Integrand size = 315, antiderivative size = 28 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=-x+25 (5+\log (2))^2 \left (8+x-\frac {x}{5 \log \left (x^2\right )}\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(129\) vs. \(2(28)=56\).
Time = 1.06 (sec) , antiderivative size = 129, normalized size of antiderivative = 4.61 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=x \left (1279999+512000 \log (2)+51200 \log ^2(2)+9600 x (5+\log (2))^2+800 x^2 (5+\log (2))^2+25 x^3 (5+\log (2))^2\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {4 x^3 (8+x) (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {6 x^2 (8+x)^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {20 x (8+x)^3 (5+\log (2))^2}{\log \left (x^2\right )} \]
Integrate[(-200*x^3 - 80*x^3*Log[2] - 8*x^3*Log[2]^2 + (24000*x^2 + 3100*x ^3 + (9600*x^2 + 1240*x^3)*Log[2] + (960*x^2 + 124*x^3)*Log[2]^2)*Log[x^2] + (-960000*x - 252000*x^2 - 17000*x^3 + (-384000*x - 100800*x^2 - 6800*x^ 3)*Log[2] + (-38400*x - 10080*x^2 - 680*x^3)*Log[2]^2)*Log[x^2]^2 + (12800 000 + 5280000*x + 780000*x^2 + 40000*x^3 + (5120000 + 2112000*x + 312000*x ^2 + 16000*x^3)*Log[2] + (512000 + 211200*x + 31200*x^2 + 1600*x^3)*Log[2] ^2)*Log[x^2]^3 + (-6400000 - 4800000*x - 900000*x^2 - 50000*x^3 + (-256000 0 - 1920000*x - 360000*x^2 - 20000*x^3)*Log[2] + (-256000 - 192000*x - 360 00*x^2 - 2000*x^3)*Log[2]^2)*Log[x^2]^4 + (31999975 + 12000000*x + 1500000 *x^2 + 62500*x^3 + (12800000 + 4800000*x + 600000*x^2 + 25000*x^3)*Log[2] + (1280000 + 480000*x + 60000*x^2 + 2500*x^3)*Log[2]^2)*Log[x^2]^5)/(25*Lo g[x^2]^5),x]
x*(1279999 + 512000*Log[2] + 51200*Log[2]^2 + 9600*x*(5 + Log[2])^2 + 800* x^2*(5 + Log[2])^2 + 25*x^3*(5 + Log[2])^2) + (x^4*(5 + Log[2])^2)/(25*Log [x^2]^4) - (4*x^3*(8 + x)*(5 + Log[2])^2)/(5*Log[x^2]^3) + (6*x^2*(8 + x)^ 2*(5 + Log[2])^2)/Log[x^2]^2 - (20*x*(8 + x)^3*(5 + Log[2])^2)/Log[x^2]
Leaf count is larger than twice the leaf count of optimal. \(220\) vs. \(2(28)=56\).
Time = 1.22 (sec) , antiderivative size = 220, normalized size of antiderivative = 7.86, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6, 6, 27, 25, 7239, 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.
| \(\displaystyle \int \frac {-200 x^3-8 x^3 \log ^2(2)-80 x^3 \log (2)+\left (-17000 x^3-252000 x^2+\left (-680 x^3-10080 x^2-38400 x\right ) \log ^2(2)+\left (-6800 x^3-100800 x^2-384000 x\right ) \log (2)-960000 x\right ) \log ^2\left (x^2\right )+\left (3100 x^3+24000 x^2+\left (124 x^3+960 x^2\right ) \log ^2(2)+\left (1240 x^3+9600 x^2\right ) \log (2)\right ) \log \left (x^2\right )+\left (62500 x^3+1500000 x^2+\left (2500 x^3+60000 x^2+480000 x+1280000\right ) \log ^2(2)+\left (25000 x^3+600000 x^2+4800000 x+12800000\right ) \log (2)+12000000 x+31999975\right ) \log ^5\left (x^2\right )+\left (-50000 x^3-900000 x^2+\left (-2000 x^3-36000 x^2-192000 x-256000\right ) \log ^2(2)+\left (-20000 x^3-360000 x^2-1920000 x-2560000\right ) \log (2)-4800000 x-6400000\right ) \log ^4\left (x^2\right )+\left (40000 x^3+780000 x^2+\left (1600 x^3+31200 x^2+211200 x+512000\right ) \log ^2(2)+\left (16000 x^3+312000 x^2+2112000 x+5120000\right ) \log (2)+5280000 x+12800000\right ) \log ^3\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-8 x^3 \log ^2(2)+x^3 (-200-80 \log (2))+\left (-17000 x^3-252000 x^2+\left (-680 x^3-10080 x^2-38400 x\right ) \log ^2(2)+\left (-6800 x^3-100800 x^2-384000 x\right ) \log (2)-960000 x\right ) \log ^2\left (x^2\right )+\left (3100 x^3+24000 x^2+\left (124 x^3+960 x^2\right ) \log ^2(2)+\left (1240 x^3+9600 x^2\right ) \log (2)\right ) \log \left (x^2\right )+\left (62500 x^3+1500000 x^2+\left (2500 x^3+60000 x^2+480000 x+1280000\right ) \log ^2(2)+\left (25000 x^3+600000 x^2+4800000 x+12800000\right ) \log (2)+12000000 x+31999975\right ) \log ^5\left (x^2\right )+\left (-50000 x^3-900000 x^2+\left (-2000 x^3-36000 x^2-192000 x-256000\right ) \log ^2(2)+\left (-20000 x^3-360000 x^2-1920000 x-2560000\right ) \log (2)-4800000 x-6400000\right ) \log ^4\left (x^2\right )+\left (40000 x^3+780000 x^2+\left (1600 x^3+31200 x^2+211200 x+512000\right ) \log ^2(2)+\left (16000 x^3+312000 x^2+2112000 x+5120000\right ) \log (2)+5280000 x+12800000\right ) \log ^3\left (x^2\right )}{25 \log ^5\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x^3 \left (-200-8 \log ^2(2)-80 \log (2)\right )+\left (-17000 x^3-252000 x^2+\left (-680 x^3-10080 x^2-38400 x\right ) \log ^2(2)+\left (-6800 x^3-100800 x^2-384000 x\right ) \log (2)-960000 x\right ) \log ^2\left (x^2\right )+\left (3100 x^3+24000 x^2+\left (124 x^3+960 x^2\right ) \log ^2(2)+\left (1240 x^3+9600 x^2\right ) \log (2)\right ) \log \left (x^2\right )+\left (62500 x^3+1500000 x^2+\left (2500 x^3+60000 x^2+480000 x+1280000\right ) \log ^2(2)+\left (25000 x^3+600000 x^2+4800000 x+12800000\right ) \log (2)+12000000 x+31999975\right ) \log ^5\left (x^2\right )+\left (-50000 x^3-900000 x^2+\left (-2000 x^3-36000 x^2-192000 x-256000\right ) \log ^2(2)+\left (-20000 x^3-360000 x^2-1920000 x-2560000\right ) \log (2)-4800000 x-6400000\right ) \log ^4\left (x^2\right )+\left (40000 x^3+780000 x^2+\left (1600 x^3+31200 x^2+211200 x+512000\right ) \log ^2(2)+\left (16000 x^3+312000 x^2+2112000 x+5120000\right ) \log (2)+5280000 x+12800000\right ) \log ^3\left (x^2\right )}{25 \log ^5\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{25} \int -\frac {-25 \left (2500 x^3+60000 x^2+480000 x+100 \left (x^3+24 x^2+192 x+512\right ) \log ^2(2)+1000 \left (x^3+24 x^2+192 x+512\right ) \log (2)+1279999\right ) \log ^5\left (x^2\right )+2000 \left (25 x^3+450 x^2+2400 x+\left (x^3+18 x^2+96 x+128\right ) \log ^2(2)+10 \left (x^3+18 x^2+96 x+128\right ) \log (2)+3200\right ) \log ^4\left (x^2\right )-800 \left (50 x^3+975 x^2+6600 x+\left (2 x^3+39 x^2+264 x+640\right ) \log ^2(2)+10 \left (2 x^3+39 x^2+264 x+640\right ) \log (2)+16000\right ) \log ^3\left (x^2\right )+40 \left (425 x^3+6300 x^2+24000 x+\left (17 x^3+252 x^2+960 x\right ) \log ^2(2)+10 \left (17 x^3+252 x^2+960 x\right ) \log (2)\right ) \log ^2\left (x^2\right )-4 \left (775 x^3+6000 x^2+\left (31 x^3+240 x^2\right ) \log ^2(2)+10 \left (31 x^3+240 x^2\right ) \log (2)\right ) \log \left (x^2\right )+8 x^3 (5+\log (2))^2}{\log ^5\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{25} \int \frac {-25 \left (2500 x^3+60000 x^2+480000 x+100 \left (x^3+24 x^2+192 x+512\right ) \log ^2(2)+1000 \left (x^3+24 x^2+192 x+512\right ) \log (2)+1279999\right ) \log ^5\left (x^2\right )+2000 \left (25 x^3+450 x^2+2400 x+\left (x^3+18 x^2+96 x+128\right ) \log ^2(2)+10 \left (x^3+18 x^2+96 x+128\right ) \log (2)+3200\right ) \log ^4\left (x^2\right )-800 \left (50 x^3+975 x^2+6600 x+\left (2 x^3+39 x^2+264 x+640\right ) \log ^2(2)+10 \left (2 x^3+39 x^2+264 x+640\right ) \log (2)+16000\right ) \log ^3\left (x^2\right )+40 \left (425 x^3+6300 x^2+24000 x+\left (17 x^3+252 x^2+960 x\right ) \log ^2(2)+10 \left (17 x^3+252 x^2+960 x\right ) \log (2)\right ) \log ^2\left (x^2\right )-4 \left (775 x^3+6000 x^2+\left (31 x^3+240 x^2\right ) \log ^2(2)+10 \left (31 x^3+240 x^2\right ) \log (2)\right ) \log \left (x^2\right )+8 x^3 (5+\log (2))^2}{\log ^5\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{25} \int \left (\frac {8 (5+\log (2))^2 x^3}{\log ^5\left (x^2\right )}-\frac {4 (31 x+240) (5+\log (2))^2 x^2}{\log ^4\left (x^2\right )}+\frac {40 \left (17 x^2+252 x+960\right ) (5+\log (2))^2 x}{\log ^3\left (x^2\right )}-25 \left (100 (5+\log (2))^2 x^3+2400 (5+\log (2))^2 x^2+19200 (5+\log (2))^2 x+51200 \log ^2(2)+512000 \log (2)+1279999\right )+\frac {2000 (x+2) (x+8)^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {800 \left (2 x^3+39 x^2+264 x+640\right ) (5+\log (2))^2}{\log ^2\left (x^2\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{25} \left (625 x^4 (5+\log (2))^2+20000 x^3 (5+\log (2))^2+\frac {9600 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {96000 x^2 (5+\log (2))^2}{\log \left (x^2\right )}+240000 x^2 (5+\log (2))^2-\frac {256000 x (5+\log (2))^2}{\log \left (x^2\right )}+\frac {x^4 (5+\log (2))^2}{\log ^4\left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log ^3\left (x^2\right )}+\frac {150 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {500 x^4 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {160 x^3 (5+\log (2))^2}{\log ^3\left (x^2\right )}+\frac {2400 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {12000 x^3 (5+\log (2))^2}{\log \left (x^2\right )}+25 x \left (1279999+51200 \log ^2(2)+512000 \log (2)\right )\right )\) |
Int[(-200*x^3 - 80*x^3*Log[2] - 8*x^3*Log[2]^2 + (24000*x^2 + 3100*x^3 + ( 9600*x^2 + 1240*x^3)*Log[2] + (960*x^2 + 124*x^3)*Log[2]^2)*Log[x^2] + (-9 60000*x - 252000*x^2 - 17000*x^3 + (-384000*x - 100800*x^2 - 6800*x^3)*Log [2] + (-38400*x - 10080*x^2 - 680*x^3)*Log[2]^2)*Log[x^2]^2 + (12800000 + 5280000*x + 780000*x^2 + 40000*x^3 + (5120000 + 2112000*x + 312000*x^2 + 1 6000*x^3)*Log[2] + (512000 + 211200*x + 31200*x^2 + 1600*x^3)*Log[2]^2)*Lo g[x^2]^3 + (-6400000 - 4800000*x - 900000*x^2 - 50000*x^3 + (-2560000 - 19 20000*x - 360000*x^2 - 20000*x^3)*Log[2] + (-256000 - 192000*x - 36000*x^2 - 2000*x^3)*Log[2]^2)*Log[x^2]^4 + (31999975 + 12000000*x + 1500000*x^2 + 62500*x^3 + (12800000 + 4800000*x + 600000*x^2 + 25000*x^3)*Log[2] + (128 0000 + 480000*x + 60000*x^2 + 2500*x^3)*Log[2]^2)*Log[x^2]^5)/(25*Log[x^2] ^5),x]
(240000*x^2*(5 + Log[2])^2 + 20000*x^3*(5 + Log[2])^2 + 625*x^4*(5 + Log[2 ])^2 + 25*x*(1279999 + 512000*Log[2] + 51200*Log[2]^2) + (x^4*(5 + Log[2]) ^2)/Log[x^2]^4 - (160*x^3*(5 + Log[2])^2)/Log[x^2]^3 - (20*x^4*(5 + Log[2] )^2)/Log[x^2]^3 + (9600*x^2*(5 + Log[2])^2)/Log[x^2]^2 + (2400*x^3*(5 + Lo g[2])^2)/Log[x^2]^2 + (150*x^4*(5 + Log[2])^2)/Log[x^2]^2 - (256000*x*(5 + Log[2])^2)/Log[x^2] - (96000*x^2*(5 + Log[2])^2)/Log[x^2] - (12000*x^3*(5 + Log[2])^2)/Log[x^2] - (500*x^4*(5 + Log[2])^2)/Log[x^2])/25
3.5.12.3.1 Defintions of rubi rules used
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_, 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. \(302\) vs. \(2(26)=52\).
Time = 1418.29 (sec) , antiderivative size = 303, normalized size of antiderivative = 10.82
| method | result | size |
| norman | \(\frac {\left (\frac {\ln \left (2\right )^{2}}{25}+\frac {2 \ln \left (2\right )}{5}+1\right ) x^{4}+\left (-96000-3840 \ln \left (2\right )^{2}-38400 \ln \left (2\right )\right ) x^{2} \ln \left (x^{2}\right )^{3}+\left (-12000-480 \ln \left (2\right )^{2}-4800 \ln \left (2\right )\right ) x^{3} \ln \left (x^{2}\right )^{3}+\left (-500-20 \ln \left (2\right )^{2}-200 \ln \left (2\right )\right ) x^{4} \ln \left (x^{2}\right )^{3}+\left (-20-\frac {4 \ln \left (2\right )^{2}}{5}-8 \ln \left (2\right )\right ) x^{4} \ln \left (x^{2}\right )+\left (150+6 \ln \left (2\right )^{2}+60 \ln \left (2\right )\right ) x^{4} \ln \left (x^{2}\right )^{2}+\left (2400+96 \ln \left (2\right )^{2}+960 \ln \left (2\right )\right ) x^{3} \ln \left (x^{2}\right )^{2}+\left (240000+9600 \ln \left (2\right )^{2}+96000 \ln \left (2\right )\right ) x^{2} \ln \left (x^{2}\right )^{4}+\left (-10240 \ln \left (2\right )^{2}-102400 \ln \left (2\right )-256000\right ) x \ln \left (x^{2}\right )^{3}+\left (25 \ln \left (2\right )^{2}+250 \ln \left (2\right )+625\right ) x^{4} \ln \left (x^{2}\right )^{4}+\left (384 \ln \left (2\right )^{2}+3840 \ln \left (2\right )+9600\right ) x^{2} \ln \left (x^{2}\right )^{2}+\left (800 \ln \left (2\right )^{2}+8000 \ln \left (2\right )+20000\right ) x^{3} \ln \left (x^{2}\right )^{4}+\left (51200 \ln \left (2\right )^{2}+512000 \ln \left (2\right )+1279999\right ) x \ln \left (x^{2}\right )^{4}+\left (-\frac {32 \ln \left (2\right )^{2}}{5}-64 \ln \left (2\right )-160\right ) x^{3} \ln \left (x^{2}\right )}{\ln \left (x^{2}\right )^{4}}\) | \(303\) |
| risch | \(25 x^{4} \ln \left (2\right )^{2}+800 x^{3} \ln \left (2\right )^{2}+250 x^{4} \ln \left (2\right )+9600 x^{2} \ln \left (2\right )^{2}+8000 x^{3} \ln \left (2\right )+625 x^{4}+51200 x \ln \left (2\right )^{2}+96000 x^{2} \ln \left (2\right )+20000 x^{3}+512000 x \ln \left (2\right )+240000 x^{2}+1279999 x -\frac {x \left (300000 x^{2} \ln \left (x^{2}\right )^{3}-3750 x^{3} \ln \left (x^{2}\right )^{2}+500 x^{3} \ln \left (x^{2}\right )-x^{3} \ln \left (2\right )^{2}-10 x^{3} \ln \left (2\right )+2400000 x \ln \left (x^{2}\right )^{3}+6400000 \ln \left (x^{2}\right )^{3}-60000 x^{2} \ln \left (x^{2}\right )^{2}-240000 x \ln \left (x^{2}\right )^{2}+4000 x^{2} \ln \left (x^{2}\right )-150 x^{3} \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2}-2400 x^{2} \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2}-25 x^{3}+500 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3} x^{3}+12000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3} x^{2}+5000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3} x^{3}+96000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3} x +20 \ln \left (2\right )^{2} \ln \left (x^{2}\right ) x^{3}+120000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3} x^{2}-1500 \ln \left (2\right ) \ln \left (x^{2}\right )^{2} x^{3}-9600 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2} x +160 \ln \left (2\right )^{2} \ln \left (x^{2}\right ) x^{2}+960000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3} x -24000 \ln \left (2\right ) \ln \left (x^{2}\right )^{2} x^{2}+200 \ln \left (2\right ) \ln \left (x^{2}\right ) x^{3}-96000 \ln \left (2\right ) \ln \left (x^{2}\right )^{2} x +1600 \ln \left (2\right ) \ln \left (x^{2}\right ) x^{2}+12500 \ln \left (x^{2}\right )^{3} x^{3}+256000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3}+2560000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3}\right )}{25 \ln \left (x^{2}\right )^{4}}\) | \(429\) |
| parallelrisch | \(\frac {63999950 x \ln \left (x^{2}\right )^{4}-4800000 x^{2} \ln \left (x^{2}\right )^{3}+120000 x^{3} \ln \left (x^{2}\right )^{2}-1000 x^{4} \ln \left (x^{2}\right )-8000 x^{3} \ln \left (x^{2}\right )+2 x^{4} \ln \left (2\right )^{2}+20 x^{4} \ln \left (2\right )-12800000 x \ln \left (x^{2}\right )^{3}+12000000 \ln \left (x^{2}\right )^{4} x^{2}+7500 x^{4} \ln \left (x^{2}\right )^{2}+480000 x^{2} \ln \left (x^{2}\right )^{2}+4800 x^{3} \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2}+19200 x^{2} \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2}+50 x^{4}+40000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{4} x^{3}+480000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{4} x^{2}-24000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3} x^{3}+400000 \ln \left (2\right ) \ln \left (x^{2}\right )^{4} x^{3}+2560000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{4} x -192000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3} x^{2}+4800000 \ln \left (2\right ) \ln \left (x^{2}\right )^{4} x^{2}-240000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3} x^{3}-512000 \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{3} x -320 \ln \left (2\right )^{2} \ln \left (x^{2}\right ) x^{3}+25600000 \ln \left (2\right ) \ln \left (x^{2}\right )^{4} x -1920000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3} x^{2}+48000 \ln \left (2\right ) \ln \left (x^{2}\right )^{2} x^{3}-5120000 \ln \left (2\right ) \ln \left (x^{2}\right )^{3} x +192000 \ln \left (2\right ) \ln \left (x^{2}\right )^{2} x^{2}-3200 \ln \left (2\right ) \ln \left (x^{2}\right ) x^{3}+1000000 \ln \left (x^{2}\right )^{4} x^{3}-600000 \ln \left (x^{2}\right )^{3} x^{3}-400 \ln \left (2\right ) x^{4} \ln \left (x^{2}\right )+3000 \ln \left (2\right ) x^{4} \ln \left (x^{2}\right )^{2}-10000 \ln \left (2\right ) x^{4} \ln \left (x^{2}\right )^{3}+12500 \ln \left (2\right ) x^{4} \ln \left (x^{2}\right )^{4}+31250 \ln \left (x^{2}\right )^{4} x^{4}-40 \ln \left (2\right )^{2} x^{4} \ln \left (x^{2}\right )+300 \ln \left (2\right )^{2} x^{4} \ln \left (x^{2}\right )^{2}-1000 \ln \left (2\right )^{2} x^{4} \ln \left (x^{2}\right )^{3}+1250 \ln \left (2\right )^{2} x^{4} \ln \left (x^{2}\right )^{4}-25000 x^{4} \ln \left (x^{2}\right )^{3}}{50 \ln \left (x^{2}\right )^{4}}\) | \(514\) |
int(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*ln(2)^2+(25000*x^3+600000 *x^2+4800000*x+12800000)*ln(2)+62500*x^3+1500000*x^2+12000000*x+31999975)* ln(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*ln(2)^2+(-20000*x^3-36000 0*x^2-1920000*x-2560000)*ln(2)-50000*x^3-900000*x^2-4800000*x-6400000)*ln( x^2)^4+((1600*x^3+31200*x^2+211200*x+512000)*ln(2)^2+(16000*x^3+312000*x^2 +2112000*x+5120000)*ln(2)+40000*x^3+780000*x^2+5280000*x+12800000)*ln(x^2) ^3+((-680*x^3-10080*x^2-38400*x)*ln(2)^2+(-6800*x^3-100800*x^2-384000*x)*l n(2)-17000*x^3-252000*x^2-960000*x)*ln(x^2)^2+((124*x^3+960*x^2)*ln(2)^2+( 1240*x^3+9600*x^2)*ln(2)+3100*x^3+24000*x^2)*ln(x^2)-8*x^3*ln(2)^2-80*x^3* ln(2)-200*x^3)/ln(x^2)^5,x,method=_RETURNVERBOSE)
((1/25*ln(2)^2+2/5*ln(2)+1)*x^4+(-96000-3840*ln(2)^2-38400*ln(2))*x^2*ln(x ^2)^3+(-12000-480*ln(2)^2-4800*ln(2))*x^3*ln(x^2)^3+(-500-20*ln(2)^2-200*l n(2))*x^4*ln(x^2)^3+(-20-4/5*ln(2)^2-8*ln(2))*x^4*ln(x^2)+(150+6*ln(2)^2+6 0*ln(2))*x^4*ln(x^2)^2+(2400+96*ln(2)^2+960*ln(2))*x^3*ln(x^2)^2+(240000+9 600*ln(2)^2+96000*ln(2))*x^2*ln(x^2)^4+(-10240*ln(2)^2-102400*ln(2)-256000 )*x*ln(x^2)^3+(25*ln(2)^2+250*ln(2)+625)*x^4*ln(x^2)^4+(384*ln(2)^2+3840*l n(2)+9600)*x^2*ln(x^2)^2+(800*ln(2)^2+8000*ln(2)+20000)*x^3*ln(x^2)^4+(512 00*ln(2)^2+512000*ln(2)+1279999)*x*ln(x^2)^4+(-32/5*ln(2)^2-64*ln(2)-160)* x^3*ln(x^2))/ln(x^2)^4
Leaf count of result is larger than twice the leaf count of optimal. 275 vs. \(2 (28) = 56\).
Time = 0.25 (sec) , antiderivative size = 275, normalized size of antiderivative = 9.82 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=\frac {x^{4} \log \left (2\right )^{2} + 10 \, x^{4} \log \left (2\right ) + 25 \, {\left (625 \, x^{4} + 20000 \, x^{3} + 25 \, {\left (x^{4} + 32 \, x^{3} + 384 \, x^{2} + 2048 \, x\right )} \log \left (2\right )^{2} + 240000 \, x^{2} + 250 \, {\left (x^{4} + 32 \, x^{3} + 384 \, x^{2} + 2048 \, x\right )} \log \left (2\right ) + 1279999 \, x\right )} \log \left (x^{2}\right )^{4} + 25 \, x^{4} - 500 \, {\left (25 \, x^{4} + 600 \, x^{3} + {\left (x^{4} + 24 \, x^{3} + 192 \, x^{2} + 512 \, x\right )} \log \left (2\right )^{2} + 4800 \, x^{2} + 10 \, {\left (x^{4} + 24 \, x^{3} + 192 \, x^{2} + 512 \, x\right )} \log \left (2\right ) + 12800 \, x\right )} \log \left (x^{2}\right )^{3} + 150 \, {\left (25 \, x^{4} + 400 \, x^{3} + {\left (x^{4} + 16 \, x^{3} + 64 \, x^{2}\right )} \log \left (2\right )^{2} + 1600 \, x^{2} + 10 \, {\left (x^{4} + 16 \, x^{3} + 64 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (x^{2}\right )^{2} - 20 \, {\left (25 \, x^{4} + 200 \, x^{3} + {\left (x^{4} + 8 \, x^{3}\right )} \log \left (2\right )^{2} + 10 \, {\left (x^{4} + 8 \, x^{3}\right )} \log \left (2\right )\right )} \log \left (x^{2}\right )}{25 \, \log \left (x^{2}\right )^{4}} \]
integrate(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*log(2)^2+(25000*x^3 +600000*x^2+4800000*x+12800000)*log(2)+62500*x^3+1500000*x^2+12000000*x+31 999975)*log(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*log(2)^2+(-20000 *x^3-360000*x^2-1920000*x-2560000)*log(2)-50000*x^3-900000*x^2-4800000*x-6 400000)*log(x^2)^4+((1600*x^3+31200*x^2+211200*x+512000)*log(2)^2+(16000*x ^3+312000*x^2+2112000*x+5120000)*log(2)+40000*x^3+780000*x^2+5280000*x+128 00000)*log(x^2)^3+((-680*x^3-10080*x^2-38400*x)*log(2)^2+(-6800*x^3-100800 *x^2-384000*x)*log(2)-17000*x^3-252000*x^2-960000*x)*log(x^2)^2+((124*x^3+ 960*x^2)*log(2)^2+(1240*x^3+9600*x^2)*log(2)+3100*x^3+24000*x^2)*log(x^2)- 8*x^3*log(2)^2-80*x^3*log(2)-200*x^3)/log(x^2)^5,x, algorithm=\
1/25*(x^4*log(2)^2 + 10*x^4*log(2) + 25*(625*x^4 + 20000*x^3 + 25*(x^4 + 3 2*x^3 + 384*x^2 + 2048*x)*log(2)^2 + 240000*x^2 + 250*(x^4 + 32*x^3 + 384* x^2 + 2048*x)*log(2) + 1279999*x)*log(x^2)^4 + 25*x^4 - 500*(25*x^4 + 600* x^3 + (x^4 + 24*x^3 + 192*x^2 + 512*x)*log(2)^2 + 4800*x^2 + 10*(x^4 + 24* x^3 + 192*x^2 + 512*x)*log(2) + 12800*x)*log(x^2)^3 + 150*(25*x^4 + 400*x^ 3 + (x^4 + 16*x^3 + 64*x^2)*log(2)^2 + 1600*x^2 + 10*(x^4 + 16*x^3 + 64*x^ 2)*log(2))*log(x^2)^2 - 20*(25*x^4 + 200*x^3 + (x^4 + 8*x^3)*log(2)^2 + 10 *(x^4 + 8*x^3)*log(2))*log(x^2))/log(x^2)^4
Leaf count of result is larger than twice the leaf count of optimal. 326 vs. \(2 (22) = 44\).
Time = 0.19 (sec) , antiderivative size = 326, normalized size of antiderivative = 11.64 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=x^{4} \cdot \left (25 \log {\left (2 \right )}^{2} + 250 \log {\left (2 \right )} + 625\right ) + x^{3} \cdot \left (800 \log {\left (2 \right )}^{2} + 8000 \log {\left (2 \right )} + 20000\right ) + x^{2} \cdot \left (9600 \log {\left (2 \right )}^{2} + 96000 \log {\left (2 \right )} + 240000\right ) + x \left (51200 \log {\left (2 \right )}^{2} + 512000 \log {\left (2 \right )} + 1279999\right ) + \frac {x^{4} \log {\left (2 \right )}^{2} + 10 x^{4} \log {\left (2 \right )} + 25 x^{4} + \left (- 500 x^{4} - 200 x^{4} \log {\left (2 \right )} - 20 x^{4} \log {\left (2 \right )}^{2} - 4000 x^{3} - 1600 x^{3} \log {\left (2 \right )} - 160 x^{3} \log {\left (2 \right )}^{2}\right ) \log {\left (x^{2} \right )} + \left (150 x^{4} \log {\left (2 \right )}^{2} + 1500 x^{4} \log {\left (2 \right )} + 3750 x^{4} + 2400 x^{3} \log {\left (2 \right )}^{2} + 24000 x^{3} \log {\left (2 \right )} + 60000 x^{3} + 9600 x^{2} \log {\left (2 \right )}^{2} + 96000 x^{2} \log {\left (2 \right )} + 240000 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (- 12500 x^{4} - 5000 x^{4} \log {\left (2 \right )} - 500 x^{4} \log {\left (2 \right )}^{2} - 300000 x^{3} - 120000 x^{3} \log {\left (2 \right )} - 12000 x^{3} \log {\left (2 \right )}^{2} - 2400000 x^{2} - 960000 x^{2} \log {\left (2 \right )} - 96000 x^{2} \log {\left (2 \right )}^{2} - 6400000 x - 2560000 x \log {\left (2 \right )} - 256000 x \log {\left (2 \right )}^{2}\right ) \log {\left (x^{2} \right )}^{3}}{25 \log {\left (x^{2} \right )}^{4}} \]
integrate(1/25*(((2500*x**3+60000*x**2+480000*x+1280000)*ln(2)**2+(25000*x **3+600000*x**2+4800000*x+12800000)*ln(2)+62500*x**3+1500000*x**2+12000000 *x+31999975)*ln(x**2)**5+((-2000*x**3-36000*x**2-192000*x-256000)*ln(2)**2 +(-20000*x**3-360000*x**2-1920000*x-2560000)*ln(2)-50000*x**3-900000*x**2- 4800000*x-6400000)*ln(x**2)**4+((1600*x**3+31200*x**2+211200*x+512000)*ln( 2)**2+(16000*x**3+312000*x**2+2112000*x+5120000)*ln(2)+40000*x**3+780000*x **2+5280000*x+12800000)*ln(x**2)**3+((-680*x**3-10080*x**2-38400*x)*ln(2)* *2+(-6800*x**3-100800*x**2-384000*x)*ln(2)-17000*x**3-252000*x**2-960000*x )*ln(x**2)**2+((124*x**3+960*x**2)*ln(2)**2+(1240*x**3+9600*x**2)*ln(2)+31 00*x**3+24000*x**2)*ln(x**2)-8*x**3*ln(2)**2-80*x**3*ln(2)-200*x**3)/ln(x* *2)**5,x)
x**4*(25*log(2)**2 + 250*log(2) + 625) + x**3*(800*log(2)**2 + 8000*log(2) + 20000) + x**2*(9600*log(2)**2 + 96000*log(2) + 240000) + x*(51200*log(2 )**2 + 512000*log(2) + 1279999) + (x**4*log(2)**2 + 10*x**4*log(2) + 25*x* *4 + (-500*x**4 - 200*x**4*log(2) - 20*x**4*log(2)**2 - 4000*x**3 - 1600*x **3*log(2) - 160*x**3*log(2)**2)*log(x**2) + (150*x**4*log(2)**2 + 1500*x* *4*log(2) + 3750*x**4 + 2400*x**3*log(2)**2 + 24000*x**3*log(2) + 60000*x* *3 + 9600*x**2*log(2)**2 + 96000*x**2*log(2) + 240000*x**2)*log(x**2)**2 + (-12500*x**4 - 5000*x**4*log(2) - 500*x**4*log(2)**2 - 300000*x**3 - 1200 00*x**3*log(2) - 12000*x**3*log(2)**2 - 2400000*x**2 - 960000*x**2*log(2) - 96000*x**2*log(2)**2 - 6400000*x - 2560000*x*log(2) - 256000*x*log(2)**2 )*log(x**2)**3)/(25*log(x**2)**4)
Leaf count of result is larger than twice the leaf count of optimal. 249 vs. \(2 (28) = 56\).
Time = 0.32 (sec) , antiderivative size = 249, normalized size of antiderivative = 8.89 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=25 \, x^{4} \log \left (2\right )^{2} + 250 \, x^{4} \log \left (2\right ) + 800 \, x^{3} \log \left (2\right )^{2} + 625 \, x^{4} + 8000 \, x^{3} \log \left (2\right ) + 9600 \, x^{2} \log \left (2\right )^{2} + 20000 \, x^{3} + 96000 \, x^{2} \log \left (2\right ) + 51200 \, x \log \left (2\right )^{2} + 240000 \, x^{2} + 512000 \, x \log \left (2\right ) + 1279999 \, x + \frac {{\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} - 4000 \, {\left ({\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 24 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3} + 192 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2} + 512 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x\right )} \log \left (x\right )^{3} + 600 \, {\left ({\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 16 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3} + 64 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2}\right )} \log \left (x\right )^{2} - 40 \, {\left ({\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 8 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3}\right )} \log \left (x\right )}{400 \, \log \left (x\right )^{4}} \]
integrate(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*log(2)^2+(25000*x^3 +600000*x^2+4800000*x+12800000)*log(2)+62500*x^3+1500000*x^2+12000000*x+31 999975)*log(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*log(2)^2+(-20000 *x^3-360000*x^2-1920000*x-2560000)*log(2)-50000*x^3-900000*x^2-4800000*x-6 400000)*log(x^2)^4+((1600*x^3+31200*x^2+211200*x+512000)*log(2)^2+(16000*x ^3+312000*x^2+2112000*x+5120000)*log(2)+40000*x^3+780000*x^2+5280000*x+128 00000)*log(x^2)^3+((-680*x^3-10080*x^2-38400*x)*log(2)^2+(-6800*x^3-100800 *x^2-384000*x)*log(2)-17000*x^3-252000*x^2-960000*x)*log(x^2)^2+((124*x^3+ 960*x^2)*log(2)^2+(1240*x^3+9600*x^2)*log(2)+3100*x^3+24000*x^2)*log(x^2)- 8*x^3*log(2)^2-80*x^3*log(2)-200*x^3)/log(x^2)^5,x, algorithm=\
25*x^4*log(2)^2 + 250*x^4*log(2) + 800*x^3*log(2)^2 + 625*x^4 + 8000*x^3*l og(2) + 9600*x^2*log(2)^2 + 20000*x^3 + 96000*x^2*log(2) + 51200*x*log(2)^ 2 + 240000*x^2 + 512000*x*log(2) + 1279999*x + 1/400*((log(2)^2 + 10*log(2 ) + 25)*x^4 - 4000*((log(2)^2 + 10*log(2) + 25)*x^4 + 24*(log(2)^2 + 10*lo g(2) + 25)*x^3 + 192*(log(2)^2 + 10*log(2) + 25)*x^2 + 512*(log(2)^2 + 10* log(2) + 25)*x)*log(x)^3 + 600*((log(2)^2 + 10*log(2) + 25)*x^4 + 16*(log( 2)^2 + 10*log(2) + 25)*x^3 + 64*(log(2)^2 + 10*log(2) + 25)*x^2)*log(x)^2 - 40*((log(2)^2 + 10*log(2) + 25)*x^4 + 8*(log(2)^2 + 10*log(2) + 25)*x^3) *log(x))/log(x)^4
Leaf count of result is larger than twice the leaf count of optimal. 423 vs. \(2 (28) = 56\).
Time = 0.47 (sec) , antiderivative size = 423, normalized size of antiderivative = 15.11 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=25 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 800 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3} + 9600 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2} + {\left (51200 \, \log \left (2\right )^{2} + 512000 \, \log \left (2\right ) + 1279999\right )} x - \frac {500 \, x^{4} \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} - 150 \, x^{4} \log \left (2\right )^{2} \log \left (x^{2}\right )^{2} + 5000 \, x^{4} \log \left (2\right ) \log \left (x^{2}\right )^{3} + 12000 \, x^{3} \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} + 20 \, x^{4} \log \left (2\right )^{2} \log \left (x^{2}\right ) - 1500 \, x^{4} \log \left (2\right ) \log \left (x^{2}\right )^{2} - 2400 \, x^{3} \log \left (2\right )^{2} \log \left (x^{2}\right )^{2} + 12500 \, x^{4} \log \left (x^{2}\right )^{3} + 120000 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right )^{3} + 96000 \, x^{2} \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} - x^{4} \log \left (2\right )^{2} + 200 \, x^{4} \log \left (2\right ) \log \left (x^{2}\right ) + 160 \, x^{3} \log \left (2\right )^{2} \log \left (x^{2}\right ) - 3750 \, x^{4} \log \left (x^{2}\right )^{2} - 24000 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right )^{2} - 9600 \, x^{2} \log \left (2\right )^{2} \log \left (x^{2}\right )^{2} + 300000 \, x^{3} \log \left (x^{2}\right )^{3} + 960000 \, x^{2} \log \left (2\right ) \log \left (x^{2}\right )^{3} + 256000 \, x \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} - 10 \, x^{4} \log \left (2\right ) + 500 \, x^{4} \log \left (x^{2}\right ) + 1600 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right ) - 60000 \, x^{3} \log \left (x^{2}\right )^{2} - 96000 \, x^{2} \log \left (2\right ) \log \left (x^{2}\right )^{2} + 2400000 \, x^{2} \log \left (x^{2}\right )^{3} + 2560000 \, x \log \left (2\right ) \log \left (x^{2}\right )^{3} - 25 \, x^{4} + 4000 \, x^{3} \log \left (x^{2}\right ) - 240000 \, x^{2} \log \left (x^{2}\right )^{2} + 6400000 \, x \log \left (x^{2}\right )^{3}}{25 \, \log \left (x^{2}\right )^{4}} \]
integrate(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*log(2)^2+(25000*x^3 +600000*x^2+4800000*x+12800000)*log(2)+62500*x^3+1500000*x^2+12000000*x+31 999975)*log(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*log(2)^2+(-20000 *x^3-360000*x^2-1920000*x-2560000)*log(2)-50000*x^3-900000*x^2-4800000*x-6 400000)*log(x^2)^4+((1600*x^3+31200*x^2+211200*x+512000)*log(2)^2+(16000*x ^3+312000*x^2+2112000*x+5120000)*log(2)+40000*x^3+780000*x^2+5280000*x+128 00000)*log(x^2)^3+((-680*x^3-10080*x^2-38400*x)*log(2)^2+(-6800*x^3-100800 *x^2-384000*x)*log(2)-17000*x^3-252000*x^2-960000*x)*log(x^2)^2+((124*x^3+ 960*x^2)*log(2)^2+(1240*x^3+9600*x^2)*log(2)+3100*x^3+24000*x^2)*log(x^2)- 8*x^3*log(2)^2-80*x^3*log(2)-200*x^3)/log(x^2)^5,x, algorithm=\
25*(log(2)^2 + 10*log(2) + 25)*x^4 + 800*(log(2)^2 + 10*log(2) + 25)*x^3 + 9600*(log(2)^2 + 10*log(2) + 25)*x^2 + (51200*log(2)^2 + 512000*log(2) + 1279999)*x - 1/25*(500*x^4*log(2)^2*log(x^2)^3 - 150*x^4*log(2)^2*log(x^2) ^2 + 5000*x^4*log(2)*log(x^2)^3 + 12000*x^3*log(2)^2*log(x^2)^3 + 20*x^4*l og(2)^2*log(x^2) - 1500*x^4*log(2)*log(x^2)^2 - 2400*x^3*log(2)^2*log(x^2) ^2 + 12500*x^4*log(x^2)^3 + 120000*x^3*log(2)*log(x^2)^3 + 96000*x^2*log(2 )^2*log(x^2)^3 - x^4*log(2)^2 + 200*x^4*log(2)*log(x^2) + 160*x^3*log(2)^2 *log(x^2) - 3750*x^4*log(x^2)^2 - 24000*x^3*log(2)*log(x^2)^2 - 9600*x^2*l og(2)^2*log(x^2)^2 + 300000*x^3*log(x^2)^3 + 960000*x^2*log(2)*log(x^2)^3 + 256000*x*log(2)^2*log(x^2)^3 - 10*x^4*log(2) + 500*x^4*log(x^2) + 1600*x ^3*log(2)*log(x^2) - 60000*x^3*log(x^2)^2 - 96000*x^2*log(2)*log(x^2)^2 + 2400000*x^2*log(x^2)^3 + 2560000*x*log(2)*log(x^2)^3 - 25*x^4 + 4000*x^3*l og(x^2) - 240000*x^2*log(x^2)^2 + 6400000*x*log(x^2)^3)/log(x^2)^4
Time = 9.18 (sec) , antiderivative size = 205, normalized size of antiderivative = 7.32 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=\frac {9600\,x^3\,{\left (\ln \left (2\right )+5\right )}^2+800\,x^4\,{\left (\ln \left (2\right )+5\right )}^2+25\,x^5\,{\left (\ln \left (2\right )+5\right )}^2+\frac {x^2\,\left (12800000\,\ln \left (2\right )+1280000\,{\ln \left (2\right )}^2+31999975\right )}{25}}{x}+\frac {\frac {x^5\,\left (10\,\ln \left (2\right )+{\ln \left (2\right )}^2+25\right )}{25}+{\ln \left (x^2\right )}^2\,\left (6\,{\left (\ln \left (2\right )+5\right )}^2\,x^5+96\,{\left (\ln \left (2\right )+5\right )}^2\,x^4+384\,{\left (\ln \left (2\right )+5\right )}^2\,x^3\right )-\ln \left (x^2\right )\,\left (\frac {4\,{\left (\ln \left (2\right )+5\right )}^2\,x^5}{5}+\frac {32\,{\left (\ln \left (2\right )+5\right )}^2\,x^4}{5}\right )-{\ln \left (x^2\right )}^3\,\left (20\,{\left (\ln \left (2\right )+5\right )}^2\,x^5+480\,{\left (\ln \left (2\right )+5\right )}^2\,x^4+3840\,{\left (\ln \left (2\right )+5\right )}^2\,x^3+10240\,{\left (\ln \left (2\right )+5\right )}^2\,x^2\right )}{x\,{\ln \left (x^2\right )}^4} \]
int(-((8*x^3*log(2)^2)/25 - (log(x^2)*(log(2)*(9600*x^2 + 1240*x^3) + 2400 0*x^2 + 3100*x^3 + log(2)^2*(960*x^2 + 124*x^3)))/25 + (16*x^3*log(2))/5 + 8*x^3 + (log(x^2)^2*(960000*x + log(2)*(384000*x + 100800*x^2 + 6800*x^3) + log(2)^2*(38400*x + 10080*x^2 + 680*x^3) + 252000*x^2 + 17000*x^3))/25 + (log(x^2)^4*(4800000*x + log(2)*(1920000*x + 360000*x^2 + 20000*x^3 + 25 60000) + log(2)^2*(192000*x + 36000*x^2 + 2000*x^3 + 256000) + 900000*x^2 + 50000*x^3 + 6400000))/25 - (log(x^2)^3*(5280000*x + log(2)*(2112000*x + 312000*x^2 + 16000*x^3 + 5120000) + log(2)^2*(211200*x + 31200*x^2 + 1600* x^3 + 512000) + 780000*x^2 + 40000*x^3 + 12800000))/25 - (log(x^2)^5*(1200 0000*x + log(2)*(4800000*x + 600000*x^2 + 25000*x^3 + 12800000) + log(2)^2 *(480000*x + 60000*x^2 + 2500*x^3 + 1280000) + 1500000*x^2 + 62500*x^3 + 3 1999975))/25)/log(x^2)^5,x)
(9600*x^3*(log(2) + 5)^2 + 800*x^4*(log(2) + 5)^2 + 25*x^5*(log(2) + 5)^2 + (x^2*(12800000*log(2) + 1280000*log(2)^2 + 31999975))/25)/x + ((x^5*(10* log(2) + log(2)^2 + 25))/25 + log(x^2)^2*(384*x^3*(log(2) + 5)^2 + 96*x^4* (log(2) + 5)^2 + 6*x^5*(log(2) + 5)^2) - log(x^2)*((32*x^4*(log(2) + 5)^2) /5 + (4*x^5*(log(2) + 5)^2)/5) - log(x^2)^3*(10240*x^2*(log(2) + 5)^2 + 38 40*x^3*(log(2) + 5)^2 + 480*x^4*(log(2) + 5)^2 + 20*x^5*(log(2) + 5)^2))/( x*log(x^2)^4)