{5}+\frac {x \ln \left (x \right )}{25+5 x}\right )\) | \(165\) |
| parts | \(x^{2}-2 \,{\mathrm e}^{8} x +\frac {256}{x^{8}}+\frac {-\frac {128}{5}-\frac {32 \,{\mathrm e}^{2}}{25}}{x^{3}}+\frac {-\frac {32}{25}+\frac {32 \,{\mathrm e}^{2}}{125}}{x^{2}}+\frac {\frac {32}{125}-\frac {32 \,{\mathrm e}^{2}}{625}}{x}-2 \left ({\mathrm e}^{8}+\frac {{\mathrm e}^{2}}{5}\right ) \ln \left (x \right )+\frac {16+64 \,{\mathrm e}^{8}+\frac {64 \,{\mathrm e}^{2}}{5}}{2 x^{4}}+\frac {25+{\mathrm e}^{4}-10 \,{\mathrm e}^{2}}{\left (5+x \right )^{2}}-2 \left (1-\frac {{\mathrm e}^{2}}{5}\right ) \ln \left (5+x \right )+\frac {-\frac {7532}{125}+\frac {7532 \,{\mathrm e}^{2}}{625}+2 \,{\mathrm e}^{10}-10 \,{\mathrm e}^{8}}{5+x}+2 x \ln \left (x \right )-2 x +\ln \left (x \right )^{2}-\frac {32 \ln \left (x \right )}{x^{4}}-\frac {8}{x^{4}}+2 \left ({\mathrm e}^{2}-5\right ) \left (-\frac {\ln \left (5+x \right )}{5}+\frac {x \ln \left (x \right )}{25+5 x}\right )\) | \(165\) |
| risch | \(\ln \left (x \right )^{2}-\frac {2 \left (-x^{6}+x^{4} {\mathrm e}^{2}-5 x^{5}-5 x^{4}+16 x +80\right ) \ln \left (x \right )}{x^{4} \left (5+x \right )}+\frac {6400+2560 x -2 \,{\mathrm e}^{8} x^{11}-20 \,{\mathrm e}^{8} x^{10}-60 \,{\mathrm e}^{8} x^{9}+160 x^{4} {\mathrm e}^{2}+32 \,{\mathrm e}^{2} x^{5}+8 x^{11}+5 x^{10}+x^{12}-275 x^{8}-110 x^{9}-288 x^{6}-32 x^{7}+256 x^{2}-640 x^{5}+10 \,{\mathrm e}^{10} x^{8}+2 \,{\mathrm e}^{10} x^{9}+800 \,{\mathrm e}^{8} x^{4}-50 \ln \left (x \right ) x^{8}-2 \ln \left (x \right ) x^{10}-20 \ln \left (x \right ) x^{9}+32 \,{\mathrm e}^{8} x^{6}+50 \,{\mathrm e}^{2} x^{8}+320 \,{\mathrm e}^{8} x^{5}-2 \,{\mathrm e}^{8} \ln \left (x \right ) x^{10}-20 \,{\mathrm e}^{8} \ln \left (x \right ) x^{9}-50 \,{\mathrm e}^{8} \ln \left (x \right ) x^{8}+{\mathrm e}^{4} x^{8}-50 \,{\mathrm e}^{8} x^{8}+12 \,{\mathrm e}^{2} x^{9}}{\left (5+x \right )^{2} x^{8}}\) | \(272\) |
| parallelrisch | \(\frac {6400+2560 x -2 \,{\mathrm e}^{8} x^{11}+140 \,{\mathrm e}^{8} x^{9}-320 x^{5} \ln \left (x \right )-800 x^{4} \ln \left (x \right )+25 x^{8} \ln \left (x \right )^{2}+160 x^{4} {\mathrm e}^{2}+32 \,{\mathrm e}^{2} x^{5}+8 x^{11}+x^{12}-400 x^{8}-160 x^{9}-288 x^{6}-32 x^{7}+256 x^{2}-640 x^{5}+\ln \left (x \right )^{2} x^{10}+10 \ln \left (x \right )^{2} x^{9}+800 \,{\mathrm e}^{8} x^{4}-32 \ln \left (x \right ) x^{6}+2 \ln \left (x \right ) x^{11}+18 \ln \left (x \right ) x^{10}+40 \ln \left (x \right ) x^{9}-10 \,{\mathrm e}^{2} \ln \left (x \right ) x^{8}-2 \,{\mathrm e}^{2} \ln \left (x \right ) x^{9}+32 \,{\mathrm e}^{8} x^{6}+50 \,{\mathrm e}^{2} x^{8}+320 \,{\mathrm e}^{8} x^{5}-2 \,{\mathrm e}^{8} \ln \left (x \right ) x^{10}-20 \,{\mathrm e}^{8} \ln \left (x \right ) x^{9}-50 \,{\mathrm e}^{8} \ln \left (x \right ) x^{8}+{\mathrm e}^{4} x^{8}+10 \,{\mathrm e}^{2} {\mathrm e}^{8} x^{8}+2 \,{\mathrm e}^{2} {\mathrm e}^{8} x^{9}+450 \,{\mathrm e}^{8} x^{8}+12 \,{\mathrm e}^{2} x^{9}}{x^{8} \left (x^{2}+10 x +25\right )}\) | \(289\) |
Input:
int((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8+128*x ^7+1920*x^6+9600*x^5+16000*x^4)*ln(x)+((-2*x^10-10*x^9)*exp(2)-2*x^12-32*x ^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)*exp(4)^2 -2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)*exp(2)+ 2*x^13+30*x^12+148*x^11+290*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7200*x^5 -4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*x^10+125*x^ 9),x,method=_RETURNVERBOSE)
Output:
x^2-2*exp(8)*x+256/x^8+2/3*(-192/5-48/25*exp(2))/x^3+(-32/25+32/125*exp(2) )/x^2+2*(16/125-16/625*exp(2))/x-2*(exp(8)+1/5*exp(2))*ln(x)+1/2*(16+64*ex p(8)+64/5*exp(2))/x^4+(25+exp(4)-10*exp(2))/(5+x)^2-2*(1-1/5*exp(2))*ln(5+ x)+2*(-3766/125+3766/625*exp(2)+exp(10)-5*exp(8))/(5+x)+2*x*ln(x)-2*x+ln(x )^2-32/x^4*ln(x)-8/x^4+2*(exp(2)-5)*(-1/5*ln(5+x)+1/5*ln(x)*x/(5+x))
Leaf count of result is larger than twice the leaf count of optimal. 230 vs. \(2 (26) = 52\).
Time = 0.10 (sec) , antiderivative size = 230, normalized size of antiderivative = 7.93 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=\frac {x^{12} + 8 \, x^{11} + 5 \, x^{10} - 110 \, x^{9} + x^{8} e^{4} - 275 \, x^{8} - 32 \, x^{7} - 288 \, x^{6} - 640 \, x^{5} + {\left (x^{10} + 10 \, x^{9} + 25 \, x^{8}\right )} \log \left (x\right )^{2} + 256 \, x^{2} + 2 \, {\left (x^{9} + 5 \, x^{8}\right )} e^{10} - 2 \, {\left (x^{11} + 10 \, x^{10} + 30 \, x^{9} + 25 \, x^{8} - 16 \, x^{6} - 160 \, x^{5} - 400 \, x^{4}\right )} e^{8} + 2 \, {\left (6 \, x^{9} + 25 \, x^{8} + 16 \, x^{5} + 80 \, x^{4}\right )} e^{2} + 2 \, {\left (x^{11} + 9 \, x^{10} + 20 \, x^{9} - 16 \, x^{6} - 160 \, x^{5} - 400 \, x^{4} - {\left (x^{10} + 10 \, x^{9} + 25 \, x^{8}\right )} e^{8} - {\left (x^{9} + 5 \, x^{8}\right )} e^{2}\right )} \log \left (x\right ) + 2560 \, x + 6400}{x^{10} + 10 \, x^{9} + 25 \, x^{8}} \] Input:
integrate((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8 +128*x^7+1920*x^6+9600*x^5+16000*x^4)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^ 12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)*e xp(4)^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)* exp(2)+2*x^13+30*x^12+148*x^11+290*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7 200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*x^10 +125*x^9),x, algorithm="fricas")
Output:
(x^12 + 8*x^11 + 5*x^10 - 110*x^9 + x^8*e^4 - 275*x^8 - 32*x^7 - 288*x^6 - 640*x^5 + (x^10 + 10*x^9 + 25*x^8)*log(x)^2 + 256*x^2 + 2*(x^9 + 5*x^8)*e ^10 - 2*(x^11 + 10*x^10 + 30*x^9 + 25*x^8 - 16*x^6 - 160*x^5 - 400*x^4)*e^ 8 + 2*(6*x^9 + 25*x^8 + 16*x^5 + 80*x^4)*e^2 + 2*(x^11 + 9*x^10 + 20*x^9 - 16*x^6 - 160*x^5 - 400*x^4 - (x^10 + 10*x^9 + 25*x^8)*e^8 - (x^9 + 5*x^8) *e^2)*log(x) + 2560*x + 6400)/(x^10 + 10*x^9 + 25*x^8)
Leaf count of result is larger than twice the leaf count of optimal. 180 vs. \(2 (22) = 44\).
Time = 27.26 (sec) , antiderivative size = 180, normalized size of antiderivative = 6.21 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=x^{2} + x \left (- 2 e^{8} - 2\right ) + \log {\left (x \right )}^{2} - 2 \cdot \left (1 + e^{8}\right ) \log {\left (x \right )} + \frac {x^{9} \left (- 10 e^{8} - 60 + 12 e^{2} + 2 e^{10}\right ) + x^{8} \left (- 50 e^{8} - 275 + e^{4} + 50 e^{2} + 10 e^{10}\right ) - 32 x^{7} + x^{6} \left (-288 + 32 e^{8}\right ) + x^{5} \left (-640 + 32 e^{2} + 320 e^{8}\right ) + x^{4} \cdot \left (160 e^{2} + 800 e^{8}\right ) + 256 x^{2} + 2560 x + 6400}{x^{10} + 10 x^{9} + 25 x^{8}} + \frac {\left (2 x^{6} + 10 x^{5} - 2 x^{4} e^{2} + 10 x^{4} - 32 x - 160\right ) \log {\left (x \right )}}{x^{5} + 5 x^{4}} \] Input:
integrate((((2*x**10+10*x**9)*exp(2)+2*x**12+32*x**11+170*x**10+350*x**9+2 50*x**8+128*x**7+1920*x**6+9600*x**5+16000*x**4)*ln(x)+((-2*x**10-10*x**9) *exp(2)-2*x**12-32*x**11-170*x**10-350*x**9-250*x**8-128*x**7-1920*x**6-96 00*x**5-16000*x**4)*exp(4)**2-2*x**9*exp(2)**2+(-14*x**10-60*x**9-50*x**8- 160*x**6-1440*x**5-3200*x**4)*exp(2)+2*x**13+30*x**12+148*x**11+290*x**10+ 200*x**9+96*x**8+1280*x**7+5600*x**6+7200*x**5-4000*x**4-2048*x**3-30720*x **2-153600*x-256000)/(x**12+15*x**11+75*x**10+125*x**9),x)
Output:
x**2 + x*(-2*exp(8) - 2) + log(x)**2 - 2*(1 + exp(8))*log(x) + (x**9*(-10* exp(8) - 60 + 12*exp(2) + 2*exp(10)) + x**8*(-50*exp(8) - 275 + exp(4) + 5 0*exp(2) + 10*exp(10)) - 32*x**7 + x**6*(-288 + 32*exp(8)) + x**5*(-640 + 32*exp(2) + 320*exp(8)) + x**4*(160*exp(2) + 800*exp(8)) + 256*x**2 + 2560 *x + 6400)/(x**10 + 10*x**9 + 25*x**8) + (2*x**6 + 10*x**5 - 2*x**4*exp(2) + 10*x**4 - 32*x - 160)*log(x)/(x**5 + 5*x**4)
Leaf count of result is larger than twice the leaf count of optimal. 1137 vs. \(2 (26) = 52\).
Time = 0.11 (sec) , antiderivative size = 1137, normalized size of antiderivative = 39.21 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=\text {Too large to display} \] Input:
integrate((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8 +128*x^7+1920*x^6+9600*x^5+16000*x^4)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^ 12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)*e xp(4)^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)* exp(2)+2*x^13+30*x^12+148*x^11+290*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7 200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*x^10 +125*x^9),x, algorithm="maxima")
Output:
x^2 - (2*x - 25*(6*x + 25)/(x^2 + 10*x + 25) - 30*log(x + 5))*e^8 - 32/125 *(5*(12*x^5 + 90*x^4 + 100*x^3 - 125*x^2 + 250*x - 625)/(x^6 + 10*x^5 + 25 *x^4) - 12*log(x + 5) + 12*log(x))*e^8 + 64/125*(5*(12*x^4 + 90*x^3 + 100* x^2 - 125*x + 250)/(x^5 + 10*x^4 + 25*x^3) - 12*log(x + 5) + 12*log(x))*e^ 8 - 192/625*(5*(12*x^3 + 90*x^2 + 100*x - 125)/(x^4 + 10*x^3 + 25*x^2) - 1 2*log(x + 5) + 12*log(x))*e^8 + 64/625*(5*(6*x^2 + 45*x + 50)/(x^3 + 10*x^ 2 + 25*x) - 6*log(x + 5) + 6*log(x))*e^8 - 16*(5*(4*x + 15)/(x^2 + 10*x + 25) + 2*log(x + 5))*e^8 - (5*(2*x + 15)/(x^2 + 10*x + 25) - 2*log(x + 5) + 2*log(x))*e^8 - 32/625*(5*(12*x^5 + 90*x^4 + 100*x^3 - 125*x^2 + 250*x - 625)/(x^6 + 10*x^5 + 25*x^4) - 12*log(x + 5) + 12*log(x))*e^2 + 48/625*(5* (12*x^4 + 90*x^3 + 100*x^2 - 125*x + 250)/(x^5 + 10*x^4 + 25*x^3) - 12*log (x + 5) + 12*log(x))*e^2 - 16/625*(5*(12*x^3 + 90*x^2 + 100*x - 125)/(x^4 + 10*x^3 + 25*x^2) - 12*log(x + 5) + 12*log(x))*e^2 - 1/5*(5*(2*x + 15)/(x ^2 + 10*x + 25) - 2*log(x + 5) + 2*log(x))*e^2 - 2/5*(e^2 - 5)*log(x + 5) + (2*x + 5)*e^10/(x^2 + 10*x + 25) + 85*(2*x + 5)*e^8/(x^2 + 10*x + 25) + 7*(2*x + 5)*e^2/(x^2 + 10*x + 25) - 256/109375*(504*x^9 + 3780*x^8 + 4200* x^7 - 5250*x^6 + 10500*x^5 - 26250*x^4 + 75000*x^3 - 234375*x^2 + 781250*x - 2734375)/(x^10 + 10*x^9 + 25*x^8) + 3072/546875*(504*x^8 + 3780*x^7 + 4 200*x^6 - 5250*x^5 + 10500*x^4 - 26250*x^3 + 75000*x^2 - 234375*x + 781250 )/(x^9 + 10*x^8 + 25*x^7) - 1024/78125*(168*x^7 + 1260*x^6 + 1400*x^5 -...
\[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=\int { \frac {2 \, {\left (x^{13} + 15 \, x^{12} + 74 \, x^{11} + 145 \, x^{10} - x^{9} e^{4} + 100 \, x^{9} + 48 \, x^{8} + 640 \, x^{7} + 2800 \, x^{6} + 3600 \, x^{5} - 2000 \, x^{4} - 1024 \, x^{3} - 15360 \, x^{2} - {\left (x^{12} + 16 \, x^{11} + 85 \, x^{10} + 175 \, x^{9} + 125 \, x^{8} + 64 \, x^{7} + 960 \, x^{6} + 4800 \, x^{5} + 8000 \, x^{4} + {\left (x^{10} + 5 \, x^{9}\right )} e^{2}\right )} e^{8} - {\left (7 \, x^{10} + 30 \, x^{9} + 25 \, x^{8} + 80 \, x^{6} + 720 \, x^{5} + 1600 \, x^{4}\right )} e^{2} + {\left (x^{12} + 16 \, x^{11} + 85 \, x^{10} + 175 \, x^{9} + 125 \, x^{8} + 64 \, x^{7} + 960 \, x^{6} + 4800 \, x^{5} + 8000 \, x^{4} + {\left (x^{10} + 5 \, x^{9}\right )} e^{2}\right )} \log \left (x\right ) - 76800 \, x - 128000\right )}}{x^{12} + 15 \, x^{11} + 75 \, x^{10} + 125 \, x^{9}} \,d x } \] Input:
integrate((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8 +128*x^7+1920*x^6+9600*x^5+16000*x^4)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^ 12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)*e xp(4)^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)* exp(2)+2*x^13+30*x^12+148*x^11+290*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7 200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*x^10 +125*x^9),x, algorithm="giac")
Output:
integrate(2*(x^13 + 15*x^12 + 74*x^11 + 145*x^10 - x^9*e^4 + 100*x^9 + 48* x^8 + 640*x^7 + 2800*x^6 + 3600*x^5 - 2000*x^4 - 1024*x^3 - 15360*x^2 - (x ^12 + 16*x^11 + 85*x^10 + 175*x^9 + 125*x^8 + 64*x^7 + 960*x^6 + 4800*x^5 + 8000*x^4 + (x^10 + 5*x^9)*e^2)*e^8 - (7*x^10 + 30*x^9 + 25*x^8 + 80*x^6 + 720*x^5 + 1600*x^4)*e^2 + (x^12 + 16*x^11 + 85*x^10 + 175*x^9 + 125*x^8 + 64*x^7 + 960*x^6 + 4800*x^5 + 8000*x^4 + (x^10 + 5*x^9)*e^2)*log(x) - 76 800*x - 128000)/(x^12 + 15*x^11 + 75*x^10 + 125*x^9), x)
Time = 7.59 (sec) , antiderivative size = 178, normalized size of antiderivative = 6.14 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx={\ln \left (x\right )}^2-\ln \left (x\right )\,\left (2\,{\mathrm {e}}^8-\frac {5}{3}\right )+\frac {\left (36\,{\mathrm {e}}^2-30\,{\mathrm {e}}^8+6\,{\mathrm {e}}^{10}-180\right )\,x^9+\left (150\,{\mathrm {e}}^2+3\,{\mathrm {e}}^4-150\,{\mathrm {e}}^8+30\,{\mathrm {e}}^{10}-825\right )\,x^8-96\,x^7+\left (96\,{\mathrm {e}}^8-864\right )\,x^6+\left (96\,{\mathrm {e}}^2+960\,{\mathrm {e}}^8-1920\right )\,x^5+\left (480\,{\mathrm {e}}^2+2400\,{\mathrm {e}}^8\right )\,x^4+768\,x^2+7680\,x+19200}{3\,x^{10}+30\,x^9+75\,x^8}+x^2-x\,\left (2\,{\mathrm {e}}^8+2\right )-\frac {\ln \left (x\right )\,\left (-2\,x^6-\frac {19\,x^5}{3}+\left (2\,{\mathrm {e}}^2+\frac {25}{3}\right )\,x^4+32\,x+160\right )}{x^5+5\,x^4} \] Input:
int((log(x)*(exp(2)*(10*x^9 + 2*x^10) + 16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^10 + 32*x^11 + 2*x^12) - 153600*x - ex p(2)*(3200*x^4 + 1440*x^5 + 160*x^6 + 50*x^8 + 60*x^9 + 14*x^10) - 2*x^9*e xp(4) - exp(8)*(exp(2)*(10*x^9 + 2*x^10) + 16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^10 + 32*x^11 + 2*x^12) - 30720*x^2 - 2048*x^3 - 4000*x^4 + 7200*x^5 + 5600*x^6 + 1280*x^7 + 96*x^8 + 200*x^9 + 290*x^10 + 148*x^11 + 30*x^12 + 2*x^13 - 256000)/(125*x^9 + 75*x^10 + 15 *x^11 + x^12),x)
Output:
log(x)^2 - log(x)*(2*exp(8) - 5/3) + (7680*x + x^4*(480*exp(2) + 2400*exp( 8)) + x^5*(96*exp(2) + 960*exp(8) - 1920) + x^6*(96*exp(8) - 864) + x^8*(1 50*exp(2) + 3*exp(4) - 150*exp(8) + 30*exp(10) - 825) + 768*x^2 - 96*x^7 + x^9*(36*exp(2) - 30*exp(8) + 6*exp(10) - 180) + 19200)/(75*x^8 + 30*x^9 + 3*x^10) + x^2 - x*(2*exp(8) + 2) - (log(x)*(32*x + x^4*(2*exp(2) + 25/3) - (19*x^5)/3 - 2*x^6 + 160))/(5*x^4 + x^5)
Time = 0.16 (sec) , antiderivative size = 288, normalized size of antiderivative = 9.93 \[ \int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx=\frac {32000-10 \,\mathrm {log}\left (x \right ) e^{8} x^{10}-100 \,\mathrm {log}\left (x \right ) e^{8} x^{9}-250 \,\mathrm {log}\left (x \right ) e^{8} x^{8}-10 \,\mathrm {log}\left (x \right ) e^{2} x^{9}-50 \,\mathrm {log}\left (x \right ) e^{2} x^{8}+12800 x +55 x^{10}+160 e^{2} x^{5}-4000 \,\mathrm {log}\left (x \right ) x^{4}+1280 x^{2}+5 x^{12}-3200 x^{5}-160 x^{7}+4000 e^{8} x^{4}-625 x^{8}-1440 x^{6}-1600 \,\mathrm {log}\left (x \right ) x^{5}-250 x^{9}+800 e^{2} x^{4}+40 x^{11}-e^{10} x^{10}+5 \mathrm {log}\left (x \right )^{2} x^{10}+50 \mathrm {log}\left (x \right )^{2} x^{9}+125 \mathrm {log}\left (x \right )^{2} x^{8}+10 \,\mathrm {log}\left (x \right ) x^{11}+90 \,\mathrm {log}\left (x \right ) x^{10}+200 \,\mathrm {log}\left (x \right ) x^{9}+25 e^{10} x^{8}-10 e^{8} x^{11}-70 e^{8} x^{10}+500 e^{8} x^{8}+160 e^{8} x^{6}+1600 e^{8} x^{5}+5 e^{4} x^{8}-6 e^{2} x^{10}+100 e^{2} x^{8}-160 \,\mathrm {log}\left (x \right ) x^{6}}{5 x^{8} \left (x^{2}+10 x +25\right )} \] Input:
int((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8+128*x ^7+1920*x^6+9600*x^5+16000*x^4)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^12-32* x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)*exp(4)^ 2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)*exp(2) +2*x^13+30*x^12+148*x^11+290*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7200*x^ 5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*x^10+125*x ^9),x)
Output:
(5*log(x)**2*x**10 + 50*log(x)**2*x**9 + 125*log(x)**2*x**8 - 10*log(x)*e* *8*x**10 - 100*log(x)*e**8*x**9 - 250*log(x)*e**8*x**8 - 10*log(x)*e**2*x* *9 - 50*log(x)*e**2*x**8 + 10*log(x)*x**11 + 90*log(x)*x**10 + 200*log(x)* x**9 - 160*log(x)*x**6 - 1600*log(x)*x**5 - 4000*log(x)*x**4 - e**10*x**10 + 25*e**10*x**8 - 10*e**8*x**11 - 70*e**8*x**10 + 500*e**8*x**8 + 160*e** 8*x**6 + 1600*e**8*x**5 + 4000*e**8*x**4 + 5*e**4*x**8 - 6*e**2*x**10 + 10 0*e**2*x**8 + 160*e**2*x**5 + 800*e**2*x**4 + 5*x**12 + 40*x**11 + 55*x**1 0 - 250*x**9 - 625*x**8 - 160*x**7 - 1440*x**6 - 3200*x**5 + 1280*x**2 + 1 2800*x + 32000)/(5*x**8*(x**2 + 10*x + 25))