Integrand size = 533, antiderivative size = 26 \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=\left (2-\frac {(-5+x)^2}{\log ^2\left (\frac {1}{4} (x+\log (5+x))^2\right )}\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(26)=52\).
Time = 0.25 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.58 \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=8 \left (\frac {(-5+x)^8}{8 \log ^8\left (\frac {1}{4} (x+\log (5+x))^2\right )}-\frac {(-5+x)^6}{\log ^6\left (\frac {1}{4} (x+\log (5+x))^2\right )}+\frac {3 (-5+x)^4}{\log ^4\left (\frac {1}{4} (x+\log (5+x))^2\right )}-\frac {4 (-5+x)^2}{\log ^2\left (\frac {1}{4} (x+\log (5+x))^2\right )}\right ) \]
Integrate[(-37500000 + 53750000*x - 32000000*x^2 + 9800000*x^3 - 1400000*x ^4 - 28000*x^5 + 44800*x^6 - 7360*x^7 + 544*x^8 - 16*x^9 + (-3125000*x + 3 750000*x^2 - 1750000*x^3 + 350000*x^4 - 14000*x^6 + 2800*x^7 - 240*x^8 + 8 *x^9 + (-3125000 + 3750000*x - 1750000*x^2 + 350000*x^3 - 14000*x^5 + 2800 *x^6 - 240*x^7 + 8*x^8)*Log[5 + x])*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x] ^2)/4] + (9000000 - 9300000*x + 3600000*x^2 - 540000*x^3 - 24000*x^4 + 187 20*x^5 - 2304*x^6 + 96*x^7)*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^2 + (750000*x - 600000*x^2 + 150000*x^3 - 6000*x^5 + 960*x^6 - 48*x^7 + (75 0000 - 600000*x + 150000*x^2 - 6000*x^4 + 960*x^5 - 48*x^6)*Log[5 + x])*Lo g[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^3 + (-720000 + 456000*x - 76800 *x^2 - 5760*x^3 + 2688*x^4 - 192*x^5)*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^4 + (-60000*x + 24000*x^2 - 960*x^4 + 96*x^5 + (-60000 + 24000*x - 960*x^3 + 96*x^4)*Log[5 + x])*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/ 4]^5 + (19200 - 4480*x - 512*x^2 + 128*x^3)*Log[(x^2 + 2*x*Log[5 + x] + Lo g[5 + x]^2)/4]^6 + (1600*x - 64*x^3 + (1600 - 64*x^2)*Log[5 + x])*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^7)/((5*x + x^2 + (5 + x)*Log[5 + x])* Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^9),x]
8*((-5 + x)^8/(8*Log[(x + Log[5 + x])^2/4]^8) - (-5 + x)^6/Log[(x + Log[5 + x])^2/4]^6 + (3*(-5 + x)^4)/Log[(x + Log[5 + x])^2/4]^4 - (4*(-5 + x)^2) /Log[(x + Log[5 + x])^2/4]^2)
Time = 4.31 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used = {7239, 27, 25, 7263, 17}
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.
| \(\displaystyle \int \frac {-16 x^9+544 x^8-7360 x^7+44800 x^6-28000 x^5-1400000 x^4+9800000 x^3-32000000 x^2+\left (-64 x^3+\left (1600-64 x^2\right ) \log (x+5)+1600 x\right ) \log ^7\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+\left (128 x^3-512 x^2-4480 x+19200\right ) \log ^6\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+\left (96 x^5-960 x^4+24000 x^2+\left (96 x^4-960 x^3+24000 x-60000\right ) \log (x+5)-60000 x\right ) \log ^5\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+\left (-192 x^5+2688 x^4-5760 x^3-76800 x^2+456000 x-720000\right ) \log ^4\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+\left (96 x^7-2304 x^6+18720 x^5-24000 x^4-540000 x^3+3600000 x^2-9300000 x+9000000\right ) \log ^2\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+\left (-48 x^7+960 x^6-6000 x^5+150000 x^3-600000 x^2+\left (-48 x^6+960 x^5-6000 x^4+150000 x^2-600000 x+750000\right ) \log (x+5)+750000 x\right ) \log ^3\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+\left (8 x^9-240 x^8+2800 x^7-14000 x^6+350000 x^4-1750000 x^3+3750000 x^2+\left (8 x^8-240 x^7+2800 x^6-14000 x^5+350000 x^3-1750000 x^2+3750000 x-3125000\right ) \log (x+5)-3125000 x\right ) \log \left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )+53750000 x-37500000}{\left (x^2+5 x+(x+5) \log (x+5)\right ) \log ^9\left (\frac {1}{4} \left (x^2+\log ^2(x+5)+2 x \log (x+5)\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 (5-x) \left (2 \left (x^2+x-30\right )-(x+5) (x+\log (x+5)) \log \left (\frac {1}{4} (x+\log (x+5))^2\right )\right ) \left ((x-5)^2-2 \log ^2\left (\frac {1}{4} (x+\log (x+5))^2\right )\right )^3}{(x+5) (x+\log (x+5)) \log ^9\left (\frac {1}{4} (x+\log (x+5))^2\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 8 \int -\frac {(5-x) \left (2 \left (-x^2-x+30\right )+(x+5) (x+\log (x+5)) \log \left (\frac {1}{4} (x+\log (x+5))^2\right )\right ) \left ((x-5)^2-2 \log ^2\left (\frac {1}{4} (x+\log (x+5))^2\right )\right )^3}{(x+5) (x+\log (x+5)) \log ^9\left (\frac {1}{4} (x+\log (x+5))^2\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -8 \int \frac {(5-x) \left (2 \left (-x^2-x+30\right )+(x+5) (x+\log (x+5)) \log \left (\frac {1}{4} (x+\log (x+5))^2\right )\right ) \left ((x-5)^2-2 \log ^2\left (\frac {1}{4} (x+\log (x+5))^2\right )\right )^3}{(x+5) (x+\log (x+5)) \log ^9\left (\frac {1}{4} (x+\log (x+5))^2\right )}dx\) |
| \(\Big \downarrow \) 7263 |
| \(\displaystyle 4 \int \left (\frac {(5-x)^2}{\log ^2\left (\frac {1}{4} (x+\log (x+5))^2\right )}-2\right )^3d\frac {(5-x)^2}{\log ^2\left (\frac {1}{4} (x+\log (x+5))^2\right )}\) |
| \(\Big \downarrow \) 17 |
| \(\displaystyle \left (2-\frac {(5-x)^2}{\log ^2\left (\frac {1}{4} (x+\log (x+5))^2\right )}\right )^4\) |
Int[(-37500000 + 53750000*x - 32000000*x^2 + 9800000*x^3 - 1400000*x^4 - 2 8000*x^5 + 44800*x^6 - 7360*x^7 + 544*x^8 - 16*x^9 + (-3125000*x + 3750000 *x^2 - 1750000*x^3 + 350000*x^4 - 14000*x^6 + 2800*x^7 - 240*x^8 + 8*x^9 + (-3125000 + 3750000*x - 1750000*x^2 + 350000*x^3 - 14000*x^5 + 2800*x^6 - 240*x^7 + 8*x^8)*Log[5 + x])*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4] + (9000000 - 9300000*x + 3600000*x^2 - 540000*x^3 - 24000*x^4 + 18720*x^5 - 2304*x^6 + 96*x^7)*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^2 + (75 0000*x - 600000*x^2 + 150000*x^3 - 6000*x^5 + 960*x^6 - 48*x^7 + (750000 - 600000*x + 150000*x^2 - 6000*x^4 + 960*x^5 - 48*x^6)*Log[5 + x])*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^3 + (-720000 + 456000*x - 76800*x^2 - 5760*x^3 + 2688*x^4 - 192*x^5)*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/ 4]^4 + (-60000*x + 24000*x^2 - 960*x^4 + 96*x^5 + (-60000 + 24000*x - 960* x^3 + 96*x^4)*Log[5 + x])*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^5 + (19200 - 4480*x - 512*x^2 + 128*x^3)*Log[(x^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^6 + (1600*x - 64*x^3 + (1600 - 64*x^2)*Log[5 + x])*Log[(x^2 + 2*x *Log[5 + x] + Log[5 + x]^2)/4]^7)/((5*x + x^2 + (5 + x)*Log[5 + x])*Log[(x ^2 + 2*x*Log[5 + x] + Log[5 + x]^2)/4]^9),x]
3.29.79.3.1 Defintions of rubi rules used
Int[(c_.)*((a_.) + (b_.)*(x_))^(m_.), x_Symbol] :> Simp[c*((a + b*x)^(m + 1 )/(b*(m + 1))), x] /; FreeQ[{a, b, c, m}, x] && NeQ[m, -1]
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[(u_)*(v_)^(r_.)*((a_.)*(v_)^(p_.) + (b_.)*(w_)^(q_.))^(m_.), x_Symbol] :> With[{c = Simplify[u/(p*w*D[v, x] - q*v*D[w, x])]}, Simp[(-c)*q Subst[ Int[(a + b*x^q)^m, x], x, v^(m*p + r + 1)*w], x] /; FreeQ[c, x]] /; FreeQ[{ a, b, m, p, q, r}, x] && EqQ[p + q*(m*p + r + 1), 0] && IntegerQ[q] && Inte gerQ[m]
Leaf count of result is larger than twice the leaf count of optimal. \(486\) vs. \(2(24)=48\).
Time = 15.40 (sec) , antiderivative size = 487, normalized size of antiderivative = 18.73
| method | result | size |
| parallelrisch | \(\frac {3906250+3200 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{6} x +2400 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2} x^{5}-320 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{6} x^{2}-6250000 x -400 x^{7}+10 x^{8}+7000 x^{6}-70000 x^{5}+437500 x^{4}-1750000 x^{3}+4375000 x^{2}+200000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2} x^{3}-750000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2} x^{2}+1500000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2} x +240 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{4} x^{4}-80 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2} x^{6}-4800 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{4} x^{3}+36000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{4} x^{2}-30000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2} x^{4}-8000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{6}+150000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{4}-1250000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{2}-120000 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{4} x}{10 \ln \left (\frac {\ln \left (5+x \right )^{2}}{4}+\frac {x \ln \left (5+x \right )}{2}+\frac {x^{2}}{4}\right )^{8}}\) | \(487\) |
| risch | \(\text {Expression too large to display}\) | \(27279\) |
| default | \(\text {Expression too large to display}\) | \(28461\) |
int((((-64*x^2+1600)*ln(5+x)-64*x^3+1600*x)*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x) +1/4*x^2)^7+(128*x^3-512*x^2-4480*x+19200)*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+ 1/4*x^2)^6+((96*x^4-960*x^3+24000*x-60000)*ln(5+x)+96*x^5-960*x^4+24000*x^ 2-60000*x)*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^5+(-192*x^5+2688*x^4-57 60*x^3-76800*x^2+456000*x-720000)*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^ 4+((-48*x^6+960*x^5-6000*x^4+150000*x^2-600000*x+750000)*ln(5+x)-48*x^7+96 0*x^6-6000*x^5+150000*x^3-600000*x^2+750000*x)*ln(1/4*ln(5+x)^2+1/2*x*ln(5 +x)+1/4*x^2)^3+(96*x^7-2304*x^6+18720*x^5-24000*x^4-540000*x^3+3600000*x^2 -9300000*x+9000000)*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2+((8*x^8-240* x^7+2800*x^6-14000*x^5+350000*x^3-1750000*x^2+3750000*x-3125000)*ln(5+x)+8 *x^9-240*x^8+2800*x^7-14000*x^6+350000*x^4-1750000*x^3+3750000*x^2-3125000 *x)*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)-16*x^9+544*x^8-7360*x^7+44800* x^6-28000*x^5-1400000*x^4+9800000*x^3-32000000*x^2+53750000*x-37500000)/(( 5+x)*ln(5+x)+x^2+5*x)/ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^9,x,method=_ RETURNVERBOSE)
1/10*(3906250+3200*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^6*x+2400*ln(1/4 *ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2*x^5-320*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x) +1/4*x^2)^6*x^2-6250000*x-400*x^7+10*x^8+7000*x^6-70000*x^5+437500*x^4-175 0000*x^3+4375000*x^2+200000*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2*x^3- 750000*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2*x^2+1500000*ln(1/4*ln(5+x )^2+1/2*x*ln(5+x)+1/4*x^2)^2*x+240*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2) ^4*x^4-80*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2*x^6-4800*ln(1/4*ln(5+x )^2+1/2*x*ln(5+x)+1/4*x^2)^4*x^3+36000*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4* x^2)^4*x^2-30000*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2*x^4-8000*ln(1/4 *ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^6+150000*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+ 1/4*x^2)^4-1250000*ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^2-120000*ln(1/4 *ln(5+x)^2+1/2*x*ln(5+x)+1/4*x^2)^4*x)/ln(1/4*ln(5+x)^2+1/2*x*ln(5+x)+1/4* x^2)^8
Leaf count of result is larger than twice the leaf count of optimal. 195 vs. \(2 (23) = 46\).
Time = 0.27 (sec) , antiderivative size = 195, normalized size of antiderivative = 7.50 \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=\frac {x^{8} - 40 \, x^{7} - 32 \, {\left (x^{2} - 10 \, x + 25\right )} \log \left (\frac {1}{4} \, x^{2} + \frac {1}{2} \, x \log \left (x + 5\right ) + \frac {1}{4} \, \log \left (x + 5\right )^{2}\right )^{6} + 700 \, x^{6} - 7000 \, x^{5} + 24 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )} \log \left (\frac {1}{4} \, x^{2} + \frac {1}{2} \, x \log \left (x + 5\right ) + \frac {1}{4} \, \log \left (x + 5\right )^{2}\right )^{4} + 43750 \, x^{4} - 175000 \, x^{3} - 8 \, {\left (x^{6} - 30 \, x^{5} + 375 \, x^{4} - 2500 \, x^{3} + 9375 \, x^{2} - 18750 \, x + 15625\right )} \log \left (\frac {1}{4} \, x^{2} + \frac {1}{2} \, x \log \left (x + 5\right ) + \frac {1}{4} \, \log \left (x + 5\right )^{2}\right )^{2} + 437500 \, x^{2} - 625000 \, x + 390625}{\log \left (\frac {1}{4} \, x^{2} + \frac {1}{2} \, x \log \left (x + 5\right ) + \frac {1}{4} \, \log \left (x + 5\right )^{2}\right )^{8}} \]
integrate((((-64*x^2+1600)*log(5+x)-64*x^3+1600*x)*log(1/4*log(5+x)^2+1/2* x*log(5+x)+1/4*x^2)^7+(128*x^3-512*x^2-4480*x+19200)*log(1/4*log(5+x)^2+1/ 2*x*log(5+x)+1/4*x^2)^6+((96*x^4-960*x^3+24000*x-60000)*log(5+x)+96*x^5-96 0*x^4+24000*x^2-60000*x)*log(1/4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2)^5+(-19 2*x^5+2688*x^4-5760*x^3-76800*x^2+456000*x-720000)*log(1/4*log(5+x)^2+1/2* x*log(5+x)+1/4*x^2)^4+((-48*x^6+960*x^5-6000*x^4+150000*x^2-600000*x+75000 0)*log(5+x)-48*x^7+960*x^6-6000*x^5+150000*x^3-600000*x^2+750000*x)*log(1/ 4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2)^3+(96*x^7-2304*x^6+18720*x^5-24000*x^ 4-540000*x^3+3600000*x^2-9300000*x+9000000)*log(1/4*log(5+x)^2+1/2*x*log(5 +x)+1/4*x^2)^2+((8*x^8-240*x^7+2800*x^6-14000*x^5+350000*x^3-1750000*x^2+3 750000*x-3125000)*log(5+x)+8*x^9-240*x^8+2800*x^7-14000*x^6+350000*x^4-175 0000*x^3+3750000*x^2-3125000*x)*log(1/4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2) -16*x^9+544*x^8-7360*x^7+44800*x^6-28000*x^5-1400000*x^4+9800000*x^3-32000 000*x^2+53750000*x-37500000)/((5+x)*log(5+x)+x^2+5*x)/log(1/4*log(5+x)^2+1 /2*x*log(5+x)+1/4*x^2)^9,x, algorithm=\
(x^8 - 40*x^7 - 32*(x^2 - 10*x + 25)*log(1/4*x^2 + 1/2*x*log(x + 5) + 1/4* log(x + 5)^2)^6 + 700*x^6 - 7000*x^5 + 24*(x^4 - 20*x^3 + 150*x^2 - 500*x + 625)*log(1/4*x^2 + 1/2*x*log(x + 5) + 1/4*log(x + 5)^2)^4 + 43750*x^4 - 175000*x^3 - 8*(x^6 - 30*x^5 + 375*x^4 - 2500*x^3 + 9375*x^2 - 18750*x + 1 5625)*log(1/4*x^2 + 1/2*x*log(x + 5) + 1/4*log(x + 5)^2)^2 + 437500*x^2 - 625000*x + 390625)/log(1/4*x^2 + 1/2*x*log(x + 5) + 1/4*log(x + 5)^2)^8
Leaf count of result is larger than twice the leaf count of optimal. 201 vs. \(2 (20) = 40\).
Time = 2.31 (sec) , antiderivative size = 201, normalized size of antiderivative = 7.73 \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=\frac {x^{8} - 40 x^{7} + 700 x^{6} - 7000 x^{5} + 43750 x^{4} - 175000 x^{3} + 437500 x^{2} - 625000 x + \left (- 32 x^{2} + 320 x - 800\right ) \log {\left (\frac {x^{2}}{4} + \frac {x \log {\left (x + 5 \right )}}{2} + \frac {\log {\left (x + 5 \right )}^{2}}{4} \right )}^{6} + \left (24 x^{4} - 480 x^{3} + 3600 x^{2} - 12000 x + 15000\right ) \log {\left (\frac {x^{2}}{4} + \frac {x \log {\left (x + 5 \right )}}{2} + \frac {\log {\left (x + 5 \right )}^{2}}{4} \right )}^{4} + \left (- 8 x^{6} + 240 x^{5} - 3000 x^{4} + 20000 x^{3} - 75000 x^{2} + 150000 x - 125000\right ) \log {\left (\frac {x^{2}}{4} + \frac {x \log {\left (x + 5 \right )}}{2} + \frac {\log {\left (x + 5 \right )}^{2}}{4} \right )}^{2} + 390625}{\log {\left (\frac {x^{2}}{4} + \frac {x \log {\left (x + 5 \right )}}{2} + \frac {\log {\left (x + 5 \right )}^{2}}{4} \right )}^{8}} \]
integrate((((-64*x**2+1600)*ln(5+x)-64*x**3+1600*x)*ln(1/4*ln(5+x)**2+1/2* x*ln(5+x)+1/4*x**2)**7+(128*x**3-512*x**2-4480*x+19200)*ln(1/4*ln(5+x)**2+ 1/2*x*ln(5+x)+1/4*x**2)**6+((96*x**4-960*x**3+24000*x-60000)*ln(5+x)+96*x* *5-960*x**4+24000*x**2-60000*x)*ln(1/4*ln(5+x)**2+1/2*x*ln(5+x)+1/4*x**2)* *5+(-192*x**5+2688*x**4-5760*x**3-76800*x**2+456000*x-720000)*ln(1/4*ln(5+ x)**2+1/2*x*ln(5+x)+1/4*x**2)**4+((-48*x**6+960*x**5-6000*x**4+150000*x**2 -600000*x+750000)*ln(5+x)-48*x**7+960*x**6-6000*x**5+150000*x**3-600000*x* *2+750000*x)*ln(1/4*ln(5+x)**2+1/2*x*ln(5+x)+1/4*x**2)**3+(96*x**7-2304*x* *6+18720*x**5-24000*x**4-540000*x**3+3600000*x**2-9300000*x+9000000)*ln(1/ 4*ln(5+x)**2+1/2*x*ln(5+x)+1/4*x**2)**2+((8*x**8-240*x**7+2800*x**6-14000* x**5+350000*x**3-1750000*x**2+3750000*x-3125000)*ln(5+x)+8*x**9-240*x**8+2 800*x**7-14000*x**6+350000*x**4-1750000*x**3+3750000*x**2-3125000*x)*ln(1/ 4*ln(5+x)**2+1/2*x*ln(5+x)+1/4*x**2)-16*x**9+544*x**8-7360*x**7+44800*x**6 -28000*x**5-1400000*x**4+9800000*x**3-32000000*x**2+53750000*x-37500000)/( (5+x)*ln(5+x)+x**2+5*x)/ln(1/4*ln(5+x)**2+1/2*x*ln(5+x)+1/4*x**2)**9,x)
(x**8 - 40*x**7 + 700*x**6 - 7000*x**5 + 43750*x**4 - 175000*x**3 + 437500 *x**2 - 625000*x + (-32*x**2 + 320*x - 800)*log(x**2/4 + x*log(x + 5)/2 + log(x + 5)**2/4)**6 + (24*x**4 - 480*x**3 + 3600*x**2 - 12000*x + 15000)*l og(x**2/4 + x*log(x + 5)/2 + log(x + 5)**2/4)**4 + (-8*x**6 + 240*x**5 - 3 000*x**4 + 20000*x**3 - 75000*x**2 + 150000*x - 125000)*log(x**2/4 + x*log (x + 5)/2 + log(x + 5)**2/4)**2 + 390625)/log(x**2/4 + x*log(x + 5)/2 + lo g(x + 5)**2/4)**8
Leaf count of result is larger than twice the leaf count of optimal. 630 vs. \(2 (23) = 46\).
Time = 0.90 (sec) , antiderivative size = 630, normalized size of antiderivative = 24.23 \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=\text {Too large to display} \]
integrate((((-64*x^2+1600)*log(5+x)-64*x^3+1600*x)*log(1/4*log(5+x)^2+1/2* x*log(5+x)+1/4*x^2)^7+(128*x^3-512*x^2-4480*x+19200)*log(1/4*log(5+x)^2+1/ 2*x*log(5+x)+1/4*x^2)^6+((96*x^4-960*x^3+24000*x-60000)*log(5+x)+96*x^5-96 0*x^4+24000*x^2-60000*x)*log(1/4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2)^5+(-19 2*x^5+2688*x^4-5760*x^3-76800*x^2+456000*x-720000)*log(1/4*log(5+x)^2+1/2* x*log(5+x)+1/4*x^2)^4+((-48*x^6+960*x^5-6000*x^4+150000*x^2-600000*x+75000 0)*log(5+x)-48*x^7+960*x^6-6000*x^5+150000*x^3-600000*x^2+750000*x)*log(1/ 4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2)^3+(96*x^7-2304*x^6+18720*x^5-24000*x^ 4-540000*x^3+3600000*x^2-9300000*x+9000000)*log(1/4*log(5+x)^2+1/2*x*log(5 +x)+1/4*x^2)^2+((8*x^8-240*x^7+2800*x^6-14000*x^5+350000*x^3-1750000*x^2+3 750000*x-3125000)*log(5+x)+8*x^9-240*x^8+2800*x^7-14000*x^6+350000*x^4-175 0000*x^3+3750000*x^2-3125000*x)*log(1/4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2) -16*x^9+544*x^8-7360*x^7+44800*x^6-28000*x^5-1400000*x^4+9800000*x^3-32000 000*x^2+53750000*x-37500000)/((5+x)*log(5+x)+x^2+5*x)/log(1/4*log(5+x)^2+1 /2*x*log(5+x)+1/4*x^2)^9,x, algorithm=\
1/256*(x^8 - 4*(8*log(2)^2 - 175)*x^6 - 40*x^7 - 2048*(x^2 - 10*x + 25)*lo g(x + log(x + 5))^6 + 40*(24*log(2)^2 - 175)*x^5 - 51200*log(2)^6 + 12288* (x^2*log(2) - 10*x*log(2) + 25*log(2))*log(x + log(x + 5))^5 + 2*(192*log( 2)^4 - 6000*log(2)^2 + 21875)*x^4 + 384*(x^4 - 10*(8*log(2)^2 - 15)*x^2 - 20*x^3 + 100*(8*log(2)^2 - 5)*x - 2000*log(2)^2 + 625)*log(x + log(x + 5)) ^4 - 40*(192*log(2)^4 - 2000*log(2)^2 + 4375)*x^3 + 240000*log(2)^4 - 512* (3*x^4*log(2) - 60*x^3*log(2) - 10*(8*log(2)^3 - 45*log(2))*x^2 - 2000*log (2)^3 + 100*(8*log(2)^3 - 15*log(2))*x + 1875*log(2))*log(x + log(x + 5))^ 3 - 4*(512*log(2)^6 - 14400*log(2)^4 + 75000*log(2)^2 - 109375)*x^2 - 32*( x^6 - 3*(24*log(2)^2 - 125)*x^4 - 30*x^5 + 20*(72*log(2)^2 - 125)*x^3 + 24 000*log(2)^4 + 15*(64*log(2)^4 - 720*log(2)^2 + 625)*x^2 - 150*(64*log(2)^ 4 - 240*log(2)^2 + 125)*x - 45000*log(2)^2 + 15625)*log(x + log(x + 5))^2 + 40*(512*log(2)^6 - 4800*log(2)^4 + 15000*log(2)^2 - 15625)*x - 500000*lo g(2)^2 + 64*(x^6*log(2) - 30*x^5*log(2) - 3*(8*log(2)^3 - 125*log(2))*x^4 + 4800*log(2)^5 + 20*(24*log(2)^3 - 125*log(2))*x^3 + 3*(64*log(2)^5 - 120 0*log(2)^3 + 3125*log(2))*x^2 - 15000*log(2)^3 - 30*(64*log(2)^5 - 400*log (2)^3 + 625*log(2))*x + 15625*log(2))*log(x + log(x + 5)) + 390625)/(log(2 )^8 - 8*log(2)^7*log(x + log(x + 5)) + 28*log(2)^6*log(x + log(x + 5))^2 - 56*log(2)^5*log(x + log(x + 5))^3 + 70*log(2)^4*log(x + log(x + 5))^4 - 5 6*log(2)^3*log(x + log(x + 5))^5 + 28*log(2)^2*log(x + log(x + 5))^6 - ...
Timed out. \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=\text {Timed out} \]
integrate((((-64*x^2+1600)*log(5+x)-64*x^3+1600*x)*log(1/4*log(5+x)^2+1/2* x*log(5+x)+1/4*x^2)^7+(128*x^3-512*x^2-4480*x+19200)*log(1/4*log(5+x)^2+1/ 2*x*log(5+x)+1/4*x^2)^6+((96*x^4-960*x^3+24000*x-60000)*log(5+x)+96*x^5-96 0*x^4+24000*x^2-60000*x)*log(1/4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2)^5+(-19 2*x^5+2688*x^4-5760*x^3-76800*x^2+456000*x-720000)*log(1/4*log(5+x)^2+1/2* x*log(5+x)+1/4*x^2)^4+((-48*x^6+960*x^5-6000*x^4+150000*x^2-600000*x+75000 0)*log(5+x)-48*x^7+960*x^6-6000*x^5+150000*x^3-600000*x^2+750000*x)*log(1/ 4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2)^3+(96*x^7-2304*x^6+18720*x^5-24000*x^ 4-540000*x^3+3600000*x^2-9300000*x+9000000)*log(1/4*log(5+x)^2+1/2*x*log(5 +x)+1/4*x^2)^2+((8*x^8-240*x^7+2800*x^6-14000*x^5+350000*x^3-1750000*x^2+3 750000*x-3125000)*log(5+x)+8*x^9-240*x^8+2800*x^7-14000*x^6+350000*x^4-175 0000*x^3+3750000*x^2-3125000*x)*log(1/4*log(5+x)^2+1/2*x*log(5+x)+1/4*x^2) -16*x^9+544*x^8-7360*x^7+44800*x^6-28000*x^5-1400000*x^4+9800000*x^3-32000 000*x^2+53750000*x-37500000)/((5+x)*log(5+x)+x^2+5*x)/log(1/4*log(5+x)^2+1 /2*x*log(5+x)+1/4*x^2)^9,x, algorithm=\
Time = 81.87 (sec) , antiderivative size = 132776, normalized size of antiderivative = 5106.77 \[ \int \frac {-37500000+53750000 x-32000000 x^2+9800000 x^3-1400000 x^4-28000 x^5+44800 x^6-7360 x^7+544 x^8-16 x^9+\left (-3125000 x+3750000 x^2-1750000 x^3+350000 x^4-14000 x^6+2800 x^7-240 x^8+8 x^9+\left (-3125000+3750000 x-1750000 x^2+350000 x^3-14000 x^5+2800 x^6-240 x^7+8 x^8\right ) \log (5+x)\right ) \log \left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (9000000-9300000 x+3600000 x^2-540000 x^3-24000 x^4+18720 x^5-2304 x^6+96 x^7\right ) \log ^2\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (750000 x-600000 x^2+150000 x^3-6000 x^5+960 x^6-48 x^7+\left (750000-600000 x+150000 x^2-6000 x^4+960 x^5-48 x^6\right ) \log (5+x)\right ) \log ^3\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-720000+456000 x-76800 x^2-5760 x^3+2688 x^4-192 x^5\right ) \log ^4\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (-60000 x+24000 x^2-960 x^4+96 x^5+\left (-60000+24000 x-960 x^3+96 x^4\right ) \log (5+x)\right ) \log ^5\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (19200-4480 x-512 x^2+128 x^3\right ) \log ^6\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )+\left (1600 x-64 x^3+\left (1600-64 x^2\right ) \log (5+x)\right ) \log ^7\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )}{\left (5 x+x^2+(5+x) \log (5+x)\right ) \log ^9\left (\frac {1}{4} \left (x^2+2 x \log (5+x)+\log ^2(5+x)\right )\right )} \, dx=\text {Too large to display} \]
int(-(log((x*log(x + 5))/2 + log(x + 5)^2/4 + x^2/4)^2*(9300000*x - 360000 0*x^2 + 540000*x^3 + 24000*x^4 - 18720*x^5 + 2304*x^6 - 96*x^7 - 9000000) - log((x*log(x + 5))/2 + log(x + 5)^2/4 + x^2/4)^5*(log(x + 5)*(24000*x - 960*x^3 + 96*x^4 - 60000) - 60000*x + 24000*x^2 - 960*x^4 + 96*x^5) - log( (x*log(x + 5))/2 + log(x + 5)^2/4 + x^2/4)*(log(x + 5)*(3750000*x - 175000 0*x^2 + 350000*x^3 - 14000*x^5 + 2800*x^6 - 240*x^7 + 8*x^8 - 3125000) - 3 125000*x + 3750000*x^2 - 1750000*x^3 + 350000*x^4 - 14000*x^6 + 2800*x^7 - 240*x^8 + 8*x^9) - 53750000*x + log((x*log(x + 5))/2 + log(x + 5)^2/4 + x ^2/4)^6*(4480*x + 512*x^2 - 128*x^3 - 19200) + log((x*log(x + 5))/2 + log( x + 5)^2/4 + x^2/4)^7*(log(x + 5)*(64*x^2 - 1600) - 1600*x + 64*x^3) + 320 00000*x^2 - 9800000*x^3 + 1400000*x^4 + 28000*x^5 - 44800*x^6 + 7360*x^7 - 544*x^8 + 16*x^9 + log((x*log(x + 5))/2 + log(x + 5)^2/4 + x^2/4)^3*(log( x + 5)*(600000*x - 150000*x^2 + 6000*x^4 - 960*x^5 + 48*x^6 - 750000) - 75 0000*x + 600000*x^2 - 150000*x^3 + 6000*x^5 - 960*x^6 + 48*x^7) + log((x*l og(x + 5))/2 + log(x + 5)^2/4 + x^2/4)^4*(76800*x^2 - 456000*x + 5760*x^3 - 2688*x^4 + 192*x^5 + 720000) + 37500000)/(log((x*log(x + 5))/2 + log(x + 5)^2/4 + x^2/4)^9*(5*x + log(x + 5)*(x + 5) + x^2)),x)
(((x + log(x + 5))*(x + 5)*(55288627410240000*x*log(x + 5) - 8482988787840 000*log(x + 5) - 12611376211092480*x + 156074108417136000*x*log(x + 5)^2 + 241862097005020800*x^2*log(x + 5) + 12988535943600000*x*log(x + 5)^3 + 21 9135555377746560*x^3*log(x + 5) - 17507453317987500*x*log(x + 5)^4 + 19466 522946388980*x^4*log(x + 5) + 729121375968750*x*log(x + 5)^5 - 60344061522 890850*x^5*log(x + 5) + 39741494343750*x*log(x + 5)^6 - 28649456555375295* x^6*log(x + 5) - 1313381299352676*x^7*log(x + 5) + 2445280974950892*x^8*lo g(x + 5) + 697746384595466*x^9*log(x + 5) + 15680466699259*x^10*log(x + 5) - 27297800938912*x^11*log(x + 5) - 5542567190600*x^12*log(x + 5) - 222496 240678*x^13*log(x + 5) + 77733390619*x^14*log(x + 5) + 15162170468*x^15*lo g(x + 5) + 1284414472*x^16*log(x + 5) + 55729694*x^17*log(x + 5) + 1011465 *x^18*log(x + 5) + 22571107060320000*log(x + 5)^2 + 33304821354000000*log( x + 5)^3 - 7272248898600000*log(x + 5)^4 - 290759903437500*log(x + 5)^5 + 41697089296875*log(x + 5)^6 + 41535961272656640*x^2 + 130170253695868800*x ^3 + 113007583910675520*x^4 + 25148133338317092*x^5 - 15396634779859881*x^ 6 - 9899427748529457*x^7 - 1219881546528954*x^8 + 552233673573928*x^9 + 20 9267584170743*x^10 + 14293906627893*x^11 - 5903632467837*x^12 - 1487104303 273*x^13 - 91140964848*x^14 + 15380571264*x^15 + 3573331363*x^16 + 3185124 09*x^17 + 14195254*x^18 + 262144*x^19 + 132121766566137600*x^2*log(x + 5)^ 2 - 53776497040875000*x^2*log(x + 5)^3 - 40686820173067320*x^3*log(x + ...