Integrand size = 202, antiderivative size = 28 \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {\log (x)}{16-8 x+\frac {5}{x^2+\frac {4}{4-\log (x)}}} \]
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\[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-16 \left (-21+8 x-37 x^2+16 x^3-16 x^4+8 x^5\right )+8 x \left (16-x+40 x^2-16 x^3+24 x^4\right ) \log (x)-x^2 \left (75+64 x-16 x^2+72 x^3\right ) \log ^2(x)+2 x^2 \left (5+4 x^3\right ) \log ^3(x)}{x \left (84-32 x+64 x^2-32 x^3+\left (-5-16 x^2+8 x^3\right ) \log (x)\right )^2} \, dx \\ & = \int \left (-\frac {x \left (1305-960 x+160 x^2-80 x^3+256 x^4-256 x^5+64 x^6\right )}{\left (-5-16 x^2+8 x^3\right )^3}+\frac {2 x \left (5+4 x^3\right ) \log (x)}{\left (-5-16 x^2+8 x^3\right )^2}+\frac {80 \left (-525-3160 x-45488 x^2+59992 x^3-67200 x^4+63232 x^5-32704 x^6+10752 x^7-3072 x^8+512 x^9\right )}{x \left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {640 \left (5+232 x-254 x^2+192 x^3-160 x^4+48 x^5\right )}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}\right ) \, dx \\ & = 2 \int \frac {x \left (5+4 x^3\right ) \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+80 \int \frac {-525-3160 x-45488 x^2+59992 x^3-67200 x^4+63232 x^5-32704 x^6+10752 x^7-3072 x^8+512 x^9}{x \left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+640 \int \frac {5+232 x-254 x^2+192 x^3-160 x^4+48 x^5}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-\int \frac {x \left (1305-960 x+160 x^2-80 x^3+256 x^4-256 x^5+64 x^6\right )}{\left (-5-16 x^2+8 x^3\right )^3} \, dx \\ & = \frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}+\frac {1}{8} \int \frac {-10440 x+7680 x^2-1280 x^3+2240 x^4-2048 x^5+3072 x^6}{\left (-5-16 x^2+8 x^3\right )^3} \, dx+2 \int \left (\frac {\left (10+15 x+32 x^2\right ) \log (x)}{2 \left (-5-16 x^2+8 x^3\right )^2}+\frac {(2+x) \log (x)}{2 \left (-5-16 x^2+8 x^3\right )}\right ) \, dx+80 \int \left (\frac {21}{5 x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {256 \left (-50-113 x+64 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {32 \left (49-80 x+32 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {8 \left (-45-32 x+16 x^2\right )}{5 \left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}\right ) \, dx+640 \int \left (-\frac {3 \left (-15-64 x+32 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}+\frac {2 \left (4-4 x+3 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}\right ) \, dx \\ & = -\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}-\frac {1}{128} \int \frac {167040 x-122880 x^2+81920 x^3-35840 x^4+32768 x^5}{\left (-5-16 x^2+8 x^3\right )^3} \, dx-128 \int \frac {-45-32 x+16 x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1280 \int \frac {4-4 x+3 x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-1920 \int \frac {-15-64 x+32 x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-2560 \int \frac {49-80 x+32 x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+20480 \int \frac {-50-113 x+64 x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {\left (10+15 x+32 x^2\right ) \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+\int \frac {(2+x) \log (x)}{-5-16 x^2+8 x^3} \, dx \\ & = \frac {32 x^3}{3 \left (5+16 x^2-8 x^3\right )^2}-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}+\frac {\int \frac {-4008960 x+3440640 x^2-1966080 x^3+335872 x^4}{\left (-5-16 x^2+8 x^3\right )^3} \, dx}{3072}-128 \int \left (-\frac {45}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {32 x}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {16 x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}\right ) \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1280 \int \left (\frac {4}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}-\frac {4 x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}+\frac {3 x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}\right ) \, dx-1920 \int \left (-\frac {15}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}-\frac {64 x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}+\frac {32 x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}\right ) \, dx-2560 \int \left (\frac {49}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {80 x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {32 x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}\right ) \, dx+20480 \int \left (-\frac {50}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {113 x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {64 x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}\right ) \, dx+\int \left (\frac {10 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2}+\frac {15 x \log (x)}{\left (-5-16 x^2+8 x^3\right )^2}+\frac {32 x^2 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2}\right ) \, dx+\int \left (\frac {2 \log (x)}{-5-16 x^2+8 x^3}+\frac {x \log (x)}{-5-16 x^2+8 x^3}\right ) \, dx \\ & = -\frac {41 x^2}{12 \left (5+16 x^2-8 x^3\right )^2}+\frac {32 x^3}{3 \left (5+16 x^2-8 x^3\right )^2}-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}-\frac {\int \frac {131645440 x-110100480 x^2+52166656 x^3}{\left (-5-16 x^2+8 x^3\right )^3} \, dx}{98304}+2 \int \frac {\log (x)}{-5-16 x^2+8 x^3} \, dx+10 \int \frac {\log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+15 \int \frac {x \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+32 \int \frac {x^2 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2048 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+3840 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+4096 \int \frac {x}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+5120 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-5120 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+5760 \int \frac {1}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+28800 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-61440 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-81920 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+122880 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-125440 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+204800 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-1024000 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1310720 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2314240 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {x \log (x)}{-5-16 x^2+8 x^3} \, dx \\ & = -\frac {41 x^2}{12 \left (5+16 x^2-8 x^3\right )^2}+\frac {32 x^3}{3 \left (5+16 x^2-8 x^3\right )^2}-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}-\frac {\int \frac {x \left (131645440-110100480 x+52166656 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^3} \, dx}{98304}+2 \int \frac {\log (x)}{-5-16 x^2+8 x^3} \, dx+10 \int \frac {\log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+15 \int \frac {x \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+32 \int \frac {x^2 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2048 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+3840 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+4096 \int \frac {x}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+5120 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-5120 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+5760 \int \frac {1}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+28800 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-61440 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-81920 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+122880 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-125440 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+204800 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-1024000 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1310720 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2314240 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {x \log (x)}{-5-16 x^2+8 x^3} \, dx \\ & = \frac {199 x}{15 \left (5+16 x^2-8 x^3\right )^2}-\frac {41 x^2}{12 \left (5+16 x^2-8 x^3\right )^2}+\frac {32 x^3}{3 \left (5+16 x^2-8 x^3\right )^2}-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}+\frac {\int \frac {260833280-5265817600 x+1900019712 x^2}{\left (-5-16 x^2+8 x^3\right )^3} \, dx}{3932160}+2 \int \frac {\log (x)}{-5-16 x^2+8 x^3} \, dx+10 \int \frac {\log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+15 \int \frac {x \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+32 \int \frac {x^2 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2048 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+3840 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+4096 \int \frac {x}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+5120 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-5120 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+5760 \int \frac {1}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+28800 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-61440 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-81920 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+122880 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-125440 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+204800 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-1024000 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1310720 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2314240 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {x \log (x)}{-5-16 x^2+8 x^3} \, dx \\ & = -\frac {151}{15 \left (5+16 x^2-8 x^3\right )^2}+\frac {199 x}{15 \left (5+16 x^2-8 x^3\right )^2}-\frac {41 x^2}{12 \left (5+16 x^2-8 x^3\right )^2}+\frac {32 x^3}{3 \left (5+16 x^2-8 x^3\right )^2}-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}+\frac {\int \frac {6259998720-65578991616 x}{\left (-5-16 x^2+8 x^3\right )^3} \, dx}{94371840}+2 \int \frac {\log (x)}{-5-16 x^2+8 x^3} \, dx+10 \int \frac {\log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+15 \int \frac {x \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+32 \int \frac {x^2 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2048 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+3840 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+4096 \int \frac {x}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+5120 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-5120 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+5760 \int \frac {1}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+28800 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-61440 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-81920 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+122880 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-125440 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+204800 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-1024000 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1310720 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2314240 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {x \log (x)}{-5-16 x^2+8 x^3} \, dx \\ & = -\frac {151}{15 \left (5+16 x^2-8 x^3\right )^2}+\frac {199 x}{15 \left (5+16 x^2-8 x^3\right )^2}-\frac {41 x^2}{12 \left (5+16 x^2-8 x^3\right )^2}+\frac {32 x^3}{3 \left (5+16 x^2-8 x^3\right )^2}-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}+\frac {\text {Subst}\left (\int \frac {-37459329024-65578991616 x}{\left (-\frac {263}{27}-\frac {32 x}{3}+8 x^3\right )^3} \, dx,x,-\frac {2}{3}+x\right )}{94371840}+2 \int \frac {\log (x)}{-5-16 x^2+8 x^3} \, dx+10 \int \frac {\log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+15 \int \frac {x \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+32 \int \frac {x^2 \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2048 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+3840 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+4096 \int \frac {x}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+5120 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-5120 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx+5760 \int \frac {1}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+28800 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-61440 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-81920 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+122880 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-125440 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+204800 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-1024000 \int \frac {1}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1310720 \int \frac {x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx-2314240 \int \frac {x}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {x \log (x)}{-5-16 x^2+8 x^3} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {\log (x) \left (4+4 x^2-x^2 \log (x)\right )}{84-32 x+64 x^2-32 x^3+\left (-5-16 x^2+8 x^3\right ) \log (x)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(28)=56\).
Time = 1.43 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07
method | result | size |
default | \(\frac {4 \ln \left (x \right )+4 x^{2} \ln \left (x \right )-x^{2} \ln \left (x \right )^{2}}{8 x^{3} \ln \left (x \right )-16 x^{2} \ln \left (x \right )-32 x^{3}+64 x^{2}-5 \ln \left (x \right )-32 x +84}\) | \(58\) |
parallelrisch | \(\frac {-8 x^{2} \ln \left (x \right )^{2}+32 \ln \left (x \right )+32 x^{2} \ln \left (x \right )}{64 x^{3} \ln \left (x \right )-128 x^{2} \ln \left (x \right )-256 x^{3}+512 x^{2}-40 \ln \left (x \right )-256 x +672}\) | \(59\) |
risch | \(-\frac {x^{2} \ln \left (x \right )}{8 x^{3}-16 x^{2}-5}-\frac {20}{64 x^{6}-256 x^{5}+256 x^{4}-80 x^{3}+160 x^{2}+25}-\frac {80 \left (8 x^{3}-16 x^{2}+8 x -21\right )}{\left (64 x^{6}-256 x^{5}+256 x^{4}-80 x^{3}+160 x^{2}+25\right ) \left (8 x^{3} \ln \left (x \right )-16 x^{2} \ln \left (x \right )-32 x^{3}+64 x^{2}-5 \ln \left (x \right )-32 x +84\right )}\) | \(135\) |
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Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {x^{2} \log \left (x\right )^{2} - 4 \, {\left (x^{2} + 1\right )} \log \left (x\right )}{32 \, x^{3} - 64 \, x^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - 5\right )} \log \left (x\right ) + 32 \, x - 84} \]
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Leaf count of result is larger than twice the leaf count of optimal. 153 vs. \(2 (19) = 38\).
Time = 0.43 (sec) , antiderivative size = 153, normalized size of antiderivative = 5.46 \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=- \frac {x^{2} \log {\left (x \right )}}{8 x^{3} - 16 x^{2} - 5} + \frac {- 640 x^{3} + 1280 x^{2} - 640 x + 1680}{- 2048 x^{9} + 12288 x^{8} - 26624 x^{7} + 32512 x^{6} - 39936 x^{5} + 34304 x^{4} - 12640 x^{3} + 15040 x^{2} - 800 x + \left (512 x^{9} - 3072 x^{8} + 6144 x^{7} - 5056 x^{6} + 3840 x^{5} - 3840 x^{4} + 600 x^{3} - 1200 x^{2} - 125\right ) \log {\left (x \right )} + 2100} - \frac {20}{64 x^{6} - 256 x^{5} + 256 x^{4} - 80 x^{3} + 160 x^{2} + 25} \]
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Time = 0.24 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {x^{2} \log \left (x\right )^{2} - 4 \, {\left (x^{2} + 1\right )} \log \left (x\right )}{32 \, x^{3} - 64 \, x^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - 5\right )} \log \left (x\right ) + 32 \, x - 84} \]
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Leaf count of result is larger than twice the leaf count of optimal. 177 vs. \(2 (27) = 54\).
Time = 0.30 (sec) , antiderivative size = 177, normalized size of antiderivative = 6.32 \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=-\frac {x^{2} \log \left (x\right )}{8 \, x^{3} - 16 \, x^{2} - 5} - \frac {80 \, {\left (8 \, x^{3} - 16 \, x^{2} + 8 \, x - 21\right )}}{512 \, x^{9} \log \left (x\right ) - 2048 \, x^{9} - 3072 \, x^{8} \log \left (x\right ) + 12288 \, x^{8} + 6144 \, x^{7} \log \left (x\right ) - 26624 \, x^{7} - 5056 \, x^{6} \log \left (x\right ) + 32512 \, x^{6} + 3840 \, x^{5} \log \left (x\right ) - 39936 \, x^{5} - 3840 \, x^{4} \log \left (x\right ) + 34304 \, x^{4} + 600 \, x^{3} \log \left (x\right ) - 12640 \, x^{3} - 1200 \, x^{2} \log \left (x\right ) + 15040 \, x^{2} - 800 \, x - 125 \, \log \left (x\right ) + 2100} - \frac {20}{64 \, x^{6} - 256 \, x^{5} + 256 \, x^{4} - 80 \, x^{3} + 160 \, x^{2} + 25} \]
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Timed out. \[ \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\int \frac {\ln \left (x\right )\,\left (192\,x^5-128\,x^4+320\,x^3-8\,x^2+128\,x\right )-128\,x+{\ln \left (x\right )}^3\,\left (8\,x^5+10\,x^2\right )+592\,x^2-256\,x^3+256\,x^4-128\,x^5-{\ln \left (x\right )}^2\,\left (72\,x^5-16\,x^4+64\,x^3+75\,x^2\right )+336}{7056\,x-\ln \left (x\right )\,\left (512\,x^7-2048\,x^6+2560\,x^5-2688\,x^4+3328\,x^3-320\,x^2+840\,x\right )-5376\,x^2+11776\,x^3-9472\,x^4+6144\,x^5-4096\,x^6+1024\,x^7+{\ln \left (x\right )}^2\,\left (64\,x^7-256\,x^6+256\,x^5-80\,x^4+160\,x^3+25\,x\right )} \,d x \]
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