Integrand size = 740, antiderivative size = 31 \[ \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=4 \left (x+\frac {16 x^2}{\left (-5+e^{-x} \left (2+\log \left (5+\frac {x}{5}\right )\right )^4\right )^2}\right ) \]
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Timed out. \[ \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=\text {\$Aborted} \]
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Rubi steps Aborted
Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(31)=62\).
Time = 0.69 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.23 \[ \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=-4 \left (-x-\frac {16 e^{2 x} x^2}{\left (16-5 e^x+32 \log \left (5+\frac {x}{5}\right )+24 \log ^2\left (5+\frac {x}{5}\right )+8 \log ^3\left (5+\frac {x}{5}\right )+\log ^4\left (5+\frac {x}{5}\right )\right )^2}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(28)=56\).
Time = 64.35 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.94
method | result | size |
risch | \(4 x +\frac {64 x^{2} {\mathrm e}^{2 x}}{\left (-\ln \left (\frac {x}{5}+5\right )^{4}-8 \ln \left (\frac {x}{5}+5\right )^{3}-24 \ln \left (\frac {x}{5}+5\right )^{2}+5 \,{\mathrm e}^{x}-32 \ln \left (\frac {x}{5}+5\right )-16\right )^{2}}\) | \(60\) |
parallelrisch | \(\frac {-8192000+163840 x +10240 \,{\mathrm e}^{2 x} x^{2}+16000 x \,{\mathrm e}^{2 x}-102400 \,{\mathrm e}^{x} x +716800 \ln \left (\frac {x}{5}+5\right )^{4} x +2560000 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{3}+1146880 \ln \left (\frac {x}{5}+5\right )^{3} x +7680000 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{2}+1146880 \ln \left (\frac {x}{5}+5\right )^{2} x +10240000 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )+655360 \ln \left (\frac {x}{5}+5\right ) x +640 \ln \left (\frac {x}{5}+5\right )^{8} x +10240 \ln \left (\frac {x}{5}+5\right )^{7} x +71680 \ln \left (\frac {x}{5}+5\right )^{6} x +286720 \ln \left (\frac {x}{5}+5\right )^{5} x +320000 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{4}-32768000 \ln \left (\frac {x}{5}+5\right )-800000 \,{\mathrm e}^{2 x}+5120000 \,{\mathrm e}^{x}-32000 \ln \left (\frac {x}{5}+5\right )^{8}-512000 \ln \left (\frac {x}{5}+5\right )^{7}-3584000 \ln \left (\frac {x}{5}+5\right )^{6}-14336000 \ln \left (\frac {x}{5}+5\right )^{5}-35840000 \ln \left (\frac {x}{5}+5\right )^{4}-57344000 \ln \left (\frac {x}{5}+5\right )^{3}-57344000 \ln \left (\frac {x}{5}+5\right )^{2}-51200 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{3} x -153600 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{2} x -6400 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{4} x -204800 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right ) x}{160 \ln \left (\frac {x}{5}+5\right )^{8}+2560 \ln \left (\frac {x}{5}+5\right )^{7}+17920 \ln \left (\frac {x}{5}+5\right )^{6}-1600 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{4}+71680 \ln \left (\frac {x}{5}+5\right )^{5}-12800 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{3}+179200 \ln \left (\frac {x}{5}+5\right )^{4}-38400 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )^{2}+286720 \ln \left (\frac {x}{5}+5\right )^{3}+4000 \,{\mathrm e}^{2 x}-51200 \,{\mathrm e}^{x} \ln \left (\frac {x}{5}+5\right )+286720 \ln \left (\frac {x}{5}+5\right )^{2}-25600 \,{\mathrm e}^{x}+163840 \ln \left (\frac {x}{5}+5\right )+40960}\) | \(435\) |
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Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 253, normalized size of antiderivative = 8.16 \[ \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=\frac {4 \, {\left (x \log \left (\frac {1}{5} \, x + 5\right )^{8} + 16 \, x \log \left (\frac {1}{5} \, x + 5\right )^{7} + 112 \, x \log \left (\frac {1}{5} \, x + 5\right )^{6} + 448 \, x \log \left (\frac {1}{5} \, x + 5\right )^{5} - 10 \, {\left (x e^{x} - 112 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} - 16 \, {\left (5 \, x e^{x} - 112 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 16 \, {\left (15 \, x e^{x} - 112 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} + {\left (16 \, x^{2} + 25 \, x\right )} e^{\left (2 \, x\right )} - 160 \, x e^{x} - 64 \, {\left (5 \, x e^{x} - 16 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right ) + 256 \, x\right )}}{\log \left (\frac {1}{5} \, x + 5\right )^{8} + 16 \, \log \left (\frac {1}{5} \, x + 5\right )^{7} + 112 \, \log \left (\frac {1}{5} \, x + 5\right )^{6} - 10 \, {\left (e^{x} - 112\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} + 448 \, \log \left (\frac {1}{5} \, x + 5\right )^{5} - 16 \, {\left (5 \, e^{x} - 112\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 16 \, {\left (15 \, e^{x} - 112\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} - 64 \, {\left (5 \, e^{x} - 16\right )} \log \left (\frac {1}{5} \, x + 5\right ) + 25 \, e^{\left (2 \, x\right )} - 160 \, e^{x} + 256} \]
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Leaf count of result is larger than twice the leaf count of optimal. 316 vs. \(2 (24) = 48\).
Time = 0.68 (sec) , antiderivative size = 316, normalized size of antiderivative = 10.19 \[ \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=\frac {64 x^{2}}{25} + 4 x + \frac {- 64 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{8} - 1024 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{7} - 7168 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{6} - 28672 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{5} - 71680 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{4} - 114688 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{3} - 114688 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{2} - 65536 x^{2} \log {\left (\frac {x}{5} + 5 \right )} - 16384 x^{2} + \left (640 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{4} + 5120 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{3} + 15360 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{2} + 20480 x^{2} \log {\left (\frac {x}{5} + 5 \right )} + 10240 x^{2}\right ) e^{x}}{\left (- 250 \log {\left (\frac {x}{5} + 5 \right )}^{4} - 2000 \log {\left (\frac {x}{5} + 5 \right )}^{3} - 6000 \log {\left (\frac {x}{5} + 5 \right )}^{2} - 8000 \log {\left (\frac {x}{5} + 5 \right )} - 4000\right ) e^{x} + 625 e^{2 x} + 25 \log {\left (\frac {x}{5} + 5 \right )}^{8} + 400 \log {\left (\frac {x}{5} + 5 \right )}^{7} + 2800 \log {\left (\frac {x}{5} + 5 \right )}^{6} + 11200 \log {\left (\frac {x}{5} + 5 \right )}^{5} + 28000 \log {\left (\frac {x}{5} + 5 \right )}^{4} + 44800 \log {\left (\frac {x}{5} + 5 \right )}^{3} + 44800 \log {\left (\frac {x}{5} + 5 \right )}^{2} + 25600 \log {\left (\frac {x}{5} + 5 \right )} + 6400} \]
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Leaf count of result is larger than twice the leaf count of optimal. 726 vs. \(2 (28) = 56\).
Time = 1.82 (sec) , antiderivative size = 726, normalized size of antiderivative = 23.42 \[ \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=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 552 vs. \(2 (28) = 56\).
Time = 0.90 (sec) , antiderivative size = 552, normalized size of antiderivative = 17.81 \[ \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=\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 )}} \]
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Timed out. \[ \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=\text {Too large to display} \]
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