\[ \int \frac {409600+e^x (-384000-15360 x)+16384 x+e^{3 x} \left (-12500-16500 x-640 x^2\right )+e^{2 x} \left (120000+56000 x+49152 x^2+2048 x^3\right )+\left (2457600+e^x (-1536000-61440 x)+98304 x+e^{2 x} \left (240000+112000 x+100352 x^2+4096 x^3\right )\right ) \log \left (\frac {25+x}{5}\right )+\left (6758400+e^x (-2688000-107520 x)+270336 x+e^{2 x} \left (180000+84000 x+76800 x^2+3072 x^3\right )\right ) \log ^2\left (\frac {25+x}{5}\right )+\left (11264000+e^x (-2688000-107520 x)+450560 x+e^{2 x} \left (60000+28000 x+26112 x^2+1024 x^3\right )\right ) \log ^3\left (\frac {25+x}{5}\right )+\left (12672000+e^x (-1680000-67200 x)+506880 x+e^{2 x} \left (7500+3500 x+3328 x^2+128 x^3\right )\right ) \log ^4\left (\frac {25+x}{5}\right )+\left (10137600+e^x (-672000-26880 x)+405504 x\right ) \log ^5\left (\frac {25+x}{5}\right )+\left (5913600+e^x (-168000-6720 x)+236544 x\right ) \log ^6\left (\frac {25+x}{5}\right )+\left (2534400+e^x (-24000-960 x)+101376 x\right ) \log ^7\left (\frac {25+x}{5}\right )+\left (792000+e^x (-1500-60 x)+31680 x\right ) \log ^8\left (\frac {25+x}{5}\right )+(176000+7040 x) \log ^9\left (\frac {25+x}{5}\right )+(26400+1056 x) \log ^{10}\left (\frac {25+x}{5}\right )+(2400+96 x) \log ^{11}\left (\frac {25+x}{5}\right )+(100+4 x) \log ^{12}\left (\frac {25+x}{5}\right )}{102400+e^x (-96000-3840 x)+e^{3 x} (-3125-125 x)+4096 x+e^{2 x} (30000+1200 x)+\left (614400+e^x (-384000-15360 x)+24576 x+e^{2 x} (60000+2400 x)\right ) \log \left (\frac {25+x}{5}\right )+\left (1689600+e^x (-672000-26880 x)+67584 x+e^{2 x} (45000+1800 x)\right ) \log ^2\left (\frac {25+x}{5}\right )+\left (2816000+e^x (-672000-26880 x)+112640 x+e^{2 x} (15000+600 x)\right ) \log ^3\left (\frac {25+x}{5}\right )+\left (3168000+e^x (-420000-16800 x)+126720 x+e^{2 x} (1875+75 x)\right ) \log ^4\left (\frac {25+x}{5}\right )+\left (2534400+e^x (-168000-6720 x)+101376 x\right ) \log ^5\left (\frac {25+x}{5}\right )+\left (1478400+e^x (-42000-1680 x)+59136 x\right ) \log ^6\left (\frac {25+x}{5}\right )+\left (633600+e^x (-6000-240 x)+25344 x\right ) \log ^7\left (\frac {25+x}{5}\right )+\left (198000+e^x (-375-15 x)+7920 x\right ) \log ^8\left (\frac {25+x}{5}\right )+(44000+1760 x) \log ^9\left (\frac {25+x}{5}\right )+(6600+264 x) \log ^{10}\left (\frac {25+x}{5}\right )+(600+24 x) \log ^{11}\left (\frac {25+x}{5}\right )+(25+x) \log ^{12}\left (\frac {25+x}{5}\right )} \, dx \]
Optimal antiderivative \[ \frac {64 x^{2}}{\left (\left (\ln \left (\frac {x}{5}+5\right )+2\right )^{4} {\mathrm e}^{-x}-5\right )^{2}}+4 x \]
command
integrate(((4*x+100)*log(1/5*x+5)^12+(96*x+2400)*log(1/5*x+5)^11+(1056*x+26400)*log(1/5*x+5)^10+(7040*x+176000)*log(1/5*x+5)^9+((-60*x-1500)*exp(x)+31680*x+792000)*log(1/5*x+5)^8+((-960*x-24000)*exp(x)+101376*x+2534400)*log(1/5*x+5)^7+((-6720*x-168000)*exp(x)+236544*x+5913600)*log(1/5*x+5)^6+((-26880*x-672000)*exp(x)+405504*x+10137600)*log(1/5*x+5)^5+((128*x^3+3328*x^2+3500*x+7500)*exp(x)^2+(-67200*x-1680000)*exp(x)+506880*x+12672000)*log(1/5*x+5)^4+((1024*x^3+26112*x^2+28000*x+60000)*exp(x)^2+(-107520*x-2688000)*exp(x)+450560*x+11264000)*log(1/5*x+5)^3+((3072*x^3+76800*x^2+84000*x+180000)*exp(x)^2+(-107520*x-2688000)*exp(x)+270336*x+6758400)*log(1/5*x+5)^2+((4096*x^3+100352*x^2+112000*x+240000)*exp(x)^2+(-61440*x-1536000)*exp(x)+98304*x+2457600)*log(1/5*x+5)+(-640*x^2-16500*x-12500)*exp(x)^3+(2048*x^3+49152*x^2+56000*x+120000)*exp(x)^2+(-15360*x-384000)*exp(x)+16384*x+409600)/((x+25)*log(1/5*x+5)^12+(24*x+600)*log(1/5*x+5)^11+(264*x+6600)*log(1/5*x+5)^10+(1760*x+44000)*log(1/5*x+5)^9+((-15*x-375)*exp(x)+7920*x+198000)*log(1/5*x+5)^8+((-240*x-6000)*exp(x)+25344*x+633600)*log(1/5*x+5)^7+((-1680*x-42000)*exp(x)+59136*x+1478400)*log(1/5*x+5)^6+((-6720*x-168000)*exp(x)+101376*x+2534400)*log(1/5*x+5)^5+((75*x+1875)*exp(x)^2+(-16800*x-420000)*exp(x)+126720*x+3168000)*log(1/5*x+5)^4+((600*x+15000)*exp(x)^2+(-26880*x-672000)*exp(x)+112640*x+2816000)*log(1/5*x+5)^3+((1800*x+45000)*exp(x)^2+(-26880*x-672000)*exp(x)+67584*x+1689600)*log(1/5*x+5)^2+((2400*x+60000)*exp(x)^2+(-15360*x-384000)*exp(x)+24576*x+614400)*log(1/5*x+5)+(-125*x-3125)*exp(x)^3+(1200*x+30000)*exp(x)^2+(-3840*x-96000)*exp(x)+4096*x+102400),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4 \, {\left ({\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{8} + 16 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{7} - 400 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{8} + 112 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{6} - 6400 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{7} + 448 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{5} - 44800 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{6} + 1120 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{4} - 10 \, {\left (x + 25\right )} e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} - 179200 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{5} + 1792 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 80 \, {\left (x + 25\right )} e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 448000 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{4} + 4000 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} + 1792 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{2} - 240 \, {\left (x + 25\right )} e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} - 716800 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{3} + 32000 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} + 16 \, {\left (x + 25\right )}^{2} e^{\left (2 \, x + 50\right )} + 1024 \, {\left (x + 25\right )} e^{50} \log \left (\frac {1}{5} \, x + 5\right ) - 320 \, {\left (x + 25\right )} e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right ) - 716800 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{2} + 96000 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} + 256 \, {\left (x + 25\right )} e^{50} - 775 \, {\left (x + 25\right )} e^{\left (2 \, x + 50\right )} - 160 \, {\left (x + 25\right )} e^{\left (x + 50\right )} - 409600 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right ) + 128000 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right ) - 102400 \, e^{50} + 64000 \, e^{\left (x + 50\right )}\right )}}{e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{8} + 16 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{7} + 112 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{6} + 448 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{5} + 1120 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{4} - 10 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} + 1792 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 80 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} + 1792 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right )^{2} - 240 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} + 1024 \, e^{50} \log \left (\frac {1}{5} \, x + 5\right ) - 320 \, e^{\left (x + 50\right )} \log \left (\frac {1}{5} \, x + 5\right ) + 256 \, e^{50} + 25 \, e^{\left (2 \, x + 50\right )} - 160 \, e^{\left (x + 50\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________