Integrand size = 347, antiderivative size = 27 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=\frac {\left (1-x+(-3+x) x+\frac {x}{(5+x-\log (4))^2}\right )^2}{x^2} \] Output:
(1-x+x/(5-2*ln(2)+x)^2+x*(-3+x))^2/x^2
Leaf count is larger than twice the leaf count of optimal. \(96\) vs. \(2(27)=54\).
Time = 0.18 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.56 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=\frac {1}{x^2}-8 x+x^2+\frac {1}{(5+x-\log (4))^4}+\frac {2 \left (46-14 \log (4)+\log ^2(4)\right )}{(5+x-\log (4))^2 (-5+\log (4))}+\frac {2 \left (24-10 \log (4)+\log ^2(4)\right )}{(5+x-\log (4)) (-5+\log (4))^2}-\frac {2 \left (99-40 \log (4)+4 \log ^2(4)\right )}{x (-5+\log (4))^2} \] Input:
Integrate[(6250 - 18500*x - 22250*x^2 + 14924*x^3 + 16596*x^4 + 3546*x^5 - 506*x^6 - 300*x^7 - 42*x^8 - 2*x^9 + (-6250 + 19850*x + 18400*x^2 - 18904 *x^3 - 12908*x^4 - 962*x^5 + 700*x^6 + 160*x^7 + 10*x^8)*Log[4] + (2500 - 8470*x - 5690*x^2 + 8774*x^3 + 3418*x^4 - 300*x^5 - 220*x^6 - 20*x^7)*Log[ 4]^2 + (-500 + 1798*x + 780*x^2 - 1918*x^3 - 300*x^4 + 120*x^5 + 20*x^6)*L og[4]^3 + (50 - 190*x - 40*x^2 + 200*x^3 - 10*x^4 - 10*x^5)*Log[4]^4 + (-2 + 8*x - 8*x^3 + 2*x^4)*Log[4]^5)/(-3125*x^3 - 3125*x^4 - 1250*x^5 - 250*x ^6 - 25*x^7 - x^8 + (3125*x^3 + 2500*x^4 + 750*x^5 + 100*x^6 + 5*x^7)*Log[ 4] + (-1250*x^3 - 750*x^4 - 150*x^5 - 10*x^6)*Log[4]^2 + (250*x^3 + 100*x^ 4 + 10*x^5)*Log[4]^3 + (-25*x^3 - 5*x^4)*Log[4]^4 + x^3*Log[4]^5),x]
Output:
x^(-2) - 8*x + x^2 + (5 + x - Log[4])^(-4) + (2*(46 - 14*Log[4] + Log[4]^2 ))/((5 + x - Log[4])^2*(-5 + Log[4])) + (2*(24 - 10*Log[4] + Log[4]^2))/(( 5 + x - Log[4])*(-5 + Log[4])^2) - (2*(99 - 40*Log[4] + 4*Log[4]^2))/(x*(- 5 + Log[4])^2)
Leaf count is larger than twice the leaf count of optimal. \(104\) vs. \(2(27)=54\).
Time = 1.06 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.85, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6, 2026, 2007, 2123, 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.
| \(\displaystyle \int \frac {-2 x^9-42 x^8-300 x^7-506 x^6+3546 x^5+16596 x^4+14924 x^3-22250 x^2+\left (2 x^4-8 x^3+8 x-2\right ) \log ^5(4)+\left (-10 x^5-10 x^4+200 x^3-40 x^2-190 x+50\right ) \log ^4(4)+\left (20 x^6+120 x^5-300 x^4-1918 x^3+780 x^2+1798 x-500\right ) \log ^3(4)+\left (-20 x^7-220 x^6-300 x^5+3418 x^4+8774 x^3-5690 x^2-8470 x+2500\right ) \log ^2(4)+\left (10 x^8+160 x^7+700 x^6-962 x^5-12908 x^4-18904 x^3+18400 x^2+19850 x-6250\right ) \log (4)-18500 x+6250}{-x^8-25 x^7-250 x^6-1250 x^5-3125 x^4-3125 x^3+x^3 \log ^5(4)+\left (-5 x^4-25 x^3\right ) \log ^4(4)+\left (10 x^5+100 x^4+250 x^3\right ) \log ^3(4)+\left (-10 x^6-150 x^5-750 x^4-1250 x^3\right ) \log ^2(4)+\left (5 x^7+100 x^6+750 x^5+2500 x^4+3125 x^3\right ) \log (4)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-2 x^9-42 x^8-300 x^7-506 x^6+3546 x^5+16596 x^4+14924 x^3-22250 x^2+\left (2 x^4-8 x^3+8 x-2\right ) \log ^5(4)+\left (-10 x^5-10 x^4+200 x^3-40 x^2-190 x+50\right ) \log ^4(4)+\left (20 x^6+120 x^5-300 x^4-1918 x^3+780 x^2+1798 x-500\right ) \log ^3(4)+\left (-20 x^7-220 x^6-300 x^5+3418 x^4+8774 x^3-5690 x^2-8470 x+2500\right ) \log ^2(4)+\left (10 x^8+160 x^7+700 x^6-962 x^5-12908 x^4-18904 x^3+18400 x^2+19850 x-6250\right ) \log (4)-18500 x+6250}{-x^8-25 x^7-250 x^6-1250 x^5-3125 x^4+x^3 \left (\log ^5(4)-3125\right )+\left (-5 x^4-25 x^3\right ) \log ^4(4)+\left (10 x^5+100 x^4+250 x^3\right ) \log ^3(4)+\left (-10 x^6-150 x^5-750 x^4-1250 x^3\right ) \log ^2(4)+\left (5 x^7+100 x^6+750 x^5+2500 x^4+3125 x^3\right ) \log (4)}dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-2 x^9-42 x^8-300 x^7-506 x^6+3546 x^5+16596 x^4+14924 x^3-22250 x^2+\left (2 x^4-8 x^3+8 x-2\right ) \log ^5(4)+\left (-10 x^5-10 x^4+200 x^3-40 x^2-190 x+50\right ) \log ^4(4)+\left (20 x^6+120 x^5-300 x^4-1918 x^3+780 x^2+1798 x-500\right ) \log ^3(4)+\left (-20 x^7-220 x^6-300 x^5+3418 x^4+8774 x^3-5690 x^2-8470 x+2500\right ) \log ^2(4)+\left (10 x^8+160 x^7+700 x^6-962 x^5-12908 x^4-18904 x^3+18400 x^2+19850 x-6250\right ) \log (4)-18500 x+6250}{x^3 \left (-x^5-5 x^4 (5-\log (4))-10 x^3 (5-\log (4))^2-10 x^2 (5-\log (4))^3-5 x (5-\log (4))^4+(\log (4)-5)^5\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {-2 x^9-42 x^8-300 x^7-506 x^6+3546 x^5+16596 x^4+14924 x^3-22250 x^2+\left (2 x^4-8 x^3+8 x-2\right ) \log ^5(4)+\left (-10 x^5-10 x^4+200 x^3-40 x^2-190 x+50\right ) \log ^4(4)+\left (20 x^6+120 x^5-300 x^4-1918 x^3+780 x^2+1798 x-500\right ) \log ^3(4)+\left (-20 x^7-220 x^6-300 x^5+3418 x^4+8774 x^3-5690 x^2-8470 x+2500\right ) \log ^2(4)+\left (10 x^8+160 x^7+700 x^6-962 x^5-12908 x^4-18904 x^3+18400 x^2+19850 x-6250\right ) \log (4)-18500 x+6250}{x^3 (-x-5+\log (4))^5}dx\) |
| \(\Big \downarrow \) 2123 |
| \(\displaystyle \int \left (-\frac {2}{x^3}+\frac {2 \left (99+4 \log ^2(4)-40 \log (4)\right )}{x^2 (\log (4)-5)^2}+2 x-\frac {4 \left (46+\log ^2(4)-14 \log (4)\right )}{(\log (4)-5) (x+5-\log (4))^3}-\frac {4}{(x+5-\log (4))^5}+\frac {2 (4-\log (4)) (\log (4)-6)}{(5-\log (4))^2 (x+5-\log (4))^2}-8\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^2+\frac {1}{x^2}-8 x-\frac {2 \left (46+\log ^2(4)-14 \log (4)\right )}{(5-\log (4)) (x+5-\log (4))^2}-\frac {2 \left (99+4 \log ^2(4)-40 \log (4)\right )}{x (5-\log (4))^2}+\frac {2 (4-\log (4)) (6-\log (4))}{(5-\log (4))^2 (x+5-\log (4))}+\frac {1}{(x+5-\log (4))^4}\) |
Input:
Int[(6250 - 18500*x - 22250*x^2 + 14924*x^3 + 16596*x^4 + 3546*x^5 - 506*x ^6 - 300*x^7 - 42*x^8 - 2*x^9 + (-6250 + 19850*x + 18400*x^2 - 18904*x^3 - 12908*x^4 - 962*x^5 + 700*x^6 + 160*x^7 + 10*x^8)*Log[4] + (2500 - 8470*x - 5690*x^2 + 8774*x^3 + 3418*x^4 - 300*x^5 - 220*x^6 - 20*x^7)*Log[4]^2 + (-500 + 1798*x + 780*x^2 - 1918*x^3 - 300*x^4 + 120*x^5 + 20*x^6)*Log[4]^ 3 + (50 - 190*x - 40*x^2 + 200*x^3 - 10*x^4 - 10*x^5)*Log[4]^4 + (-2 + 8*x - 8*x^3 + 2*x^4)*Log[4]^5)/(-3125*x^3 - 3125*x^4 - 1250*x^5 - 250*x^6 - 2 5*x^7 - x^8 + (3125*x^3 + 2500*x^4 + 750*x^5 + 100*x^6 + 5*x^7)*Log[4] + ( -1250*x^3 - 750*x^4 - 150*x^5 - 10*x^6)*Log[4]^2 + (250*x^3 + 100*x^4 + 10 *x^5)*Log[4]^3 + (-25*x^3 - 5*x^4)*Log[4]^4 + x^3*Log[4]^5),x]
Output:
x^(-2) - 8*x + x^2 + (5 + x - Log[4])^(-4) + (2*(4 - Log[4])*(6 - Log[4])) /((5 - Log[4])^2*(5 + x - Log[4])) - (2*(46 - 14*Log[4] + Log[4]^2))/((5 - Log[4])*(5 + x - Log[4])^2) - (2*(99 - 40*Log[4] + 4*Log[4]^2))/(x*(5 - L og[4])^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[(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[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c , d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2])
Leaf count of result is larger than twice the leaf count of optimal. \(106\) vs. \(2(27)=54\).
Time = 0.91 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.96
| method | result | size |
| default | \(x^{2}-8 x -\frac {2 \left (16 \ln \left (2\right )^{2}-80 \ln \left (2\right )+99\right )}{\left (2 \ln \left (2\right )-5\right )^{2} x}+\frac {1}{x^{2}}-\frac {-8 \ln \left (2\right )^{2}+56 \ln \left (2\right )-92}{\left (2 \ln \left (2\right )-5\right ) \left (5-2 \ln \left (2\right )+x \right )^{2}}-\frac {2 \left (-4 \ln \left (2\right )^{2}+20 \ln \left (2\right )-24\right )}{\left (2 \ln \left (2\right )-5\right )^{2} \left (5-2 \ln \left (2\right )+x \right )}+\frac {1}{\left (5-2 \ln \left (2\right )+x \right )^{4}}\) | \(107\) |
| risch | \(x^{2}-8 x +\frac {-6 x^{5}+16 \left (\frac {7 \ln \left (2\right )}{2}-\frac {147}{16}\right ) x^{4}+16 \left (-\frac {23 \ln \left (2\right )^{2}}{2}+59 \ln \left (2\right )-\frac {151}{2}\right ) x^{3}+16 \left (16 \ln \left (2\right )^{3}-\frac {241 \ln \left (2\right )^{2}}{2}+302 \ln \left (2\right )-\frac {4029}{16}\right ) x^{2}+16 \left (-8 \ln \left (2\right )^{4}+78 \ln \left (2\right )^{3}-\frac {569 \ln \left (2\right )^{2}}{2}+460 \ln \left (2\right )-\frac {2225}{8}\right ) x +16 \ln \left (2\right )^{4}-160 \ln \left (2\right )^{3}+600 \ln \left (2\right )^{2}-1000 \ln \left (2\right )+625}{x^{2} \left (16 \ln \left (2\right )^{4}-32 x \ln \left (2\right )^{3}+24 x^{2} \ln \left (2\right )^{2}-8 x^{3} \ln \left (2\right )+x^{4}-160 \ln \left (2\right )^{3}+240 x \ln \left (2\right )^{2}-120 x^{2} \ln \left (2\right )+20 x^{3}+600 \ln \left (2\right )^{2}-600 x \ln \left (2\right )+150 x^{2}-1000 \ln \left (2\right )+500 x +625\right )}\) | \(198\) |
| norman | \(\frac {x^{8}+\left (12-8 \ln \left (2\right )\right ) x^{7}+\left (-128 \ln \left (2\right )^{4}+1248 \ln \left (2\right )^{3}-4552 \ln \left (2\right )^{2}+7360 \ln \left (2\right )-4450\right ) x +\left (160 \ln \left (2\right )^{3}-880 \ln \left (2\right )^{2}+1400 \ln \left (2\right )-506\right ) x^{5}+\left (-560 \ln \left (2\right )^{4}+4320 \ln \left (2\right )^{3}-11400 \ln \left (2\right )^{2}+11056 \ln \left (2\right )-2022\right ) x^{4}+\left (768 \ln \left (2\right )^{5}-7680 \ln \left (2\right )^{4}+28800 \ln \left (2\right )^{3}-48184 \ln \left (2\right )^{2}+30944 \ln \left (2\right )-1208\right ) x^{3}+\left (-384 \ln \left (2\right )^{6}+4736 \ln \left (2\right )^{5}-23200 \ln \left (2\right )^{4}+56256 \ln \left (2\right )^{3}-66928 \ln \left (2\right )^{2}+29832 \ln \left (2\right )+2221\right ) x^{2}+16 \ln \left (2\right )^{4}-160 \ln \left (2\right )^{3}+600 \ln \left (2\right )^{2}-1000 \ln \left (2\right )+625}{x^{2} \left (2 \ln \left (2\right )-x -5\right )^{4}}\) | \(203\) |
| gosper | \(-\frac {-625-4736 x^{2} \ln \left (2\right )^{5}+4450 x +880 x^{5} \ln \left (2\right )^{2}-768 x^{3} \ln \left (2\right )^{5}-1248 x \ln \left (2\right )^{3}+128 x \ln \left (2\right )^{4}+8 x^{7} \ln \left (2\right )+11400 x^{4} \ln \left (2\right )^{2}+48184 x^{3} \ln \left (2\right )^{2}+4552 x \ln \left (2\right )^{2}-11056 x^{4} \ln \left (2\right )-1400 x^{5} \ln \left (2\right )+66928 x^{2} \ln \left (2\right )^{2}-7360 x \ln \left (2\right )-29832 x^{2} \ln \left (2\right )-30944 x^{3} \ln \left (2\right )-16 \ln \left (2\right )^{4}+1000 \ln \left (2\right )-600 \ln \left (2\right )^{2}+160 \ln \left (2\right )^{3}-12 x^{7}-x^{8}+2022 x^{4}+1208 x^{3}-2221 x^{2}+506 x^{5}-56256 \ln \left (2\right )^{3} x^{2}-160 \ln \left (2\right )^{3} x^{5}+560 \ln \left (2\right )^{4} x^{4}-4320 \ln \left (2\right )^{3} x^{4}+7680 \ln \left (2\right )^{4} x^{3}+23200 \ln \left (2\right )^{4} x^{2}-28800 \ln \left (2\right )^{3} x^{3}+384 \ln \left (2\right )^{6} x^{2}}{x^{2} \left (16 \ln \left (2\right )^{4}-32 x \ln \left (2\right )^{3}+24 x^{2} \ln \left (2\right )^{2}-8 x^{3} \ln \left (2\right )+x^{4}-160 \ln \left (2\right )^{3}+240 x \ln \left (2\right )^{2}-120 x^{2} \ln \left (2\right )+20 x^{3}+600 \ln \left (2\right )^{2}-600 x \ln \left (2\right )+150 x^{2}-1000 \ln \left (2\right )+500 x +625\right )}\) | \(334\) |
| parallelrisch | \(-\frac {-625-4736 x^{2} \ln \left (2\right )^{5}+4450 x +880 x^{5} \ln \left (2\right )^{2}-768 x^{3} \ln \left (2\right )^{5}-1248 x \ln \left (2\right )^{3}+128 x \ln \left (2\right )^{4}+8 x^{7} \ln \left (2\right )+11400 x^{4} \ln \left (2\right )^{2}+48184 x^{3} \ln \left (2\right )^{2}+4552 x \ln \left (2\right )^{2}-11056 x^{4} \ln \left (2\right )-1400 x^{5} \ln \left (2\right )+66928 x^{2} \ln \left (2\right )^{2}-7360 x \ln \left (2\right )-29832 x^{2} \ln \left (2\right )-30944 x^{3} \ln \left (2\right )-16 \ln \left (2\right )^{4}+1000 \ln \left (2\right )-600 \ln \left (2\right )^{2}+160 \ln \left (2\right )^{3}-12 x^{7}-x^{8}+2022 x^{4}+1208 x^{3}-2221 x^{2}+506 x^{5}-56256 \ln \left (2\right )^{3} x^{2}-160 \ln \left (2\right )^{3} x^{5}+560 \ln \left (2\right )^{4} x^{4}-4320 \ln \left (2\right )^{3} x^{4}+7680 \ln \left (2\right )^{4} x^{3}+23200 \ln \left (2\right )^{4} x^{2}-28800 \ln \left (2\right )^{3} x^{3}+384 \ln \left (2\right )^{6} x^{2}}{x^{2} \left (16 \ln \left (2\right )^{4}-32 x \ln \left (2\right )^{3}+24 x^{2} \ln \left (2\right )^{2}-8 x^{3} \ln \left (2\right )+x^{4}-160 \ln \left (2\right )^{3}+240 x \ln \left (2\right )^{2}-120 x^{2} \ln \left (2\right )+20 x^{3}+600 \ln \left (2\right )^{2}-600 x \ln \left (2\right )+150 x^{2}-1000 \ln \left (2\right )+500 x +625\right )}\) | \(334\) |
Input:
int((32*(2*x^4-8*x^3+8*x-2)*ln(2)^5+16*(-10*x^5-10*x^4+200*x^3-40*x^2-190* x+50)*ln(2)^4+8*(20*x^6+120*x^5-300*x^4-1918*x^3+780*x^2+1798*x-500)*ln(2) ^3+4*(-20*x^7-220*x^6-300*x^5+3418*x^4+8774*x^3-5690*x^2-8470*x+2500)*ln(2 )^2+2*(10*x^8+160*x^7+700*x^6-962*x^5-12908*x^4-18904*x^3+18400*x^2+19850* x-6250)*ln(2)-2*x^9-42*x^8-300*x^7-506*x^6+3546*x^5+16596*x^4+14924*x^3-22 250*x^2-18500*x+6250)/(32*x^3*ln(2)^5+16*(-5*x^4-25*x^3)*ln(2)^4+8*(10*x^5 +100*x^4+250*x^3)*ln(2)^3+4*(-10*x^6-150*x^5-750*x^4-1250*x^3)*ln(2)^2+2*( 5*x^7+100*x^6+750*x^5+2500*x^4+3125*x^3)*ln(2)-x^8-25*x^7-250*x^6-1250*x^5 -3125*x^4-3125*x^3),x,method=_RETURNVERBOSE)
Output:
x^2-8*x-2*(16*ln(2)^2-80*ln(2)+99)/(2*ln(2)-5)^2/x+1/x^2-(-8*ln(2)^2+56*ln (2)-92)/(2*ln(2)-5)/(5-2*ln(2)+x)^2-2*(-4*ln(2)^2+20*ln(2)-24)/(2*ln(2)-5) ^2/(5-2*ln(2)+x)+1/(5-2*ln(2)+x)^4
Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (27) = 54\).
Time = 0.07 (sec) , antiderivative size = 253, normalized size of antiderivative = 9.37 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=\frac {x^{8} + 12 \, x^{7} - 10 \, x^{6} - 706 \, x^{5} + 16 \, {\left (x^{4} - 8 \, x^{3} - 8 \, x + 1\right )} \log \left (2\right )^{4} - 3522 \, x^{4} - 32 \, {\left (x^{5} - 3 \, x^{4} - 40 \, x^{3} - 8 \, x^{2} - 39 \, x + 5\right )} \log \left (2\right )^{3} - 6208 \, x^{3} + 8 \, {\left (3 \, x^{6} + 6 \, x^{5} - 165 \, x^{4} - 623 \, x^{3} - 241 \, x^{2} - 569 \, x + 75\right )} \log \left (2\right )^{2} - 4029 \, x^{2} - 8 \, {\left (x^{7} + 7 \, x^{6} - 45 \, x^{5} - 482 \, x^{4} - 1118 \, x^{3} - 604 \, x^{2} - 920 \, x + 125\right )} \log \left (2\right ) - 4450 \, x + 625}{x^{6} + 16 \, x^{2} \log \left (2\right )^{4} + 20 \, x^{5} + 150 \, x^{4} - 32 \, {\left (x^{3} + 5 \, x^{2}\right )} \log \left (2\right )^{3} + 500 \, x^{3} + 24 \, {\left (x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )} \log \left (2\right )^{2} + 625 \, x^{2} - 8 \, {\left (x^{5} + 15 \, x^{4} + 75 \, x^{3} + 125 \, x^{2}\right )} \log \left (2\right )} \] Input:
integrate((32*(2*x^4-8*x^3+8*x-2)*log(2)^5+16*(-10*x^5-10*x^4+200*x^3-40*x ^2-190*x+50)*log(2)^4+8*(20*x^6+120*x^5-300*x^4-1918*x^3+780*x^2+1798*x-50 0)*log(2)^3+4*(-20*x^7-220*x^6-300*x^5+3418*x^4+8774*x^3-5690*x^2-8470*x+2 500)*log(2)^2+2*(10*x^8+160*x^7+700*x^6-962*x^5-12908*x^4-18904*x^3+18400* x^2+19850*x-6250)*log(2)-2*x^9-42*x^8-300*x^7-506*x^6+3546*x^5+16596*x^4+1 4924*x^3-22250*x^2-18500*x+6250)/(32*x^3*log(2)^5+16*(-5*x^4-25*x^3)*log(2 )^4+8*(10*x^5+100*x^4+250*x^3)*log(2)^3+4*(-10*x^6-150*x^5-750*x^4-1250*x^ 3)*log(2)^2+2*(5*x^7+100*x^6+750*x^5+2500*x^4+3125*x^3)*log(2)-x^8-25*x^7- 250*x^6-1250*x^5-3125*x^4-3125*x^3),x, algorithm="fricas")
Output:
(x^8 + 12*x^7 - 10*x^6 - 706*x^5 + 16*(x^4 - 8*x^3 - 8*x + 1)*log(2)^4 - 3 522*x^4 - 32*(x^5 - 3*x^4 - 40*x^3 - 8*x^2 - 39*x + 5)*log(2)^3 - 6208*x^3 + 8*(3*x^6 + 6*x^5 - 165*x^4 - 623*x^3 - 241*x^2 - 569*x + 75)*log(2)^2 - 4029*x^2 - 8*(x^7 + 7*x^6 - 45*x^5 - 482*x^4 - 1118*x^3 - 604*x^2 - 920*x + 125)*log(2) - 4450*x + 625)/(x^6 + 16*x^2*log(2)^4 + 20*x^5 + 150*x^4 - 32*(x^3 + 5*x^2)*log(2)^3 + 500*x^3 + 24*(x^4 + 10*x^3 + 25*x^2)*log(2)^2 + 625*x^2 - 8*(x^5 + 15*x^4 + 75*x^3 + 125*x^2)*log(2))
Leaf count of result is larger than twice the leaf count of optimal. 202 vs. \(2 (24) = 48\).
Time = 6.48 (sec) , antiderivative size = 202, normalized size of antiderivative = 7.48 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=x^{2} - 8 x + \frac {- 6 x^{5} + x^{4} \left (-147 + 56 \log {\left (2 \right )}\right ) + x^{3} \left (-1208 - 184 \log {\left (2 \right )}^{2} + 944 \log {\left (2 \right )}\right ) + x^{2} \left (-4029 - 1928 \log {\left (2 \right )}^{2} + 256 \log {\left (2 \right )}^{3} + 4832 \log {\left (2 \right )}\right ) + x \left (-4450 - 4552 \log {\left (2 \right )}^{2} - 128 \log {\left (2 \right )}^{4} + 1248 \log {\left (2 \right )}^{3} + 7360 \log {\left (2 \right )}\right ) - 1000 \log {\left (2 \right )} - 160 \log {\left (2 \right )}^{3} + 16 \log {\left (2 \right )}^{4} + 600 \log {\left (2 \right )}^{2} + 625}{x^{6} + x^{5} \cdot \left (20 - 8 \log {\left (2 \right )}\right ) + x^{4} \left (- 120 \log {\left (2 \right )} + 24 \log {\left (2 \right )}^{2} + 150\right ) + x^{3} \left (- 600 \log {\left (2 \right )} - 32 \log {\left (2 \right )}^{3} + 240 \log {\left (2 \right )}^{2} + 500\right ) + x^{2} \left (- 1000 \log {\left (2 \right )} - 160 \log {\left (2 \right )}^{3} + 16 \log {\left (2 \right )}^{4} + 600 \log {\left (2 \right )}^{2} + 625\right )} \] Input:
integrate((32*(2*x**4-8*x**3+8*x-2)*ln(2)**5+16*(-10*x**5-10*x**4+200*x**3 -40*x**2-190*x+50)*ln(2)**4+8*(20*x**6+120*x**5-300*x**4-1918*x**3+780*x** 2+1798*x-500)*ln(2)**3+4*(-20*x**7-220*x**6-300*x**5+3418*x**4+8774*x**3-5 690*x**2-8470*x+2500)*ln(2)**2+2*(10*x**8+160*x**7+700*x**6-962*x**5-12908 *x**4-18904*x**3+18400*x**2+19850*x-6250)*ln(2)-2*x**9-42*x**8-300*x**7-50 6*x**6+3546*x**5+16596*x**4+14924*x**3-22250*x**2-18500*x+6250)/(32*x**3*l n(2)**5+16*(-5*x**4-25*x**3)*ln(2)**4+8*(10*x**5+100*x**4+250*x**3)*ln(2)* *3+4*(-10*x**6-150*x**5-750*x**4-1250*x**3)*ln(2)**2+2*(5*x**7+100*x**6+75 0*x**5+2500*x**4+3125*x**3)*ln(2)-x**8-25*x**7-250*x**6-1250*x**5-3125*x** 4-3125*x**3),x)
Output:
x**2 - 8*x + (-6*x**5 + x**4*(-147 + 56*log(2)) + x**3*(-1208 - 184*log(2) **2 + 944*log(2)) + x**2*(-4029 - 1928*log(2)**2 + 256*log(2)**3 + 4832*lo g(2)) + x*(-4450 - 4552*log(2)**2 - 128*log(2)**4 + 1248*log(2)**3 + 7360* log(2)) - 1000*log(2) - 160*log(2)**3 + 16*log(2)**4 + 600*log(2)**2 + 625 )/(x**6 + x**5*(20 - 8*log(2)) + x**4*(-120*log(2) + 24*log(2)**2 + 150) + x**3*(-600*log(2) - 32*log(2)**3 + 240*log(2)**2 + 500) + x**2*(-1000*log (2) - 160*log(2)**3 + 16*log(2)**4 + 600*log(2)**2 + 625))
Leaf count of result is larger than twice the leaf count of optimal. 201 vs. \(2 (27) = 54\).
Time = 0.05 (sec) , antiderivative size = 201, normalized size of antiderivative = 7.44 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=x^{2} - 8 \, x - \frac {6 \, x^{5} - 7 \, x^{4} {\left (8 \, \log \left (2\right ) - 21\right )} + 8 \, {\left (23 \, \log \left (2\right )^{2} - 118 \, \log \left (2\right ) + 151\right )} x^{3} - 16 \, \log \left (2\right )^{4} - {\left (256 \, \log \left (2\right )^{3} - 1928 \, \log \left (2\right )^{2} + 4832 \, \log \left (2\right ) - 4029\right )} x^{2} + 160 \, \log \left (2\right )^{3} + 2 \, {\left (64 \, \log \left (2\right )^{4} - 624 \, \log \left (2\right )^{3} + 2276 \, \log \left (2\right )^{2} - 3680 \, \log \left (2\right ) + 2225\right )} x - 600 \, \log \left (2\right )^{2} + 1000 \, \log \left (2\right ) - 625}{x^{6} - 4 \, x^{5} {\left (2 \, \log \left (2\right ) - 5\right )} + 6 \, {\left (4 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 25\right )} x^{4} - 4 \, {\left (8 \, \log \left (2\right )^{3} - 60 \, \log \left (2\right )^{2} + 150 \, \log \left (2\right ) - 125\right )} x^{3} + {\left (16 \, \log \left (2\right )^{4} - 160 \, \log \left (2\right )^{3} + 600 \, \log \left (2\right )^{2} - 1000 \, \log \left (2\right ) + 625\right )} x^{2}} \] Input:
integrate((32*(2*x^4-8*x^3+8*x-2)*log(2)^5+16*(-10*x^5-10*x^4+200*x^3-40*x ^2-190*x+50)*log(2)^4+8*(20*x^6+120*x^5-300*x^4-1918*x^3+780*x^2+1798*x-50 0)*log(2)^3+4*(-20*x^7-220*x^6-300*x^5+3418*x^4+8774*x^3-5690*x^2-8470*x+2 500)*log(2)^2+2*(10*x^8+160*x^7+700*x^6-962*x^5-12908*x^4-18904*x^3+18400* x^2+19850*x-6250)*log(2)-2*x^9-42*x^8-300*x^7-506*x^6+3546*x^5+16596*x^4+1 4924*x^3-22250*x^2-18500*x+6250)/(32*x^3*log(2)^5+16*(-5*x^4-25*x^3)*log(2 )^4+8*(10*x^5+100*x^4+250*x^3)*log(2)^3+4*(-10*x^6-150*x^5-750*x^4-1250*x^ 3)*log(2)^2+2*(5*x^7+100*x^6+750*x^5+2500*x^4+3125*x^3)*log(2)-x^8-25*x^7- 250*x^6-1250*x^5-3125*x^4-3125*x^3),x, algorithm="maxima")
Output:
x^2 - 8*x - (6*x^5 - 7*x^4*(8*log(2) - 21) + 8*(23*log(2)^2 - 118*log(2) + 151)*x^3 - 16*log(2)^4 - (256*log(2)^3 - 1928*log(2)^2 + 4832*log(2) - 40 29)*x^2 + 160*log(2)^3 + 2*(64*log(2)^4 - 624*log(2)^3 + 2276*log(2)^2 - 3 680*log(2) + 2225)*x - 600*log(2)^2 + 1000*log(2) - 625)/(x^6 - 4*x^5*(2*l og(2) - 5) + 6*(4*log(2)^2 - 20*log(2) + 25)*x^4 - 4*(8*log(2)^3 - 60*log( 2)^2 + 150*log(2) - 125)*x^3 + (16*log(2)^4 - 160*log(2)^3 + 600*log(2)^2 - 1000*log(2) + 625)*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 181 vs. \(2 (27) = 54\).
Time = 0.13 (sec) , antiderivative size = 181, normalized size of antiderivative = 6.70 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=x^{2} - 8 \, x - \frac {32 \, x \log \left (2\right )^{2} - 160 \, x \log \left (2\right ) - 4 \, \log \left (2\right )^{2} + 198 \, x + 20 \, \log \left (2\right ) - 25}{{\left (4 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 25\right )} x^{2}} + \frac {8 \, x^{3} \log \left (2\right )^{2} - 32 \, x^{2} \log \left (2\right )^{3} + 32 \, x \log \left (2\right )^{4} - 40 \, x^{3} \log \left (2\right ) + 208 \, x^{2} \log \left (2\right )^{2} - 192 \, x \log \left (2\right )^{3} - 128 \, \log \left (2\right )^{4} + 48 \, x^{3} - 424 \, x^{2} \log \left (2\right ) + 200 \, x \log \left (2\right )^{2} + 1312 \, \log \left (2\right )^{3} + 260 \, x^{2} + 600 \, x \log \left (2\right ) - 5036 \, \log \left (2\right )^{2} - 1000 \, x + 8580 \, \log \left (2\right ) - 5475}{{\left (4 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 25\right )} {\left (x - 2 \, \log \left (2\right ) + 5\right )}^{4}} \] Input:
integrate((32*(2*x^4-8*x^3+8*x-2)*log(2)^5+16*(-10*x^5-10*x^4+200*x^3-40*x ^2-190*x+50)*log(2)^4+8*(20*x^6+120*x^5-300*x^4-1918*x^3+780*x^2+1798*x-50 0)*log(2)^3+4*(-20*x^7-220*x^6-300*x^5+3418*x^4+8774*x^3-5690*x^2-8470*x+2 500)*log(2)^2+2*(10*x^8+160*x^7+700*x^6-962*x^5-12908*x^4-18904*x^3+18400* x^2+19850*x-6250)*log(2)-2*x^9-42*x^8-300*x^7-506*x^6+3546*x^5+16596*x^4+1 4924*x^3-22250*x^2-18500*x+6250)/(32*x^3*log(2)^5+16*(-5*x^4-25*x^3)*log(2 )^4+8*(10*x^5+100*x^4+250*x^3)*log(2)^3+4*(-10*x^6-150*x^5-750*x^4-1250*x^ 3)*log(2)^2+2*(5*x^7+100*x^6+750*x^5+2500*x^4+3125*x^3)*log(2)-x^8-25*x^7- 250*x^6-1250*x^5-3125*x^4-3125*x^3),x, algorithm="giac")
Output:
x^2 - 8*x - (32*x*log(2)^2 - 160*x*log(2) - 4*log(2)^2 + 198*x + 20*log(2) - 25)/((4*log(2)^2 - 20*log(2) + 25)*x^2) + (8*x^3*log(2)^2 - 32*x^2*log( 2)^3 + 32*x*log(2)^4 - 40*x^3*log(2) + 208*x^2*log(2)^2 - 192*x*log(2)^3 - 128*log(2)^4 + 48*x^3 - 424*x^2*log(2) + 200*x*log(2)^2 + 1312*log(2)^3 + 260*x^2 + 600*x*log(2) - 5036*log(2)^2 - 1000*x + 8580*log(2) - 5475)/((4 *log(2)^2 - 20*log(2) + 25)*(x - 2*log(2) + 5)^4)
Time = 17.89 (sec) , antiderivative size = 67153, normalized size of antiderivative = 2487.15 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx=\text {Too large to display} \] Input:
int((18500*x + 16*log(2)^4*(190*x + 40*x^2 - 200*x^3 + 10*x^4 + 10*x^5 - 5 0) - 8*log(2)^3*(1798*x + 780*x^2 - 1918*x^3 - 300*x^4 + 120*x^5 + 20*x^6 - 500) - 2*log(2)*(19850*x + 18400*x^2 - 18904*x^3 - 12908*x^4 - 962*x^5 + 700*x^6 + 160*x^7 + 10*x^8 - 6250) + 4*log(2)^2*(8470*x + 5690*x^2 - 8774 *x^3 - 3418*x^4 + 300*x^5 + 220*x^6 + 20*x^7 - 2500) - 32*log(2)^5*(8*x - 8*x^3 + 2*x^4 - 2) + 22250*x^2 - 14924*x^3 - 16596*x^4 - 3546*x^5 + 506*x^ 6 + 300*x^7 + 42*x^8 + 2*x^9 - 6250)/(4*log(2)^2*(1250*x^3 + 750*x^4 + 150 *x^5 + 10*x^6) - 8*log(2)^3*(250*x^3 + 100*x^4 + 10*x^5) - 2*log(2)*(3125* x^3 + 2500*x^4 + 750*x^5 + 100*x^6 + 5*x^7) - 32*x^3*log(2)^5 + 3125*x^3 + 3125*x^4 + 1250*x^5 + 250*x^6 + 25*x^7 + x^8 + 16*log(2)^4*(25*x^3 + 5*x^ 4)),x)
Output:
symsum(log(10189632000*log(4) - 20379264000*log(2) - x*(5121515520*log(2) - 2560757760*log(4) - 183373189683200*log(2)*log(4) + 65070439264405760*lo g(2)*log(4)^2 - 130089547537717760*log(2)^2*log(4) + 300848175646856960*lo g(2)*log(4)^3 + 1554705236755399680*log(2)^3*log(4) + 3119888985694438080* log(2)*log(4)^4 - 29164899808895198720*log(2)^4*log(4) - 30351004986029232 00*log(2)*log(4)^5 + 31813267530887623680*log(2)^5*log(4) + 35676213669869 7920*log(2)*log(4)^6 + 21356986495361761280*log(2)^6*log(4) + 953392826051 81440*log(2)*log(4)^7 - 62613826035041566720*log(2)^7*log(4) - 22887718193 767040*log(2)*log(4)^8 + 53314422765398630400*log(2)^8*log(4) + 1571191660 405120*log(2)*log(4)^9 - 25007848806246563840*log(2)^9*log(4) - 3052984907 7120*log(2)*log(4)^10 + 7218364284413870080*log(2)^10*log(4) - 13716614784 0*log(2)*log(4)^11 - 1300088716591431680*log(2)^11*log(4) + 1557028800*log (2)*log(4)^12 + 139923667605258240*log(2)^12*log(4) - 23129280*log(2)*log( 4)^13 - 7992880629022720*log(2)^13*log(4) + 492480*log(2)*log(4)^14 + 1759 83600599040*log(2)^14*log(4) + 183367415756800*log(2)^2 + 8669214810127872 0*log(2)^3 - 865469177042723840*log(2)^4 + 45844740902400*log(4)^2 + 12357 128329472556032*log(2)^5 - 10849351260433280*log(4)^3 - 182533857083338956 80*log(2)^6 - 32134789989896640*log(4)^4 + 2226341505819074560*log(2)^7 - 298508110387303136*log(4)^5 + 15734200043962777600*log(2)^8 + 345550159922 333280*log(4)^6 - 17317193418711449600*log(2)^9 - 110941231732000480*lo...
Time = 0.18 (sec) , antiderivative size = 429, normalized size of antiderivative = 15.89 \[ \int \frac {6250-18500 x-22250 x^2+14924 x^3+16596 x^4+3546 x^5-506 x^6-300 x^7-42 x^8-2 x^9+\left (-6250+19850 x+18400 x^2-18904 x^3-12908 x^4-962 x^5+700 x^6+160 x^7+10 x^8\right ) \log (4)+\left (2500-8470 x-5690 x^2+8774 x^3+3418 x^4-300 x^5-220 x^6-20 x^7\right ) \log ^2(4)+\left (-500+1798 x+780 x^2-1918 x^3-300 x^4+120 x^5+20 x^6\right ) \log ^3(4)+\left (50-190 x-40 x^2+200 x^3-10 x^4-10 x^5\right ) \log ^4(4)+\left (-2+8 x-8 x^3+2 x^4\right ) \log ^5(4)}{-3125 x^3-3125 x^4-1250 x^5-250 x^6-25 x^7-x^8+\left (3125 x^3+2500 x^4+750 x^5+100 x^6+5 x^7\right ) \log (4)+\left (-1250 x^3-750 x^4-150 x^5-10 x^6\right ) \log ^2(4)+\left (250 x^3+100 x^4+10 x^5\right ) \log ^3(4)+\left (-25 x^3-5 x^4\right ) \log ^4(4)+x^3 \log ^5(4)} \, dx =\text {Too large to display} \] Input:
int((32*(2*x^4-8*x^3+8*x-2)*log(2)^5+16*(-10*x^5-10*x^4+200*x^3-40*x^2-190 *x+50)*log(2)^4+8*(20*x^6+120*x^5-300*x^4-1918*x^3+780*x^2+1798*x-500)*log (2)^3+4*(-20*x^7-220*x^6-300*x^5+3418*x^4+8774*x^3-5690*x^2-8470*x+2500)*l og(2)^2+2*(10*x^8+160*x^7+700*x^6-962*x^5-12908*x^4-18904*x^3+18400*x^2+19 850*x-6250)*log(2)-2*x^9-42*x^8-300*x^7-506*x^6+3546*x^5+16596*x^4+14924*x ^3-22250*x^2-18500*x+6250)/(32*x^3*log(2)^5+16*(-5*x^4-25*x^3)*log(2)^4+8* (10*x^5+100*x^4+250*x^3)*log(2)^3+4*(-10*x^6-150*x^5-750*x^4-1250*x^3)*log (2)^2+2*(5*x^7+100*x^6+750*x^5+2500*x^4+3125*x^3)*log(2)-x^8-25*x^7-250*x^ 6-1250*x^5-3125*x^4-3125*x^3),x)
Output:
( - 256*log(2)**7*x**2 + 512*log(2)**6*x**3 + 2944*log(2)**6*x**2 - 320*lo g(2)**5*x**4 - 5120*log(2)**5*x**3 - 10560*log(2)**5*x**2 - 512*log(2)**5* x + 64*log(2)**5 + 2720*log(2)**4*x**4 + 16000*log(2)**4*x**3 - 3024*log(2 )**4*x**2 + 6272*log(2)**4*x - 800*log(2)**4 + 80*log(2)**3*x**6 - 7200*lo g(2)**3*x**4 - 640*log(2)**3*x**3 + 120208*log(2)**3*x**2 - 30688*log(2)** 3*x + 4000*log(2)**3 - 32*log(2)**2*x**7 - 440*log(2)**2*x**6 + 2152*log(2 )**2*x**4 - 95104*log(2)**2*x**3 - 338192*log(2)**2*x**2 + 74960*log(2)**2 *x - 10000*log(2)**2 + 4*log(2)*x**8 + 128*log(2)*x**7 + 700*log(2)*x**6 + 16712*log(2)*x**4 + 187528*log(2)*x**3 + 401064*log(2)*x**2 - 91400*log(2 )*x + 12500*log(2) - 10*x**8 - 120*x**7 - 253*x**6 - 17730*x**4 - 114420*x **3 - 180335*x**2 + 44500*x - 6250)/(2*x**2*(32*log(2)**5 - 64*log(2)**4*x - 400*log(2)**4 + 48*log(2)**3*x**2 + 640*log(2)**3*x + 2000*log(2)**3 - 16*log(2)**2*x**3 - 360*log(2)**2*x**2 - 2400*log(2)**2*x - 5000*log(2)**2 + 2*log(2)*x**4 + 80*log(2)*x**3 + 900*log(2)*x**2 + 4000*log(2)*x + 6250 *log(2) - 5*x**4 - 100*x**3 - 750*x**2 - 2500*x - 3125))