Integrand size = 315, antiderivative size = 28 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=-x+25 (5+\log (2))^2 \left (8+x-\frac {x}{5 \log \left (x^2\right )}\right )^4 \]
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Leaf count is larger than twice the leaf count of optimal. \(222\) vs. \(2(28)=56\).
Time = 0.56 (sec) , antiderivative size = 222, normalized size of antiderivative = 7.93, number of steps used = 62, number of rules used = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6, 12, 6820, 2343, 2347, 2209, 2395, 2403, 2344, 2335, 2334, 2337} \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=25 x^4 (5+\log (2))^2+800 x^3 (5+\log (2))^2+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}+9600 x^2 (5+\log (2))^2-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}+x \left (1279999+51200 \log ^2(2)+512000 \log (2)\right ) \]
[In]
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Rule 6
Rule 12
Rule 2209
Rule 2334
Rule 2335
Rule 2337
Rule 2343
Rule 2344
Rule 2347
Rule 2395
Rule 2403
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {x^3 (-200-80 \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 \\ & = \int \frac {x^3 \left (-200-80 \log (2)-8 \log ^2(2)\right )+\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 {1}{25} \int \frac {x^3 \left (-200-80 \log (2)-8 \log ^2(2)\right )+\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 )}{\log ^5\left (x^2\right )} \, dx \\ & = \frac {1}{25} \int \left (25 \left (1279999+512000 \log (2)+51200 \log ^2(2)+19200 x (5+\log (2))^2+2400 x^2 (5+\log (2))^2+100 x^3 (5+\log (2))^2\right )-\frac {8 x^3 (5+\log (2))^2}{\log ^5\left (x^2\right )}+\frac {4 x^2 (240+31 x) (5+\log (2))^2}{\log ^4\left (x^2\right )}-\frac {40 x \left (960+252 x+17 x^2\right ) (5+\log (2))^2}{\log ^3\left (x^2\right )}+\frac {800 \left (640+264 x+39 x^2+2 x^3\right ) (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {2000 (2+x) (8+x)^2 (5+\log (2))^2}{\log \left (x^2\right )}\right ) \, dx \\ & = \frac {1}{25} \left (4 (5+\log (2))^2\right ) \int \frac {x^2 (240+31 x)}{\log ^4\left (x^2\right )} \, dx-\frac {1}{25} \left (8 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^5\left (x^2\right )} \, dx-\frac {1}{5} \left (8 (5+\log (2))^2\right ) \int \frac {x \left (960+252 x+17 x^2\right )}{\log ^3\left (x^2\right )} \, dx+\left (32 (5+\log (2))^2\right ) \int \frac {640+264 x+39 x^2+2 x^3}{\log ^2\left (x^2\right )} \, dx-\left (80 (5+\log (2))^2\right ) \int \frac {(2+x) (8+x)^2}{\log \left (x^2\right )} \, dx+\int \left (1279999+512000 \log (2)+51200 \log ^2(2)+19200 x (5+\log (2))^2+2400 x^2 (5+\log (2))^2+100 x^3 (5+\log (2))^2\right ) \, dx \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}+\frac {1}{25} \left (4 (5+\log (2))^2\right ) \int \left (\frac {240 x^2}{\log ^4\left (x^2\right )}+\frac {31 x^3}{\log ^4\left (x^2\right )}\right ) \, dx-\frac {1}{25} \left (4 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^4\left (x^2\right )} \, dx-\frac {1}{5} \left (8 (5+\log (2))^2\right ) \int \left (\frac {960 x}{\log ^3\left (x^2\right )}+\frac {252 x^2}{\log ^3\left (x^2\right )}+\frac {17 x^3}{\log ^3\left (x^2\right )}\right ) \, dx+\left (32 (5+\log (2))^2\right ) \int \left (\frac {640}{\log ^2\left (x^2\right )}+\frac {264 x}{\log ^2\left (x^2\right )}+\frac {39 x^2}{\log ^2\left (x^2\right )}+\frac {2 x^3}{\log ^2\left (x^2\right )}\right ) \, dx-\left (80 (5+\log (2))^2\right ) \int \left (\frac {128}{\log \left (x^2\right )}+\frac {96 x}{\log \left (x^2\right )}+\frac {18 x^2}{\log \left (x^2\right )}+\frac {x^3}{\log \left (x^2\right )}\right ) \, dx \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}+\frac {2 x^4 (5+\log (2))^2}{75 \log ^3\left (x^2\right )}-\frac {1}{75} \left (8 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^3\left (x^2\right )} \, dx+\frac {1}{25} \left (124 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^4\left (x^2\right )} \, dx-\frac {1}{5} \left (136 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^3\left (x^2\right )} \, dx+\frac {1}{5} \left (192 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^4\left (x^2\right )} \, dx+\left (64 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx-\left (80 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx-\frac {1}{5} \left (2016 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^3\left (x^2\right )} \, dx+\left (1248 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^2\left (x^2\right )} \, dx-\left (1440 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\left (1536 (5+\log (2))^2\right ) \int \frac {x}{\log ^3\left (x^2\right )} \, dx-\left (7680 (5+\log (2))^2\right ) \int \frac {x}{\log \left (x^2\right )} \, dx+\left (8448 (5+\log (2))^2\right ) \int \frac {x}{\log ^2\left (x^2\right )} \, dx-\left (10240 (5+\log (2))^2\right ) \int \frac {1}{\log \left (x^2\right )} \, dx+\left (20480 (5+\log (2))^2\right ) \int \frac {1}{\log ^2\left (x^2\right )} \, dx \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {504 x^3 (5+\log (2))^2}{5 \log ^2\left (x^2\right )}+\frac {512 x^4 (5+\log (2))^2}{75 \log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {4224 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {624 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {32 x^4 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {1}{75} \left (8 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx+\frac {1}{75} \left (248 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^3\left (x^2\right )} \, dx+\frac {1}{5} \left (96 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^3\left (x^2\right )} \, dx-\frac {1}{5} \left (136 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx-\left (40 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+\left (128 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx-\frac {1}{5} \left (1512 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^2\left (x^2\right )} \, dx-\left (768 (5+\log (2))^2\right ) \int \frac {x}{\log ^2\left (x^2\right )} \, dx+\left (1872 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\left (3840 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )+\left (8448 (5+\log (2))^2\right ) \int \frac {x}{\log \left (x^2\right )} \, dx+\left (10240 (5+\log (2))^2\right ) \int \frac {1}{\log \left (x^2\right )} \, dx-\frac {\left (720 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\left (x^2\right )^{3/2}}-\frac {\left (5120 x (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\sqrt {x^2}} \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2-\frac {5120 x \text {Ei}\left (\frac {\log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{\sqrt {x^2}}-\frac {720 x^3 \text {Ei}\left (\frac {3 \log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{\left (x^2\right )^{3/2}}-40 \text {Ei}\left (2 \log \left (x^2\right )\right ) (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {2364 x^3 (5+\log (2))^2}{5 \log \left (x^2\right )}-\frac {1376 x^4 (5+\log (2))^2}{75 \log \left (x^2\right )}-3840 (5+\log (2))^2 \text {li}\left (x^2\right )-\frac {1}{75} \left (16 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx+\frac {1}{75} \left (248 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx+\frac {1}{5} \left (72 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^2\left (x^2\right )} \, dx-\frac {1}{5} \left (272 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx+\left (64 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )-\frac {1}{5} \left (2268 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\left (768 (5+\log (2))^2\right ) \int \frac {x}{\log \left (x^2\right )} \, dx+\left (4224 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )+\frac {\left (936 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\left (x^2\right )^{3/2}}+\frac {\left (5120 x (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\sqrt {x^2}} \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+\frac {216 x^3 \text {Ei}\left (\frac {3 \log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{\left (x^2\right )^{3/2}}+24 \text {Ei}\left (2 \log \left (x^2\right )\right ) (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}+384 (5+\log (2))^2 \text {li}\left (x^2\right )-\frac {1}{75} \left (8 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+\frac {1}{75} \left (496 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx+\frac {1}{5} \left (108 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\frac {1}{5} \left (136 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )-\left (384 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )-\frac {\left (1134 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{5 \left (x^2\right )^{3/2}} \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2-\frac {54 x^3 \text {Ei}\left (\frac {3 \log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{5 \left (x^2\right )^{3/2}}-\frac {248}{75} \text {Ei}\left (2 \log \left (x^2\right )\right ) (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}+\frac {1}{75} \left (248 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+\frac {\left (54 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{5 \left (x^2\right )^{3/2}} \\ & = 9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )} \\ \end{align*}
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 \[ \int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx=x \left (1279999+512000 \log (2)+51200 \log ^2(2)+9600 x (5+\log (2))^2+800 x^2 (5+\log (2))^2+25 x^3 (5+\log (2))^2\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {4 x^3 (8+x) (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {6 x^2 (8+x)^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {20 x (8+x)^3 (5+\log (2))^2}{\log \left (x^2\right )} \]
[In]
[Out]
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}}\) | \(514\) |
[In]
[Out]
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}} \]
[In]
[Out]
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}} \]
[In]
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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}} \]
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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}} \]
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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} \]
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