Integrand size = 121, antiderivative size = 31 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=-x+\frac {1}{12} x \left (-2+\frac {\log ^2\left (\frac {5}{x}-x^2\right )}{(-5+x)^2}\right ) \]
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Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 7.25 (sec) , antiderivative size = 3583, normalized size of antiderivative = 115.58, number of steps used = 295, number of rules used = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.198, Rules used = {6873, 12, 6857, 1889, 31, 648, 631, 210, 642, 2608, 2605, 2604, 2465, 2441, 2352, 266, 2463, 2440, 2438, 2439, 2437, 2338, 2404, 2375} \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx =\text {Too large to display} \]
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Rule 12
Rule 31
Rule 210
Rule 266
Rule 631
Rule 642
Rule 648
Rule 1889
Rule 2338
Rule 2352
Rule 2375
Rule 2404
Rule 2437
Rule 2438
Rule 2439
Rule 2440
Rule 2441
Rule 2463
Rule 2465
Rule 2604
Rule 2605
Rule 2608
Rule 6857
Rule 6873
Rubi steps \begin{align*} \text {integral}& = \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)^3 \left (5-x^3\right )} \, dx \\ & = \frac {1}{12} \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{(5-x)^3 \left (5-x^3\right )} \, dx \\ & = \frac {1}{12} \int \left (-\frac {8750}{(-5+x)^3 \left (-5+x^3\right )}+\frac {5250 x}{(-5+x)^3 \left (-5+x^3\right )}-\frac {1050 x^2}{(-5+x)^3 \left (-5+x^3\right )}+\frac {1820 x^3}{(-5+x)^3 \left (-5+x^3\right )}-\frac {1050 x^4}{(-5+x)^3 \left (-5+x^3\right )}+\frac {210 x^5}{(-5+x)^3 \left (-5+x^3\right )}-\frac {14 x^6}{(-5+x)^3 \left (-5+x^3\right )}+\frac {2 \left (5+2 x^3\right ) \log \left (\frac {5-x^3}{x}\right )}{(-5+x)^2 \left (-5+x^3\right )}-\frac {(5+x) \log ^2\left (\frac {5-x^3}{x}\right )}{(-5+x)^3}\right ) \, dx \\ & = -\left (\frac {1}{12} \int \frac {(5+x) \log ^2\left (\frac {5-x^3}{x}\right )}{(-5+x)^3} \, dx\right )+\frac {1}{6} \int \frac {\left (5+2 x^3\right ) \log \left (\frac {5-x^3}{x}\right )}{(-5+x)^2 \left (-5+x^3\right )} \, dx-\frac {7}{6} \int \frac {x^6}{(-5+x)^3 \left (-5+x^3\right )} \, dx+\frac {35}{2} \int \frac {x^5}{(-5+x)^3 \left (-5+x^3\right )} \, dx-\frac {175}{2} \int \frac {x^2}{(-5+x)^3 \left (-5+x^3\right )} \, dx-\frac {175}{2} \int \frac {x^4}{(-5+x)^3 \left (-5+x^3\right )} \, dx+\frac {455}{3} \int \frac {x^3}{(-5+x)^3 \left (-5+x^3\right )} \, dx+\frac {875}{2} \int \frac {x}{(-5+x)^3 \left (-5+x^3\right )} \, dx-\frac {4375}{6} \int \frac {1}{(-5+x)^3 \left (-5+x^3\right )} \, dx \\ & = -\left (\frac {1}{12} \int \left (\frac {10 \log ^2\left (\frac {5-x^3}{x}\right )}{(-5+x)^3}+\frac {\log ^2\left (\frac {5-x^3}{x}\right )}{(-5+x)^2}\right ) \, dx\right )+\frac {1}{6} \int \left (\frac {17 \log \left (\frac {5-x^3}{x}\right )}{8 (-5+x)^2}-\frac {5 \log \left (\frac {5-x^3}{x}\right )}{64 (-5+x)}+\frac {\left (45+17 x+5 x^2\right ) \log \left (\frac {5-x^3}{x}\right )}{64 \left (-5+x^3\right )}\right ) \, dx-\frac {7}{6} \int \left (1+\frac {3125}{24 (-5+x)^3}+\frac {14375}{192 (-5+x)^2}+\frac {23125}{1536 (-5+x)}-\frac {5 \left (89+45 x+17 x^2\right )}{1536 \left (-5+x^3\right )}\right ) \, dx+\frac {35}{2} \int \left (\frac {625}{24 (-5+x)^3}+\frac {625}{64 (-5+x)^2}+\frac {1625}{1536 (-5+x)}+\frac {-225-85 x-89 x^2}{1536 \left (-5+x^3\right )}\right ) \, dx-\frac {175}{2} \int \left (\frac {5}{24 (-5+x)^3}-\frac {3}{64 (-5+x)^2}+\frac {89}{7680 (-5+x)}+\frac {-225-85 x-89 x^2}{7680 \left (-5+x^3\right )}\right ) \, dx-\frac {175}{2} \int \left (\frac {125}{24 (-5+x)^3}+\frac {175}{192 (-5+x)^2}+\frac {15}{512 (-5+x)}+\frac {-85-89 x-45 x^2}{1536 \left (-5+x^3\right )}\right ) \, dx+\frac {455}{3} \int \left (\frac {25}{24 (-5+x)^3}-\frac {5}{192 (-5+x)^2}+\frac {17}{1536 (-5+x)}+\frac {-89-45 x-17 x^2}{1536 \left (-5+x^3\right )}\right ) \, dx+\frac {875}{2} \int \left (\frac {1}{24 (-5+x)^3}-\frac {17}{960 (-5+x)^2}+\frac {3}{512 (-5+x)}+\frac {-85-89 x-45 x^2}{7680 \left (-5+x^3\right )}\right ) \, dx-\frac {4375}{6} \int \left (\frac {1}{120 (-5+x)^3}-\frac {1}{192 (-5+x)^2}+\frac {17}{7680 (-5+x)}+\frac {-89-45 x-17 x^2}{7680 \left (-5+x^3\right )}\right ) \, dx \\ & = -\frac {7 x}{6}+\frac {1}{384} \int \frac {\left (45+17 x+5 x^2\right ) \log \left (\frac {5-x^3}{x}\right )}{-5+x^3} \, dx+\frac {35 \int \frac {89+45 x+17 x^2}{-5+x^3} \, dx}{9216}-\frac {5}{384} \int \frac {\log \left (\frac {5-x^3}{x}\right )}{-5+x} \, dx-\frac {1}{12} \int \frac {\log ^2\left (\frac {5-x^3}{x}\right )}{(-5+x)^2} \, dx-\frac {875 \int \frac {-89-45 x-17 x^2}{-5+x^3} \, dx}{9216}+\frac {455 \int \frac {-89-45 x-17 x^2}{-5+x^3} \, dx}{4608}+\frac {17}{48} \int \frac {\log \left (\frac {5-x^3}{x}\right )}{(-5+x)^2} \, dx-\frac {5}{6} \int \frac {\log ^2\left (\frac {5-x^3}{x}\right )}{(-5+x)^3} \, dx \\ & = -\frac {7 x}{6}+\frac {17 \log \left (\frac {5-x^3}{x}\right )}{48 (5-x)}-\frac {5}{384} \log (-5+x) \log \left (\frac {5-x^3}{x}\right )+\frac {5 \log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)^2}-\frac {\log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)}+\frac {1}{384} \int \left (-\frac {\left (25+45 \sqrt [3]{5}+17\ 5^{2/3}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}-x\right )}-\frac {\left (17 (-5)^{2/3}-25 \sqrt [3]{-1}+45 \sqrt [3]{5}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right )}-\frac {\left (25 (-1)^{2/3}+45 \sqrt [3]{5}-17 \sqrt [3]{-1} 5^{2/3}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}-(-1)^{2/3} x\right )}\right ) \, dx+\frac {5}{384} \int \frac {x \left (-3 x-\frac {5-x^3}{x^2}\right ) \log (-5+x)}{5-x^3} \, dx-\frac {1}{6} \int \frac {\left (5+2 x^3\right ) \log \left (\frac {5-x^3}{x}\right )}{(5-x) x \left (5-x^3\right )} \, dx+\frac {17}{48} \int \frac {5+2 x^3}{(5-x) x \left (5-x^3\right )} \, dx-\frac {5}{6} \int \frac {\left (-5-2 x^3\right ) \log \left (\frac {5-x^3}{x}\right )}{(5-x)^2 x \left (5-x^3\right )} \, dx-\frac {\left (7 \sqrt [3]{5}\right ) \int \frac {\sqrt [3]{5} \left (178-45 \sqrt [3]{5}-17\ 5^{2/3}\right )+\left (89+45 \sqrt [3]{5}-34\ 5^{2/3}\right ) x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{27648}+\frac {\left (175 \sqrt [3]{5}\right ) \int \frac {\sqrt [3]{5} \left (-178+45 \sqrt [3]{5}+17\ 5^{2/3}\right )+\left (-89-45 \sqrt [3]{5}+34\ 5^{2/3}\right ) x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{27648}-\frac {\left (91 \sqrt [3]{5}\right ) \int \frac {\sqrt [3]{5} \left (-178+45 \sqrt [3]{5}+17\ 5^{2/3}\right )+\left (-89-45 \sqrt [3]{5}+34\ 5^{2/3}\right ) x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{13824}+\frac {\left (7 \sqrt [3]{5} \left (-89-45 \sqrt [3]{5}-17\ 5^{2/3}\right )\right ) \int \frac {1}{\sqrt [3]{5}-x} \, dx}{27648}-\frac {\left (175 \sqrt [3]{5} \left (89+45 \sqrt [3]{5}+17\ 5^{2/3}\right )\right ) \int \frac {1}{\sqrt [3]{5}-x} \, dx}{27648}+\frac {\left (91 \sqrt [3]{5} \left (89+45 \sqrt [3]{5}+17\ 5^{2/3}\right )\right ) \int \frac {1}{\sqrt [3]{5}-x} \, dx}{13824} \\ & = -\frac {7 x}{6}+\frac {17 \log \left (\frac {5-x^3}{x}\right )}{48 (5-x)}-\frac {5}{384} \log (-5+x) \log \left (\frac {5-x^3}{x}\right )+\frac {5 \log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)^2}-\frac {\log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)}+\frac {5}{384} \int \left (-\frac {\log (-5+x)}{x}+\frac {3 x^2 \log (-5+x)}{-5+x^3}\right ) \, dx-\frac {1}{6} \int \left (\frac {17 \log \left (\frac {5-x^3}{x}\right )}{40 (-5+x)}+\frac {\log \left (\frac {5-x^3}{x}\right )}{5 x}+\frac {\left (-5-x-5 x^2\right ) \log \left (\frac {5-x^3}{x}\right )}{8 \left (-5+x^3\right )}\right ) \, dx+\frac {17}{48} \int \left (\frac {17}{40 (-5+x)}+\frac {1}{5 x}+\frac {-5-x-5 x^2}{8 \left (-5+x^3\right )}\right ) \, dx-\frac {5}{6} \int \left (\frac {17 \log \left (\frac {5-x^3}{x}\right )}{40 (-5+x)^2}-\frac {161 \log \left (\frac {5-x^3}{x}\right )}{1600 (-5+x)}-\frac {\log \left (\frac {5-x^3}{x}\right )}{25 x}+\frac {\left (17+5 x+9 x^2\right ) \log \left (\frac {5-x^3}{x}\right )}{64 \left (-5+x^3\right )}\right ) \, dx+\frac {\left (-17 (-5)^{2/3}+25 \sqrt [3]{-1}-45 \sqrt [3]{5}\right ) \int \frac {\log \left (\frac {5-x^3}{x}\right )}{\sqrt [3]{5}+\sqrt [3]{-1} x} \, dx}{5760}+\frac {\left (7 \left (225-89\ 5^{2/3}\right )\right ) \int \frac {1}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{18432}+\frac {\left (175 \left (225-89\ 5^{2/3}\right )\right ) \int \frac {1}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{18432}-\frac {\left (91 \left (225-89\ 5^{2/3}\right )\right ) \int \frac {1}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{9216}-\frac {\left (7 \sqrt [3]{5} \left (89+45 \sqrt [3]{5}-34\ 5^{2/3}\right )\right ) \int \frac {\sqrt [3]{5}+2 x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{55296}-\frac {\left (25+45 \sqrt [3]{5}+17\ 5^{2/3}\right ) \int \frac {\log \left (\frac {5-x^3}{x}\right )}{\sqrt [3]{5}-x} \, dx}{5760}+\frac {\left (175 \sqrt [3]{5} \left (-89-45 \sqrt [3]{5}+34\ 5^{2/3}\right )\right ) \int \frac {\sqrt [3]{5}+2 x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{55296}-\frac {\left (91 \sqrt [3]{5} \left (-89-45 \sqrt [3]{5}+34\ 5^{2/3}\right )\right ) \int \frac {\sqrt [3]{5}+2 x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{27648}+\frac {\left (-25 (-1)^{2/3}-45 \sqrt [3]{5}+17 \sqrt [3]{-1} 5^{2/3}\right ) \int \frac {\log \left (\frac {5-x^3}{x}\right )}{\sqrt [3]{5}-(-1)^{2/3} x} \, dx}{5760} \\ & = -\frac {7 x}{6}+\frac {289 \log (5-x)}{1920}+\frac {17 \log (x)}{240}+\frac {17 \log \left (\frac {5-x^3}{x}\right )}{48 (5-x)}+\frac {\left (25+5^{2/3} \left (17+9\ 5^{2/3}\right )\right ) \log \left (\sqrt [3]{5}-x\right ) \log \left (\frac {5-x^3}{x}\right )}{5760}-\frac {5}{384} \log (-5+x) \log \left (\frac {5-x^3}{x}\right )+\frac {(-1)^{2/3} \left (17 (-5)^{2/3}-25 \sqrt [3]{-1}+45 \sqrt [3]{5}\right ) \log \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right ) \log \left (\frac {5-x^3}{x}\right )}{5760}+\frac {\left (25-45 \sqrt [3]{-5}+17 (-5)^{2/3}\right ) \log \left (\sqrt [3]{5}-(-1)^{2/3} x\right ) \log \left (\frac {5-x^3}{x}\right )}{5760}+\frac {5 \log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)^2}-\frac {\log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)}-\frac {5}{384} \int \frac {\log (-5+x)}{x} \, dx-\frac {5}{384} \int \frac {\left (17+5 x+9 x^2\right ) \log \left (\frac {5-x^3}{x}\right )}{-5+x^3} \, dx-\frac {1}{48} \int \frac {\left (-5-x-5 x^2\right ) \log \left (\frac {5-x^3}{x}\right )}{-5+x^3} \, dx+\frac {5}{128} \int \frac {x^2 \log (-5+x)}{-5+x^3} \, dx+\frac {17}{384} \int \frac {-5-x-5 x^2}{-5+x^3} \, dx-\frac {17}{240} \int \frac {\log \left (\frac {5-x^3}{x}\right )}{-5+x} \, dx+\frac {161 \int \frac {\log \left (\frac {5-x^3}{x}\right )}{-5+x} \, dx}{1920}-\frac {17}{48} \int \frac {\log \left (\frac {5-x^3}{x}\right )}{(-5+x)^2} \, dx+\frac {\left (-25+45 \sqrt [3]{-5}-17 (-5)^{2/3}\right ) \int \frac {x \left (-3 x-\frac {5-x^3}{x^2}\right ) \log \left (\sqrt [3]{5}-(-1)^{2/3} x\right )}{5-x^3} \, dx}{5760}+\frac {\left (7 \sqrt [3]{5} \left (89-45 \sqrt [3]{5}\right )\right ) \text {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,1+\frac {2 x}{\sqrt [3]{5}}\right )}{9216}+\frac {\left (175 \sqrt [3]{5} \left (89-45 \sqrt [3]{5}\right )\right ) \text {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,1+\frac {2 x}{\sqrt [3]{5}}\right )}{9216}-\frac {\left (91 \sqrt [3]{5} \left (89-45 \sqrt [3]{5}\right )\right ) \text {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,1+\frac {2 x}{\sqrt [3]{5}}\right )}{4608}-\frac {\left ((-1)^{2/3} \left (17 (-5)^{2/3}-25 \sqrt [3]{-1}+45 \sqrt [3]{5}\right )\right ) \int \frac {x \left (-3 x-\frac {5-x^3}{x^2}\right ) \log \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right )}{5-x^3} \, dx}{5760}-\frac {\left (25+45 \sqrt [3]{5}+17\ 5^{2/3}\right ) \int \frac {x \left (-3 x-\frac {5-x^3}{x^2}\right ) \log \left (\sqrt [3]{5}-x\right )}{5-x^3} \, dx}{5760} \\ & = -\frac {7 x}{6}+\frac {289 \log (5-x)}{1920}-\frac {5}{384} \log (-5+x) \log \left (\frac {x}{5}\right )+\frac {17 \log (x)}{240}+\frac {\left (25+5^{2/3} \left (17+9\ 5^{2/3}\right )\right ) \log \left (\sqrt [3]{5}-x\right ) \log \left (\frac {5-x^3}{x}\right )}{5760}+\frac {(-1)^{2/3} \left (17 (-5)^{2/3}-25 \sqrt [3]{-1}+45 \sqrt [3]{5}\right ) \log \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right ) \log \left (\frac {5-x^3}{x}\right )}{5760}+\frac {\left (25-45 \sqrt [3]{-5}+17 (-5)^{2/3}\right ) \log \left (\sqrt [3]{5}-(-1)^{2/3} x\right ) \log \left (\frac {5-x^3}{x}\right )}{5760}+\frac {5 \log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)^2}-\frac {\log ^2\left (\frac {5-x^3}{x}\right )}{12 (5-x)}+\frac {5}{384} \int \frac {\log \left (\frac {x}{5}\right )}{-5+x} \, dx-\frac {5}{384} \int \left (-\frac {\left (45+17 \sqrt [3]{5}+5\ 5^{2/3}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}-x\right )}-\frac {\left (5 (-5)^{2/3}-45 \sqrt [3]{-1}+17 \sqrt [3]{5}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right )}-\frac {\left (45 (-1)^{2/3}+17 \sqrt [3]{5}-5 \sqrt [3]{-1} 5^{2/3}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}-(-1)^{2/3} x\right )}\right ) \, dx-\frac {1}{48} \int \left (-\frac {\left (-25-5 \sqrt [3]{5}-5^{2/3}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}-x\right )}-\frac {\left (-(-5)^{2/3}+25 \sqrt [3]{-1}-5 \sqrt [3]{5}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right )}-\frac {\left (-25 (-1)^{2/3}-5 \sqrt [3]{5}+\sqrt [3]{-1} 5^{2/3}\right ) \log \left (\frac {5-x^3}{x}\right )}{15 \left (\sqrt [3]{5}-(-1)^{2/3} x\right )}\right ) \, dx+\frac {5}{128} \int \left (-\frac {\log (-5+x)}{3 \left (-\sqrt [3]{-5}-x\right )}-\frac {\log (-5+x)}{3 \left (\sqrt [3]{5}-x\right )}-\frac {\log (-5+x)}{3 \left ((-1)^{2/3} \sqrt [3]{5}-x\right )}\right ) \, dx+\frac {17}{240} \int \frac {x \left (-3 x-\frac {5-x^3}{x^2}\right ) \log (-5+x)}{5-x^3} \, dx-\frac {161 \int \frac {x \left (-3 x-\frac {5-x^3}{x^2}\right ) \log (-5+x)}{5-x^3} \, dx}{1920}-\frac {17}{48} \int \frac {5+2 x^3}{(5-x) x \left (5-x^3\right )} \, dx-\frac {17 \int \frac {\sqrt [3]{5} \left (-10+\sqrt [3]{5}+5\ 5^{2/3}\right )+\left (-5-\sqrt [3]{5}+10\ 5^{2/3}\right ) x}{5^{2/3}+\sqrt [3]{5} x+x^2} \, dx}{1152\ 5^{2/3}}+\frac {\left (-25+45 \sqrt [3]{-5}-17 (-5)^{2/3}\right ) \int \left (-\frac {\log \left (\sqrt [3]{5}-(-1)^{2/3} x\right )}{x}+\frac {3 x^2 \log \left (\sqrt [3]{5}-(-1)^{2/3} x\right )}{-5+x^3}\right ) \, dx}{5760}-\frac {\left ((-1)^{2/3} \left (17 (-5)^{2/3}-25 \sqrt [3]{-1}+45 \sqrt [3]{5}\right )\right ) \int \left (-\frac {\log \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right )}{x}+\frac {3 x^2 \log \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right )}{-5+x^3}\right ) \, dx}{5760}+\frac {\left (17 \left (5+\sqrt [3]{5}+5\ 5^{2/3}\right )\right ) \int \frac {1}{\sqrt [3]{5}-x} \, dx}{1152\ 5^{2/3}}-\frac {\left (25+45 \sqrt [3]{5}+17\ 5^{2/3}\right ) \int \left (-\frac {\log \left (\sqrt [3]{5}-x\right )}{x}+\frac {3 x^2 \log \left (\sqrt [3]{5}-x\right )}{-5+x^3}\right ) \, dx}{5760} \\ & = \text {Too large to display} \\ \end{align*}
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 48.77 (sec) , antiderivative size = 184188, normalized size of antiderivative = 5941.55 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=\text {Result too large to show} \]
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Time = 0.21 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.03
method | result | size |
risch | \(\frac {\ln \left (\frac {-x^{3}+5}{x}\right )^{2} x}{12 x^{2}-120 x +300}-\frac {7 x}{6}\) | \(32\) |
norman | \(\frac {\frac {175 x}{2}-\frac {7 x^{3}}{6}+\frac {\ln \left (\frac {-x^{3}+5}{x}\right )^{2} x}{12}-\frac {875}{3}}{\left (-5+x \right )^{2}}\) | \(34\) |
parallelrisch | \(-\frac {3500+14 x^{3}-\ln \left (-\frac {x^{3}-5}{x}\right )^{2} x -1050 x}{12 \left (x^{2}-10 x +25\right )}\) | \(39\) |
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Time = 0.25 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=-\frac {14 \, x^{3} - x \log \left (-\frac {x^{3} - 5}{x}\right )^{2} - 140 \, x^{2} + 350 \, x}{12 \, {\left (x^{2} - 10 \, x + 25\right )}} \]
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Time = 0.14 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=- \frac {7 x}{6} + \frac {x \log {\left (\frac {5 - x^{3}}{x} \right )}^{2}}{12 x^{2} - 120 x + 300} \]
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Leaf count of result is larger than twice the leaf count of optimal. 165 vs. \(2 (29) = 58\).
Time = 3.61 (sec) , antiderivative size = 165, normalized size of antiderivative = 5.32 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=-\frac {7}{6} \, x + \frac {x \log \left (-x^{3} + 5\right )^{2} - 2 \, x \log \left (-x^{3} + 5\right ) \log \left (x\right ) + x \log \left (x\right )^{2}}{12 \, {\left (x^{2} - 10 \, x + 25\right )}} + \frac {4375 \, {\left (23 \, x - 95\right )}}{1152 \, {\left (x^{2} - 10 \, x + 25\right )}} + \frac {175 \, {\left (17 \, x - 105\right )}}{384 \, {\left (x^{2} - 10 \, x + 25\right )}} - \frac {175 \, {\left (9 \, x - 65\right )}}{384 \, {\left (x^{2} - 10 \, x + 25\right )}} + \frac {4375 \, {\left (7 \, x - 15\right )}}{384 \, {\left (x^{2} - 10 \, x + 25\right )}} - \frac {875 \, {\left (5 \, x - 29\right )}}{1152 \, {\left (x^{2} - 10 \, x + 25\right )}} - \frac {21875 \, {\left (3 \, x - 11\right )}}{384 \, {\left (x^{2} - 10 \, x + 25\right )}} + \frac {2275 \, {\left (x - 25\right )}}{576 \, {\left (x^{2} - 10 \, x + 25\right )}} \]
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Time = 0.52 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.97 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=\frac {x \log \left (-\frac {x^{3} - 5}{x}\right )^{2}}{12 \, {\left (x^{2} - 10 \, x + 25\right )}} - \frac {7}{6} \, x \]
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Time = 9.83 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.81 \[ \int \frac {-8750+5250 x-1050 x^2+1820 x^3-1050 x^4+210 x^5-14 x^6+\left (-50+10 x-20 x^3+4 x^4\right ) \log \left (\frac {5-x^3}{x}\right )+\left (25+5 x-5 x^3-x^4\right ) \log ^2\left (\frac {5-x^3}{x}\right )}{7500-4500 x+900 x^2-1560 x^3+900 x^4-180 x^5+12 x^6} \, dx=\frac {x\,{\ln \left (-\frac {x^3-5}{x}\right )}^2}{12\,{\left (x-5\right )}^2}-\frac {7\,x}{6} \]
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