Integrand size = 60, antiderivative size = 28 \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=\log ^2\left (\frac {4}{3 e^3 \left (5-\frac {5}{8 (5-x)}\right )^2 x^2}\right ) \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(203\) vs. \(2(28)=56\).
Time = 0.93 (sec) , antiderivative size = 203, normalized size of antiderivative = 7.25, number of steps used = 48, number of rules used = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.233, Rules used = {1608, 2608, 2604, 12, 27, 2465, 2437, 2338, 2441, 2352, 2440, 2438, 2404, 2353} \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=4 \log \left (\frac {256 \left (x^2-10 x+25\right )}{75 e^3 \left (64 x^4-624 x^3+1521 x^2\right )}\right ) \log (x-5)-4 \log (x) \log \left (\frac {256 \left (x^2-10 x+25\right )}{75 e^3 \left (64 x^4-624 x^3+1521 x^2\right )}\right )-4 \log (8 x-39) \log \left (\frac {256 \left (x^2-10 x+25\right )}{75 e^3 \left (64 x^4-624 x^3+1521 x^2\right )}\right )-4 \log ^2(x-5)-4 \log ^2(x)-4 \log ^2(8 x-39)+8 \log \left (\frac {x}{5}\right ) \log (x-5)+8 \log (8 x-39) \log (x-5)+8 \log (5) \log (x-5)-8 \log \left (\frac {8 x}{39}\right ) \log (8 x-39)-8 \log \left (\frac {39}{8}\right ) \log (8 x-39) \]
[In]
[Out]
Rule 12
Rule 27
Rule 1608
Rule 2338
Rule 2352
Rule 2353
Rule 2404
Rule 2437
Rule 2438
Rule 2440
Rule 2441
Rule 2465
Rule 2604
Rule 2608
Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{x \left (195-79 x+8 x^2\right )} \, dx \\ & = \int \left (\frac {4 \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{-5+x}-\frac {4 \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{x}-\frac {32 \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{-39+8 x}\right ) \, dx \\ & = 4 \int \frac {\log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{-5+x} \, dx-4 \int \frac {\log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{x} \, dx-32 \int \frac {\log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{-39+8 x} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \int \frac {e^3 \left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{6400-2560 x+256 x^2} \, dx+4 \int \frac {e^3 \left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{6400-2560 x+256 x^2} \, dx+4 \int \frac {e^3 \left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{6400-2560 x+256 x^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\left (4 e^3\right ) \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{6400-2560 x+256 x^2} \, dx+\left (4 e^3\right ) \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{6400-2560 x+256 x^2} \, dx+\left (4 e^3\right ) \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{6400-2560 x+256 x^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\left (4 e^3\right ) \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{256 (-5+x)^2} \, dx+\left (4 e^3\right ) \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{256 (-5+x)^2} \, dx+\left (4 e^3\right ) \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{256 (-5+x)^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\frac {1}{64} e^3 \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{(-5+x)^2} \, dx+\frac {1}{64} e^3 \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{(-5+x)^2} \, dx+\frac {1}{64} e^3 \int \frac {\left (114075 x^2-46800 x^3+4800 x^4\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{(-5+x)^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\frac {1}{64} e^3 \int \frac {x^2 \left (114075-46800 x+4800 x^2\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{(-5+x)^2} \, dx+\frac {1}{64} e^3 \int \frac {x^2 \left (114075-46800 x+4800 x^2\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{(-5+x)^2} \, dx+\frac {1}{64} e^3 \int \frac {x^2 \left (114075-46800 x+4800 x^2\right ) \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{(-5+x)^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\frac {1}{64} e^3 \int \frac {75 x^2 (-39+8 x)^2 \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{(-5+x)^2} \, dx+\frac {1}{64} e^3 \int \frac {75 x^2 (-39+8 x)^2 \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{(-5+x)^2} \, dx+\frac {1}{64} e^3 \int \frac {75 x^2 (-39+8 x)^2 \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{(-5+x)^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\frac {1}{64} \left (75 e^3\right ) \int \frac {x^2 (-39+8 x)^2 \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-5+x)}{(-5+x)^2} \, dx+\frac {1}{64} \left (75 e^3\right ) \int \frac {x^2 (-39+8 x)^2 \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (x)}{(-5+x)^2} \, dx+\frac {1}{64} \left (75 e^3\right ) \int \frac {x^2 (-39+8 x)^2 \left (-\frac {\left (6400-2560 x+256 x^2\right ) \left (228150 x-140400 x^2+19200 x^3\right )}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )^2}+\frac {-2560+512 x}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right ) \log (-39+8 x)}{(-5+x)^2} \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-\frac {1}{64} \left (75 e^3\right ) \int \left (\frac {512 \log (-5+x)}{75 e^3 (-5+x)}-\frac {512 \log (-5+x)}{75 e^3 x}-\frac {4096 \log (-5+x)}{75 e^3 (-39+8 x)}\right ) \, dx+\frac {1}{64} \left (75 e^3\right ) \int \left (\frac {512 \log (x)}{75 e^3 (-5+x)}-\frac {512 \log (x)}{75 e^3 x}-\frac {4096 \log (x)}{75 e^3 (-39+8 x)}\right ) \, dx+\frac {1}{64} \left (75 e^3\right ) \int \left (\frac {512 \log (-39+8 x)}{75 e^3 (-5+x)}-\frac {512 \log (-39+8 x)}{75 e^3 x}-\frac {4096 \log (-39+8 x)}{75 e^3 (-39+8 x)}\right ) \, dx \\ & = 4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-8 \int \frac {\log (-5+x)}{-5+x} \, dx+8 \int \frac {\log (-5+x)}{x} \, dx+8 \int \frac {\log (x)}{-5+x} \, dx-8 \int \frac {\log (x)}{x} \, dx+8 \int \frac {\log (-39+8 x)}{-5+x} \, dx-8 \int \frac {\log (-39+8 x)}{x} \, dx+64 \int \frac {\log (-5+x)}{-39+8 x} \, dx-64 \int \frac {\log (x)}{-39+8 x} \, dx-64 \int \frac {\log (-39+8 x)}{-39+8 x} \, dx \\ & = 8 \log (5) \log (-5+x)+8 \log (-5+x) \log \left (\frac {x}{5}\right )-4 \log ^2(x)-8 \log \left (\frac {39}{8}\right ) \log (-39+8 x)+8 \log (-5+x) \log (-39+8 x)-8 \log \left (\frac {8 x}{39}\right ) \log (-39+8 x)+4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-8 \int \frac {\log (-39+8 x)}{-5+x} \, dx-8 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-5+x\right )-8 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-39+8 x\right )+8 \text {Subst}\left (\int \frac {\log (1+8 x)}{x} \, dx,x,-5+x\right ) \\ & = 8 \log (5) \log (-5+x)-4 \log ^2(-5+x)+8 \log (-5+x) \log \left (\frac {x}{5}\right )-4 \log ^2(x)-8 \log \left (\frac {39}{8}\right ) \log (-39+8 x)+8 \log (-5+x) \log (-39+8 x)-8 \log \left (\frac {8 x}{39}\right ) \log (-39+8 x)-4 \log ^2(-39+8 x)+4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-8 \operatorname {PolyLog}(2,8 (5-x))-8 \text {Subst}\left (\int \frac {\log (1+8 x)}{x} \, dx,x,-5+x\right ) \\ & = 8 \log (5) \log (-5+x)-4 \log ^2(-5+x)+8 \log (-5+x) \log \left (\frac {x}{5}\right )-4 \log ^2(x)-8 \log \left (\frac {39}{8}\right ) \log (-39+8 x)+8 \log (-5+x) \log (-39+8 x)-8 \log \left (\frac {8 x}{39}\right ) \log (-39+8 x)-4 \log ^2(-39+8 x)+4 \log (-5+x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right )-4 \log (-39+8 x) \log \left (\frac {256 \left (25-10 x+x^2\right )}{75 e^3 \left (1521 x^2-624 x^3+64 x^4\right )}\right ) \\ \end{align*}
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 0.10 (sec) , antiderivative size = 197, normalized size of antiderivative = 7.04 \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=-4 \left (\log ^2(5-x)-2 \log (5) \log (-5+x)-2 \log (5) \log (x)+\log ^2(x)-\log (5-x) \left (-3+\log \left (\frac {256}{75}\right )+\log \left (\frac {(-5+x)^2}{x^2 (-39+8 x)^2}\right )\right )+\log (x) \left (-3+\log \left (\frac {256}{75}\right )+\log \left (\frac {(-5+x)^2}{x^2 (-39+8 x)^2}\right )\right )+2 \log \left (\frac {39}{8}\right ) \log (-39+8 x)+\log (64) \log (-39+8 x)+2 \log \left (\frac {8 x}{39}\right ) \log (-39+8 x)+\left (-3+\log \left (\frac {256}{75}\right )+\log \left (\frac {(-5+x)^2}{x^2 (-39+8 x)^2}\right )\right ) \log (-39+8 x)+\log ^2(-39+8 x)+2 \operatorname {PolyLog}(2,40-8 x)+2 \operatorname {PolyLog}\left (2,1-\frac {x}{5}\right )+2 \operatorname {PolyLog}\left (2,\frac {x}{5}\right )+2 \operatorname {PolyLog}(2,-39+8 x)\right ) \]
[In]
[Out]
Time = 0.19 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32
method | result | size |
norman | \({\ln \left (\frac {\left (256 x^{2}-2560 x +6400\right ) {\mathrm e}^{-3}}{4800 x^{4}-46800 x^{3}+114075 x^{2}}\right )}^{2}\) | \(37\) |
default | \(4 \ln \left (75\right ) \left (\ln \left (x \right )-\ln \left (-5+x \right )+\ln \left (8 x -39\right )\right )+12 \ln \left (x \right )-12 \ln \left (-5+x \right )+12 \ln \left (8 x -39\right )-32 \ln \left (2\right ) \left (\ln \left (x \right )-\ln \left (-5+x \right )+\ln \left (8 x -39\right )\right )-4 \ln \left (x \right ) \ln \left (\frac {x^{2}-10 x +25}{x^{2} \left (64 x^{2}-624 x +1521\right )}\right )-4 \ln \left (x \right )^{2}+8 \left (\ln \left (x \right )-\ln \left (\frac {x}{5}\right )\right ) \ln \left (1-\frac {x}{5}\right )-8 \left (\ln \left (x \right )-\ln \left (\frac {8 x}{39}\right )\right ) \ln \left (-\frac {8 x}{39}+1\right )+4 \ln \left (-5+x \right ) \ln \left (\frac {x^{2}-10 x +25}{x^{2} \left (64 x^{2}-624 x +1521\right )}\right )-4 \ln \left (-5+x \right )^{2}+8 \ln \left (-5+x \right ) \ln \left (8 x -39\right )+8 \ln \left (-5+x \right ) \ln \left (\frac {x}{5}\right )-4 \ln \left (8 x -39\right ) \ln \left (\frac {x^{2}-10 x +25}{x^{2} \left (64 x^{2}-624 x +1521\right )}\right )-4 \ln \left (8 x -39\right )^{2}-8 \ln \left (8 x -39\right ) \ln \left (\frac {8 x}{39}\right )\) | \(243\) |
risch | \(-4 \ln \left (x \right )^{2}-32 \ln \left (2\right ) \ln \left (x \right )+4 \ln \left (75\right ) \ln \left (x \right )-4 \ln \left (x \right ) \ln \left (\frac {\left (x^{2}-10 x +25\right ) {\mathrm e}^{-3}}{x^{2} \left (64 x^{2}-624 x +1521\right )}\right )-8 \ln \left (-\frac {8 x}{39}+1\right ) \ln \left (x \right )+8 \ln \left (1-\frac {x}{5}\right ) \ln \left (x \right )+32 \ln \left (2\right ) \ln \left (-5+x \right )-32 \ln \left (2\right ) \ln \left (8 x -39\right )-4 \ln \left (75\right ) \ln \left (-5+x \right )+4 \ln \left (75\right ) \ln \left (8 x -39\right )+4 \ln \left (-5+x \right ) \ln \left (\frac {\left (x^{2}-10 x +25\right ) {\mathrm e}^{-3}}{x^{2} \left (64 x^{2}-624 x +1521\right )}\right )-4 \ln \left (8 x -39\right ) \ln \left (\frac {\left (x^{2}-10 x +25\right ) {\mathrm e}^{-3}}{x^{2} \left (64 x^{2}-624 x +1521\right )}\right )+8 \ln \left (-\frac {8 x}{39}+1\right ) \ln \left (\frac {8 x}{39}\right )-8 \ln \left (1-\frac {x}{5}\right ) \ln \left (\frac {x}{5}\right )-8 \ln \left (8 x -39\right ) \ln \left (\frac {8 x}{39}\right )+8 \ln \left (-5+x \right ) \ln \left (\frac {x}{5}\right )-4 \ln \left (-5+x \right )^{2}+8 \ln \left (-5+x \right ) \ln \left (8 x -39\right )-4 \ln \left (8 x -39\right )^{2}\) | \(251\) |
parts | \(-4 \ln \left (\frac {\left (256 x^{2}-2560 x +6400\right ) {\mathrm e}^{-3}}{4800 x^{4}-46800 x^{3}+114075 x^{2}}\right ) \ln \left (x \right )+4 \ln \left (\frac {\left (256 x^{2}-2560 x +6400\right ) {\mathrm e}^{-3}}{4800 x^{4}-46800 x^{3}+114075 x^{2}}\right ) \ln \left (-5+x \right )-4 \ln \left (\frac {\left (256 x^{2}-2560 x +6400\right ) {\mathrm e}^{-3}}{4800 x^{4}-46800 x^{3}+114075 x^{2}}\right ) \ln \left (8 x -39\right )-\frac {75 \,{\mathrm e}^{3} \left (\frac {512 \,{\mathrm e}^{-3} \left (\frac {\ln \left (x \right )^{2}}{2}-\left (\ln \left (x \right )-\ln \left (\frac {x}{5}\right )\right ) \ln \left (1-\frac {x}{5}\right )+\operatorname {dilog}\left (\frac {x}{5}\right )+\left (\ln \left (x \right )-\ln \left (\frac {8 x}{39}\right )\right ) \ln \left (-\frac {8 x}{39}+1\right )-\operatorname {dilog}\left (\frac {8 x}{39}\right )\right )}{75}-\frac {512 \,{\mathrm e}^{-3} \left (-\frac {\ln \left (-5+x \right )^{2}}{2}+\operatorname {dilog}\left (8 x -39\right )+\ln \left (-5+x \right ) \ln \left (8 x -39\right )+\operatorname {dilog}\left (\frac {x}{5}\right )+\ln \left (-5+x \right ) \ln \left (\frac {x}{5}\right )\right )}{75}+\frac {512 \,{\mathrm e}^{-3} \left (\frac {\ln \left (8 x -39\right )^{2}}{2}+\operatorname {dilog}\left (8 x -39\right )+\operatorname {dilog}\left (\frac {8 x}{39}\right )+\ln \left (8 x -39\right ) \ln \left (\frac {8 x}{39}\right )\right )}{75}\right )}{64}\) | \(266\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=\log \left (\frac {256 \, {\left (x^{2} - 10 \, x + 25\right )} e^{\left (-3\right )}}{75 \, {\left (64 \, x^{4} - 624 \, x^{3} + 1521 \, x^{2}\right )}}\right )^{2} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=\log {\left (\frac {256 x^{2} - 2560 x + 6400}{\left (4800 x^{4} - 46800 x^{3} + 114075 x^{2}\right ) e^{3}} \right )}^{2} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 98 vs. \(2 (19) = 38\).
Time = 0.21 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.50 \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=8 \, {\left (\log \left (x - 5\right ) - \log \left (x\right )\right )} \log \left (8 \, x - 39\right ) - 4 \, \log \left (8 \, x - 39\right )^{2} - 4 \, \log \left (x - 5\right )^{2} + 8 \, \log \left (x - 5\right ) \log \left (x\right ) - 4 \, \log \left (x\right )^{2} - 4 \, {\left (\log \left (8 \, x - 39\right ) - \log \left (x - 5\right ) + \log \left (x\right )\right )} \log \left (\frac {256 \, {\left (x^{2} - 10 \, x + 25\right )} e^{\left (-3\right )}}{75 \, {\left (64 \, x^{4} - 624 \, x^{3} + 1521 \, x^{2}\right )}}\right ) \]
[In]
[Out]
\[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx=\int { -\frac {4 \, {\left (8 \, x^{2} - 80 \, x + 195\right )} \log \left (\frac {256 \, {\left (x^{2} - 10 \, x + 25\right )} e^{\left (-3\right )}}{75 \, {\left (64 \, x^{4} - 624 \, x^{3} + 1521 \, x^{2}\right )}}\right )}{8 \, x^{3} - 79 \, x^{2} + 195 \, x} \,d x } \]
[In]
[Out]
Time = 9.60 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {\left (-780+320 x-32 x^2\right ) \log \left (\frac {6400-2560 x+256 x^2}{e^3 \left (114075 x^2-46800 x^3+4800 x^4\right )}\right )}{195 x-79 x^2+8 x^3} \, dx={\left (\ln \left (\frac {256\,x^2-2560\,x+6400}{4800\,x^4-46800\,x^3+114075\,x^2}\right )-3\right )}^2 \]
[In]
[Out]