Integrand size = 439, antiderivative size = 31 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=(25+\log (4))^2 \left (x-\frac {-e-\frac {4}{x}+\log (x)}{x+x^2}\right )^2 \]
[Out]
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 1.34 (sec) , antiderivative size = 836, normalized size of antiderivative = 26.97, number of steps used = 49, number of rules used = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6820, 12, 6874, 46, 37, 45, 2404, 2341, 2338, 2356, 2351, 31, 2354, 2438, 2342, 2389, 2379, 2355} \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=-\frac {e (25+\log (4))^2 x^2}{(x+1)^2}+(25+\log (4))^2 x^2-\frac {2 (25+\log (4))^2 \log ^2(x) x}{x+1}-\frac {4 (6-e) (25+\log (4))^2 \log (x) x}{x+1}+\frac {2 (25+\log (4))^2 \log (x) x}{x+1}+\frac {(25+\log (4))^2 \log ^2(x)}{(x+1)^2}+3 (25+\log (4))^2 \log ^2(x)+2 (25+\log (4))^2 \log \left (1+\frac {1}{x}\right ) \log (x)+\frac {2 (4-e) (25+\log (4))^2 \log (x)}{(x+1)^2}+6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x)-12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x)+80 (13+3 e) (25+\log (4))^2 \log (x)-2 (4-e) (25+\log (4))^2 \log (x)-986 (25+\log (4))^2 \log (x)-2 (25+\log (4))^2 \log (x) \log (x+1)-6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x+1)+12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x+1)-80 (13+3 e) (25+\log (4))^2 \log (x+1)+4 (6-e) (25+\log (4))^2 \log (x+1)+2 (4-e) (25+\log (4))^2 \log (x+1)+984 (25+\log (4))^2 \log (x+1)-2 (25+\log (4))^2 \operatorname {PolyLog}\left (2,-\frac {1}{x}\right )-2 (25+\log (4))^2 \operatorname {PolyLog}(2,-x)+\frac {4 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x+1}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x+1}+\frac {32 (13+3 e) (25+\log (4))^2}{x+1}-\frac {2 (4-e) (25+\log (4))^2}{x+1}-\frac {344 (25+\log (4))^2}{x+1}+\frac {\left (4+e+2 e^2\right ) (25+\log (4))^2}{(x+1)^2}-\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{(x+1)^2}+\frac {4 (13+3 e) (25+\log (4))^2}{(x+1)^2}+\frac {(10+e) (25+\log (4))^2}{(x+1)^2}-\frac {46 (25+\log (4))^2}{(x+1)^2}-\frac {2 (25+\log (4))^2 \log ^2(x)}{x}-\frac {4 (5-e) (25+\log (4))^2 \log (x)}{x}-\frac {4 (25+\log (4))^2 \log (x)}{x}+\frac {2 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x}+\frac {48 (13+3 e) (25+\log (4))^2}{x}-\frac {4 (5-e) (25+\log (4))^2}{x}-\frac {644 (25+\log (4))^2}{x}+\frac {(25+\log (4))^2 \log ^2(x)}{x^2}+\frac {(15-2 e) (25+\log (4))^2 \log (x)}{x^2}+\frac {(25+\log (4))^2 \log (x)}{x^2}+\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{x^2}-\frac {12 (13+3 e) (25+\log (4))^2}{x^2}+\frac {(15-2 e) (25+\log (4))^2}{2 x^2}+\frac {385 (25+\log (4))^2}{2 x^2}-\frac {8 (25+\log (4))^2 \log (x)}{x^3}+\frac {8 (13+3 e) (25+\log (4))^2}{3 x^3}-\frac {200 (25+\log (4))^2}{3 x^3}+\frac {16 (25+\log (4))^2}{x^4} \]
[In]
[Out]
Rule 12
Rule 31
Rule 37
Rule 45
Rule 46
Rule 2338
Rule 2341
Rule 2342
Rule 2351
Rule 2354
Rule 2355
Rule 2356
Rule 2379
Rule 2389
Rule 2404
Rule 2438
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 (25+\log (4))^2 \left (-32-4 (13+3 e) x-\left (4+21 e+e^2\right ) x^2-\left (4+e+2 e^2\right ) x^3-13 x^4-(10+e) x^5-e x^6+3 x^7+3 x^8+x^9+x \left (12+(21+2 e) x+(1+4 e) x^2+x^4+x^5\right ) \log (x)-x^2 (1+2 x) \log ^2(x)\right )}{x^5 (1+x)^3} \, dx \\ & = \left (2 (25+\log (4))^2\right ) \int \frac {-32-4 (13+3 e) x-\left (4+21 e+e^2\right ) x^2-\left (4+e+2 e^2\right ) x^3-13 x^4-(10+e) x^5-e x^6+3 x^7+3 x^8+x^9+x \left (12+(21+2 e) x+(1+4 e) x^2+x^4+x^5\right ) \log (x)-x^2 (1+2 x) \log ^2(x)}{x^5 (1+x)^3} \, dx \\ & = \left (2 (25+\log (4))^2\right ) \int \left (\frac {-10-e}{(1+x)^3}-\frac {32}{x^5 (1+x)^3}-\frac {4 (13+3 e)}{x^4 (1+x)^3}+\frac {-4-21 e-e^2}{x^3 (1+x)^3}+\frac {-4-e-2 e^2}{x^2 (1+x)^3}-\frac {13}{x (1+x)^3}-\frac {e x}{(1+x)^3}+\frac {3 x^2}{(1+x)^3}+\frac {3 x^3}{(1+x)^3}+\frac {x^4}{(1+x)^3}+\frac {\left (12+21 \left (1+\frac {2 e}{21}\right ) x+(1+4 e) x^2+x^4+x^5\right ) \log (x)}{x^4 (1+x)^3}-\frac {(1+2 x) \log ^2(x)}{x^3 (1+x)^3}\right ) \, dx \\ & = \frac {(10+e) (25+\log (4))^2}{(1+x)^2}+\left (2 (25+\log (4))^2\right ) \int \frac {x^4}{(1+x)^3} \, dx+\left (2 (25+\log (4))^2\right ) \int \frac {\left (12+21 \left (1+\frac {2 e}{21}\right ) x+(1+4 e) x^2+x^4+x^5\right ) \log (x)}{x^4 (1+x)^3} \, dx-\left (2 (25+\log (4))^2\right ) \int \frac {(1+2 x) \log ^2(x)}{x^3 (1+x)^3} \, dx+\left (6 (25+\log (4))^2\right ) \int \frac {x^2}{(1+x)^3} \, dx+\left (6 (25+\log (4))^2\right ) \int \frac {x^3}{(1+x)^3} \, dx-\left (26 (25+\log (4))^2\right ) \int \frac {1}{x (1+x)^3} \, dx-\left (64 (25+\log (4))^2\right ) \int \frac {1}{x^5 (1+x)^3} \, dx-\left (2 e (25+\log (4))^2\right ) \int \frac {x}{(1+x)^3} \, dx-\left (8 (13+3 e) (25+\log (4))^2\right ) \int \frac {1}{x^4 (1+x)^3} \, dx-\left (2 \left (4+21 e+e^2\right ) (25+\log (4))^2\right ) \int \frac {1}{x^3 (1+x)^3} \, dx-\left (2 \left (4+e+2 e^2\right ) (25+\log (4))^2\right ) \int \frac {1}{x^2 (1+x)^3} \, dx \\ & = \frac {(10+e) (25+\log (4))^2}{(1+x)^2}-\frac {e x^2 (25+\log (4))^2}{(1+x)^2}+\left (2 (25+\log (4))^2\right ) \int \left (-3+x+\frac {1}{(1+x)^3}-\frac {4}{(1+x)^2}+\frac {6}{1+x}\right ) \, dx+\left (2 (25+\log (4))^2\right ) \int \left (\frac {12 \log (x)}{x^4}+\frac {(-15+2 e) \log (x)}{x^3}-\frac {2 (-5+e) \log (x)}{x^2}+\frac {3 \log (x)}{x}+\frac {2 (-4+e) \log (x)}{(1+x)^3}+\frac {2 (-6+e) \log (x)}{(1+x)^2}-\frac {3 \log (x)}{1+x}\right ) \, dx-\left (2 (25+\log (4))^2\right ) \int \left (\frac {\log ^2(x)}{x^3}-\frac {\log ^2(x)}{x^2}+\frac {\log ^2(x)}{(1+x)^3}+\frac {\log ^2(x)}{(1+x)^2}\right ) \, dx+\left (6 (25+\log (4))^2\right ) \int \left (1-\frac {1}{(1+x)^3}+\frac {3}{(1+x)^2}-\frac {3}{1+x}\right ) \, dx+\left (6 (25+\log (4))^2\right ) \int \left (\frac {1}{(1+x)^3}-\frac {2}{(1+x)^2}+\frac {1}{1+x}\right ) \, dx-\left (26 (25+\log (4))^2\right ) \int \left (\frac {1}{-1-x}+\frac {1}{x}-\frac {1}{(1+x)^3}-\frac {1}{(1+x)^2}\right ) \, dx-\left (64 (25+\log (4))^2\right ) \int \left (\frac {1}{x^5}-\frac {3}{x^4}+\frac {6}{x^3}-\frac {10}{x^2}+\frac {15}{x}-\frac {1}{(1+x)^3}-\frac {5}{(1+x)^2}-\frac {15}{1+x}\right ) \, dx-\left (8 (13+3 e) (25+\log (4))^2\right ) \int \left (\frac {1}{x^4}-\frac {3}{x^3}+\frac {6}{x^2}-\frac {10}{x}+\frac {1}{(1+x)^3}+\frac {4}{(1+x)^2}+\frac {10}{1+x}\right ) \, dx-\left (2 \left (4+21 e+e^2\right ) (25+\log (4))^2\right ) \int \left (\frac {1}{x^3}-\frac {3}{x^2}+\frac {6}{x}-\frac {1}{(1+x)^3}-\frac {3}{(1+x)^2}-\frac {6}{1+x}\right ) \, dx-\left (2 \left (4+e+2 e^2\right ) (25+\log (4))^2\right ) \int \left (\frac {1}{x^2}-\frac {3}{x}+\frac {1}{(1+x)^3}+\frac {2}{(1+x)^2}+\frac {3}{1+x}\right ) \, dx \\ & = \frac {16 (25+\log (4))^2}{x^4}-\frac {64 (25+\log (4))^2}{x^3}+\frac {8 (13+3 e) (25+\log (4))^2}{3 x^3}+\frac {192 (25+\log (4))^2}{x^2}-\frac {12 (13+3 e) (25+\log (4))^2}{x^2}+\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{x^2}-\frac {640 (25+\log (4))^2}{x}+\frac {48 (13+3 e) (25+\log (4))^2}{x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x}+\frac {2 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x}+x^2 (25+\log (4))^2-\frac {46 (25+\log (4))^2}{(1+x)^2}+\frac {(10+e) (25+\log (4))^2}{(1+x)^2}+\frac {4 (13+3 e) (25+\log (4))^2}{(1+x)^2}-\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{(1+x)^2}+\frac {\left (4+e+2 e^2\right ) (25+\log (4))^2}{(1+x)^2}-\frac {e x^2 (25+\log (4))^2}{(1+x)^2}-\frac {344 (25+\log (4))^2}{1+x}+\frac {32 (13+3 e) (25+\log (4))^2}{1+x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{1+x}+\frac {4 \left (4+e+2 e^2\right ) (25+\log (4))^2}{1+x}-986 (25+\log (4))^2 \log (x)+80 (13+3 e) (25+\log (4))^2 \log (x)-12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x)+6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x)+986 (25+\log (4))^2 \log (1+x)-80 (13+3 e) (25+\log (4))^2 \log (1+x)+12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (1+x)-6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (1+x)-\left (2 (25+\log (4))^2\right ) \int \frac {\log ^2(x)}{x^3} \, dx+\left (2 (25+\log (4))^2\right ) \int \frac {\log ^2(x)}{x^2} \, dx-\left (2 (25+\log (4))^2\right ) \int \frac {\log ^2(x)}{(1+x)^3} \, dx-\left (2 (25+\log (4))^2\right ) \int \frac {\log ^2(x)}{(1+x)^2} \, dx+\left (6 (25+\log (4))^2\right ) \int \frac {\log (x)}{x} \, dx-\left (6 (25+\log (4))^2\right ) \int \frac {\log (x)}{1+x} \, dx+\left (24 (25+\log (4))^2\right ) \int \frac {\log (x)}{x^4} \, dx-\left (2 (15-2 e) (25+\log (4))^2\right ) \int \frac {\log (x)}{x^3} \, dx-\left (4 (4-e) (25+\log (4))^2\right ) \int \frac {\log (x)}{(1+x)^3} \, dx+\left (4 (5-e) (25+\log (4))^2\right ) \int \frac {\log (x)}{x^2} \, dx-\left (4 (6-e) (25+\log (4))^2\right ) \int \frac {\log (x)}{(1+x)^2} \, dx \\ & = \frac {16 (25+\log (4))^2}{x^4}-\frac {200 (25+\log (4))^2}{3 x^3}+\frac {8 (13+3 e) (25+\log (4))^2}{3 x^3}+\frac {192 (25+\log (4))^2}{x^2}+\frac {(15-2 e) (25+\log (4))^2}{2 x^2}-\frac {12 (13+3 e) (25+\log (4))^2}{x^2}+\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{x^2}-\frac {640 (25+\log (4))^2}{x}-\frac {4 (5-e) (25+\log (4))^2}{x}+\frac {48 (13+3 e) (25+\log (4))^2}{x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x}+\frac {2 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x}+x^2 (25+\log (4))^2-\frac {46 (25+\log (4))^2}{(1+x)^2}+\frac {(10+e) (25+\log (4))^2}{(1+x)^2}+\frac {4 (13+3 e) (25+\log (4))^2}{(1+x)^2}-\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{(1+x)^2}+\frac {\left (4+e+2 e^2\right ) (25+\log (4))^2}{(1+x)^2}-\frac {e x^2 (25+\log (4))^2}{(1+x)^2}-\frac {344 (25+\log (4))^2}{1+x}+\frac {32 (13+3 e) (25+\log (4))^2}{1+x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{1+x}+\frac {4 \left (4+e+2 e^2\right ) (25+\log (4))^2}{1+x}-986 (25+\log (4))^2 \log (x)+80 (13+3 e) (25+\log (4))^2 \log (x)-12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x)+6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x)-\frac {8 (25+\log (4))^2 \log (x)}{x^3}+\frac {(15-2 e) (25+\log (4))^2 \log (x)}{x^2}-\frac {4 (5-e) (25+\log (4))^2 \log (x)}{x}+\frac {2 (4-e) (25+\log (4))^2 \log (x)}{(1+x)^2}-\frac {4 (6-e) x (25+\log (4))^2 \log (x)}{1+x}+3 (25+\log (4))^2 \log ^2(x)+\frac {(25+\log (4))^2 \log ^2(x)}{x^2}-\frac {2 (25+\log (4))^2 \log ^2(x)}{x}+\frac {(25+\log (4))^2 \log ^2(x)}{(1+x)^2}-\frac {2 x (25+\log (4))^2 \log ^2(x)}{1+x}+986 (25+\log (4))^2 \log (1+x)-80 (13+3 e) (25+\log (4))^2 \log (1+x)+12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (1+x)-6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (1+x)-6 (25+\log (4))^2 \log (x) \log (1+x)-\left (2 (25+\log (4))^2\right ) \int \frac {\log (x)}{x^3} \, dx-\left (2 (25+\log (4))^2\right ) \int \frac {\log (x)}{x (1+x)^2} \, dx+\left (4 (25+\log (4))^2\right ) \int \frac {\log (x)}{x^2} \, dx+\left (4 (25+\log (4))^2\right ) \int \frac {\log (x)}{1+x} \, dx+\left (6 (25+\log (4))^2\right ) \int \frac {\log (1+x)}{x} \, dx-\left (2 (4-e) (25+\log (4))^2\right ) \int \frac {1}{x (1+x)^2} \, dx+\left (4 (6-e) (25+\log (4))^2\right ) \int \frac {1}{1+x} \, dx \\ & = \frac {16 (25+\log (4))^2}{x^4}-\frac {200 (25+\log (4))^2}{3 x^3}+\frac {8 (13+3 e) (25+\log (4))^2}{3 x^3}+\frac {385 (25+\log (4))^2}{2 x^2}+\frac {(15-2 e) (25+\log (4))^2}{2 x^2}-\frac {12 (13+3 e) (25+\log (4))^2}{x^2}+\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{x^2}-\frac {644 (25+\log (4))^2}{x}-\frac {4 (5-e) (25+\log (4))^2}{x}+\frac {48 (13+3 e) (25+\log (4))^2}{x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x}+\frac {2 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x}+x^2 (25+\log (4))^2-\frac {46 (25+\log (4))^2}{(1+x)^2}+\frac {(10+e) (25+\log (4))^2}{(1+x)^2}+\frac {4 (13+3 e) (25+\log (4))^2}{(1+x)^2}-\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{(1+x)^2}+\frac {\left (4+e+2 e^2\right ) (25+\log (4))^2}{(1+x)^2}-\frac {e x^2 (25+\log (4))^2}{(1+x)^2}-\frac {344 (25+\log (4))^2}{1+x}+\frac {32 (13+3 e) (25+\log (4))^2}{1+x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{1+x}+\frac {4 \left (4+e+2 e^2\right ) (25+\log (4))^2}{1+x}-986 (25+\log (4))^2 \log (x)+80 (13+3 e) (25+\log (4))^2 \log (x)-12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x)+6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x)-\frac {8 (25+\log (4))^2 \log (x)}{x^3}+\frac {(25+\log (4))^2 \log (x)}{x^2}+\frac {(15-2 e) (25+\log (4))^2 \log (x)}{x^2}-\frac {4 (25+\log (4))^2 \log (x)}{x}-\frac {4 (5-e) (25+\log (4))^2 \log (x)}{x}+\frac {2 (4-e) (25+\log (4))^2 \log (x)}{(1+x)^2}-\frac {4 (6-e) x (25+\log (4))^2 \log (x)}{1+x}+3 (25+\log (4))^2 \log ^2(x)+\frac {(25+\log (4))^2 \log ^2(x)}{x^2}-\frac {2 (25+\log (4))^2 \log ^2(x)}{x}+\frac {(25+\log (4))^2 \log ^2(x)}{(1+x)^2}-\frac {2 x (25+\log (4))^2 \log ^2(x)}{1+x}+986 (25+\log (4))^2 \log (1+x)+4 (6-e) (25+\log (4))^2 \log (1+x)-80 (13+3 e) (25+\log (4))^2 \log (1+x)+12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (1+x)-6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (1+x)-2 (25+\log (4))^2 \log (x) \log (1+x)-6 (25+\log (4))^2 \operatorname {PolyLog}(2,-x)+\left (2 (25+\log (4))^2\right ) \int \frac {\log (x)}{(1+x)^2} \, dx-\left (2 (25+\log (4))^2\right ) \int \frac {\log (x)}{x (1+x)} \, dx-\left (4 (25+\log (4))^2\right ) \int \frac {\log (1+x)}{x} \, dx-\left (2 (4-e) (25+\log (4))^2\right ) \int \left (\frac {1}{-1-x}+\frac {1}{x}-\frac {1}{(1+x)^2}\right ) \, dx \\ & = \frac {16 (25+\log (4))^2}{x^4}-\frac {200 (25+\log (4))^2}{3 x^3}+\frac {8 (13+3 e) (25+\log (4))^2}{3 x^3}+\frac {385 (25+\log (4))^2}{2 x^2}+\frac {(15-2 e) (25+\log (4))^2}{2 x^2}-\frac {12 (13+3 e) (25+\log (4))^2}{x^2}+\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{x^2}-\frac {644 (25+\log (4))^2}{x}-\frac {4 (5-e) (25+\log (4))^2}{x}+\frac {48 (13+3 e) (25+\log (4))^2}{x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x}+\frac {2 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x}+x^2 (25+\log (4))^2-\frac {46 (25+\log (4))^2}{(1+x)^2}+\frac {(10+e) (25+\log (4))^2}{(1+x)^2}+\frac {4 (13+3 e) (25+\log (4))^2}{(1+x)^2}-\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{(1+x)^2}+\frac {\left (4+e+2 e^2\right ) (25+\log (4))^2}{(1+x)^2}-\frac {e x^2 (25+\log (4))^2}{(1+x)^2}-\frac {344 (25+\log (4))^2}{1+x}-\frac {2 (4-e) (25+\log (4))^2}{1+x}+\frac {32 (13+3 e) (25+\log (4))^2}{1+x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{1+x}+\frac {4 \left (4+e+2 e^2\right ) (25+\log (4))^2}{1+x}-986 (25+\log (4))^2 \log (x)-2 (4-e) (25+\log (4))^2 \log (x)+80 (13+3 e) (25+\log (4))^2 \log (x)-12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x)+6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x)-\frac {8 (25+\log (4))^2 \log (x)}{x^3}+\frac {(25+\log (4))^2 \log (x)}{x^2}+\frac {(15-2 e) (25+\log (4))^2 \log (x)}{x^2}-\frac {4 (25+\log (4))^2 \log (x)}{x}-\frac {4 (5-e) (25+\log (4))^2 \log (x)}{x}+\frac {2 (4-e) (25+\log (4))^2 \log (x)}{(1+x)^2}+\frac {2 x (25+\log (4))^2 \log (x)}{1+x}-\frac {4 (6-e) x (25+\log (4))^2 \log (x)}{1+x}+2 (25+\log (4))^2 \log \left (1+\frac {1}{x}\right ) \log (x)+3 (25+\log (4))^2 \log ^2(x)+\frac {(25+\log (4))^2 \log ^2(x)}{x^2}-\frac {2 (25+\log (4))^2 \log ^2(x)}{x}+\frac {(25+\log (4))^2 \log ^2(x)}{(1+x)^2}-\frac {2 x (25+\log (4))^2 \log ^2(x)}{1+x}+986 (25+\log (4))^2 \log (1+x)+2 (4-e) (25+\log (4))^2 \log (1+x)+4 (6-e) (25+\log (4))^2 \log (1+x)-80 (13+3 e) (25+\log (4))^2 \log (1+x)+12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (1+x)-6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (1+x)-2 (25+\log (4))^2 \log (x) \log (1+x)-2 (25+\log (4))^2 \operatorname {PolyLog}(2,-x)-\left (2 (25+\log (4))^2\right ) \int \frac {1}{1+x} \, dx-\left (2 (25+\log (4))^2\right ) \int \frac {\log \left (1+\frac {1}{x}\right )}{x} \, dx \\ & = \frac {16 (25+\log (4))^2}{x^4}-\frac {200 (25+\log (4))^2}{3 x^3}+\frac {8 (13+3 e) (25+\log (4))^2}{3 x^3}+\frac {385 (25+\log (4))^2}{2 x^2}+\frac {(15-2 e) (25+\log (4))^2}{2 x^2}-\frac {12 (13+3 e) (25+\log (4))^2}{x^2}+\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{x^2}-\frac {644 (25+\log (4))^2}{x}-\frac {4 (5-e) (25+\log (4))^2}{x}+\frac {48 (13+3 e) (25+\log (4))^2}{x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{x}+\frac {2 \left (4+e+2 e^2\right ) (25+\log (4))^2}{x}+x^2 (25+\log (4))^2-\frac {46 (25+\log (4))^2}{(1+x)^2}+\frac {(10+e) (25+\log (4))^2}{(1+x)^2}+\frac {4 (13+3 e) (25+\log (4))^2}{(1+x)^2}-\frac {\left (4+21 e+e^2\right ) (25+\log (4))^2}{(1+x)^2}+\frac {\left (4+e+2 e^2\right ) (25+\log (4))^2}{(1+x)^2}-\frac {e x^2 (25+\log (4))^2}{(1+x)^2}-\frac {344 (25+\log (4))^2}{1+x}-\frac {2 (4-e) (25+\log (4))^2}{1+x}+\frac {32 (13+3 e) (25+\log (4))^2}{1+x}-\frac {6 \left (4+21 e+e^2\right ) (25+\log (4))^2}{1+x}+\frac {4 \left (4+e+2 e^2\right ) (25+\log (4))^2}{1+x}-986 (25+\log (4))^2 \log (x)-2 (4-e) (25+\log (4))^2 \log (x)+80 (13+3 e) (25+\log (4))^2 \log (x)-12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (x)+6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (x)-\frac {8 (25+\log (4))^2 \log (x)}{x^3}+\frac {(25+\log (4))^2 \log (x)}{x^2}+\frac {(15-2 e) (25+\log (4))^2 \log (x)}{x^2}-\frac {4 (25+\log (4))^2 \log (x)}{x}-\frac {4 (5-e) (25+\log (4))^2 \log (x)}{x}+\frac {2 (4-e) (25+\log (4))^2 \log (x)}{(1+x)^2}+\frac {2 x (25+\log (4))^2 \log (x)}{1+x}-\frac {4 (6-e) x (25+\log (4))^2 \log (x)}{1+x}+2 (25+\log (4))^2 \log \left (1+\frac {1}{x}\right ) \log (x)+3 (25+\log (4))^2 \log ^2(x)+\frac {(25+\log (4))^2 \log ^2(x)}{x^2}-\frac {2 (25+\log (4))^2 \log ^2(x)}{x}+\frac {(25+\log (4))^2 \log ^2(x)}{(1+x)^2}-\frac {2 x (25+\log (4))^2 \log ^2(x)}{1+x}+984 (25+\log (4))^2 \log (1+x)+2 (4-e) (25+\log (4))^2 \log (1+x)+4 (6-e) (25+\log (4))^2 \log (1+x)-80 (13+3 e) (25+\log (4))^2 \log (1+x)+12 \left (4+21 e+e^2\right ) (25+\log (4))^2 \log (1+x)-6 \left (4+e+2 e^2\right ) (25+\log (4))^2 \log (1+x)-2 (25+\log (4))^2 \log (x) \log (1+x)-2 (25+\log (4))^2 \operatorname {PolyLog}\left (2,-\frac {1}{x}\right )-2 (25+\log (4))^2 \operatorname {PolyLog}(2,-x) \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=\frac {(25+\log (4))^2 \left (4+e x+x^3+x^4-x \log (x)\right )^2}{x^4 (1+x)^2} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(356\) vs. \(2(34)=68\).
Time = 0.34 (sec) , antiderivative size = 357, normalized size of antiderivative = 11.52
method | result | size |
risch | \(\frac {\left (4 \ln \left (2\right )^{2}+100 \ln \left (2\right )+625\right ) \ln \left (x \right )^{2}}{x^{2} \left (x^{2}+2 x +1\right )}-\frac {2 \left (4 x^{4} \ln \left (2\right )^{2}+4 x^{3} \ln \left (2\right )^{2}+100 x^{4} \ln \left (2\right )+4 \ln \left (2\right )^{2} {\mathrm e} x +100 x^{3} \ln \left (2\right )+625 x^{4}+100 x \,{\mathrm e} \ln \left (2\right )+625 x^{3}+625 x \,{\mathrm e}+16 \ln \left (2\right )^{2}+400 \ln \left (2\right )+2500\right ) \ln \left (x \right )}{x^{3} \left (x^{2}+2 x +1\right )}+\frac {10000+1250 x^{5} {\mathrm e}+32 \ln \left (2\right )^{2} {\mathrm e} x +4 \,{\mathrm e}^{2} \ln \left (2\right )^{2} x^{2}+100 \,{\mathrm e}^{2} \ln \left (2\right ) x^{2}+100 x^{8} \ln \left (2\right )+8 x^{7} \ln \left (2\right )^{2}+200 x^{7} \ln \left (2\right )+32 x^{4} \ln \left (2\right )^{2}+32 x^{3} \ln \left (2\right )^{2}+800 x^{4} \ln \left (2\right )+100 x^{6} \ln \left (2\right )+5000 x \,{\mathrm e}+800 x^{3} \ln \left (2\right )+1250 x^{4} {\mathrm e}+625 x^{2} {\mathrm e}^{2}+4 x^{6} \ln \left (2\right )^{2}+800 x \,{\mathrm e} \ln \left (2\right )+1600 \ln \left (2\right )+64 \ln \left (2\right )^{2}+1250 x^{7}+625 x^{8}+5000 x^{4}+5000 x^{3}+625 x^{6}+8 \ln \left (2\right )^{2} {\mathrm e} x^{4}+200 \ln \left (2\right ) {\mathrm e} x^{5}+200 \ln \left (2\right ) {\mathrm e} x^{4}+8 \,{\mathrm e} \ln \left (2\right )^{2} x^{5}+4 \ln \left (2\right )^{2} x^{8}}{x^{4} \left (x^{2}+2 x +1\right )}\) | \(357\) |
parallelrisch | \(\frac {10000-8 x^{4} \ln \left (2\right )^{2} \ln \left (x \right )+1250 x^{5} {\mathrm e}-1250 x^{2} {\mathrm e} \ln \left (x \right )+32 \ln \left (2\right )^{2} {\mathrm e} x +4 \,{\mathrm e}^{2} \ln \left (2\right )^{2} x^{2}+100 \,{\mathrm e}^{2} \ln \left (2\right ) x^{2}+100 x^{8} \ln \left (2\right )-8 x^{5} \ln \left (2\right )^{2}+8 x^{7} \ln \left (2\right )^{2}+200 x^{7} \ln \left (2\right )+28 x^{4} \ln \left (2\right )^{2}+32 x^{3} \ln \left (2\right )^{2}-1250 x^{5} \ln \left (x \right )+700 x^{4} \ln \left (2\right )-200 x^{5} \ln \left (2\right )-1250 x^{4} \ln \left (x \right )+5000 x \,{\mathrm e}+800 x^{3} \ln \left (2\right )+1250 x^{4} {\mathrm e}+625 x^{2} {\mathrm e}^{2}-5000 x \ln \left (x \right )-8 \ln \left (x \right ) {\mathrm e} \ln \left (2\right )^{2} x^{2}-200 \ln \left (x \right ) {\mathrm e} \ln \left (2\right ) x^{2}+100 x^{2} \ln \left (2\right ) \ln \left (x \right )^{2}+625 x^{2} \ln \left (x \right )^{2}+800 x \,{\mathrm e} \ln \left (2\right )-800 x \ln \left (2\right ) \ln \left (x \right )+1600 \ln \left (2\right )+64 \ln \left (2\right )^{2}+1250 x^{7}+625 x^{8}+4375 x^{4}+5000 x^{3}-1250 x^{5}-200 \ln \left (x \right ) \ln \left (2\right ) x^{4}+8 \ln \left (2\right )^{2} {\mathrm e} x^{4}+200 \ln \left (2\right ) {\mathrm e} x^{5}+200 \ln \left (2\right ) {\mathrm e} x^{4}-8 \ln \left (x \right ) \ln \left (2\right )^{2} x^{5}+8 \,{\mathrm e} \ln \left (2\right )^{2} x^{5}-200 \ln \left (x \right ) \ln \left (2\right ) x^{5}+4 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{2}-32 \ln \left (x \right ) \ln \left (2\right )^{2} x +4 \ln \left (2\right )^{2} x^{8}}{x^{4} \left (x^{2}+2 x +1\right )}\) | \(381\) |
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Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (33) = 66\).
Time = 0.28 (sec) , antiderivative size = 253, normalized size of antiderivative = 8.16 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=\frac {625 \, x^{8} + 1250 \, x^{7} + 625 \, x^{6} + 5000 \, x^{4} + 5000 \, x^{3} + 625 \, x^{2} e^{2} + 4 \, {\left (x^{8} + 2 \, x^{7} + x^{6} + 8 \, x^{4} + 8 \, x^{3} + x^{2} e^{2} + 2 \, {\left (x^{5} + x^{4} + 4 \, x\right )} e + 16\right )} \log \left (2\right )^{2} + {\left (4 \, x^{2} \log \left (2\right )^{2} + 100 \, x^{2} \log \left (2\right ) + 625 \, x^{2}\right )} \log \left (x\right )^{2} + 1250 \, {\left (x^{5} + x^{4} + 4 \, x\right )} e + 100 \, {\left (x^{8} + 2 \, x^{7} + x^{6} + 8 \, x^{4} + 8 \, x^{3} + x^{2} e^{2} + 2 \, {\left (x^{5} + x^{4} + 4 \, x\right )} e + 16\right )} \log \left (2\right ) - 2 \, {\left (625 \, x^{5} + 625 \, x^{4} + 625 \, x^{2} e + 4 \, {\left (x^{5} + x^{4} + x^{2} e + 4 \, x\right )} \log \left (2\right )^{2} + 100 \, {\left (x^{5} + x^{4} + x^{2} e + 4 \, x\right )} \log \left (2\right ) + 2500 \, x\right )} \log \left (x\right ) + 10000}{x^{6} + 2 \, x^{5} + x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 316 vs. \(2 (26) = 52\).
Time = 157.59 (sec) , antiderivative size = 316, normalized size of antiderivative = 10.19 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=x^{2} \cdot \left (4 \log {\left (2 \right )}^{2} + 100 \log {\left (2 \right )} + 625\right ) + \frac {x^{5} \cdot \left (8 e \log {\left (2 \right )}^{2} + 200 e \log {\left (2 \right )} + 1250 e\right ) + x^{4} \cdot \left (8 e \log {\left (2 \right )}^{2} + 32 \log {\left (2 \right )}^{2} + 200 e \log {\left (2 \right )} + 800 \log {\left (2 \right )} + 1250 e + 5000\right ) + x^{3} \cdot \left (32 \log {\left (2 \right )}^{2} + 800 \log {\left (2 \right )} + 5000\right ) + x^{2} \cdot \left (4 e^{2} \log {\left (2 \right )}^{2} + 100 e^{2} \log {\left (2 \right )} + 625 e^{2}\right ) + x \left (32 e \log {\left (2 \right )}^{2} + 800 e \log {\left (2 \right )} + 5000 e\right ) + 64 \log {\left (2 \right )}^{2} + 1600 \log {\left (2 \right )} + 10000}{x^{6} + 2 x^{5} + x^{4}} + \frac {\left (- 1250 x^{4} - 200 x^{4} \log {\left (2 \right )} - 8 x^{4} \log {\left (2 \right )}^{2} - 1250 x^{3} - 200 x^{3} \log {\left (2 \right )} - 8 x^{3} \log {\left (2 \right )}^{2} - 1250 e x - 200 e x \log {\left (2 \right )} - 8 e x \log {\left (2 \right )}^{2} - 5000 - 800 \log {\left (2 \right )} - 32 \log {\left (2 \right )}^{2}\right ) \log {\left (x \right )}}{x^{5} + 2 x^{4} + x^{3}} + \frac {\left (4 \log {\left (2 \right )}^{2} + 100 \log {\left (2 \right )} + 625\right ) \log {\left (x \right )}^{2}}{x^{4} + 2 x^{3} + x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1988 vs. \(2 (33) = 66\).
Time = 0.37 (sec) , antiderivative size = 1988, normalized size of antiderivative = 64.13 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 375 vs. \(2 (33) = 66\).
Time = 0.34 (sec) , antiderivative size = 375, normalized size of antiderivative = 12.10 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=\frac {4 \, x^{8} \log \left (2\right )^{2} + 100 \, x^{8} \log \left (2\right ) + 8 \, x^{7} \log \left (2\right )^{2} + 625 \, x^{8} + 200 \, x^{7} \log \left (2\right ) + 4 \, x^{6} \log \left (2\right )^{2} + 8 \, x^{5} e \log \left (2\right )^{2} - 8 \, x^{5} \log \left (2\right )^{2} \log \left (x\right ) + 1250 \, x^{7} + 100 \, x^{6} \log \left (2\right ) + 200 \, x^{5} e \log \left (2\right ) + 8 \, x^{4} e \log \left (2\right )^{2} - 200 \, x^{5} \log \left (2\right ) \log \left (x\right ) - 8 \, x^{4} \log \left (2\right )^{2} \log \left (x\right ) + 625 \, x^{6} + 1250 \, x^{5} e + 200 \, x^{4} e \log \left (2\right ) + 32 \, x^{4} \log \left (2\right )^{2} - 1250 \, x^{5} \log \left (x\right ) - 200 \, x^{4} \log \left (2\right ) \log \left (x\right ) - 8 \, x^{2} e \log \left (2\right )^{2} \log \left (x\right ) + 4 \, x^{2} \log \left (2\right )^{2} \log \left (x\right )^{2} + 1250 \, x^{4} e + 800 \, x^{4} \log \left (2\right ) + 32 \, x^{3} \log \left (2\right )^{2} + 4 \, x^{2} e^{2} \log \left (2\right )^{2} - 1250 \, x^{4} \log \left (x\right ) - 200 \, x^{2} e \log \left (2\right ) \log \left (x\right ) + 100 \, x^{2} \log \left (2\right ) \log \left (x\right )^{2} + 5000 \, x^{4} + 800 \, x^{3} \log \left (2\right ) + 100 \, x^{2} e^{2} \log \left (2\right ) + 32 \, x e \log \left (2\right )^{2} - 1250 \, x^{2} e \log \left (x\right ) - 32 \, x \log \left (2\right )^{2} \log \left (x\right ) + 625 \, x^{2} \log \left (x\right )^{2} + 5000 \, x^{3} + 625 \, x^{2} e^{2} + 800 \, x e \log \left (2\right ) - 800 \, x \log \left (2\right ) \log \left (x\right ) + 5000 \, x e + 64 \, \log \left (2\right )^{2} - 5000 \, x \log \left (x\right ) + 1600 \, \log \left (2\right ) + 10000}{x^{6} + 2 \, x^{5} + x^{4}} \]
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Time = 9.07 (sec) , antiderivative size = 163, normalized size of antiderivative = 5.26 \[ \int \frac {-40000-65000 x-5000 x^2-5000 x^3-16250 x^4-12500 x^5+3750 x^7+3750 x^8+1250 x^9+e^2 \left (-1250 x^2-2500 x^3\right )+e \left (-15000 x-26250 x^2-1250 x^3-1250 x^5-1250 x^6\right )+\left (-3200-5200 x-400 x^2-400 x^3-1300 x^4-1000 x^5+300 x^7+300 x^8+100 x^9+e^2 \left (-100 x^2-200 x^3\right )+e \left (-1200 x-2100 x^2-100 x^3-100 x^5-100 x^6\right )\right ) \log (4)+\left (-64-104 x-8 x^2-8 x^3-26 x^4-20 x^5+6 x^7+6 x^8+2 x^9+e^2 \left (-2 x^2-4 x^3\right )+e \left (-24 x-42 x^2-2 x^3-2 x^5-2 x^6\right )\right ) \log ^2(4)+\left (15000 x+26250 x^2+1250 x^3+1250 x^5+1250 x^6+e \left (2500 x^2+5000 x^3\right )+\left (1200 x+2100 x^2+100 x^3+100 x^5+100 x^6+e \left (200 x^2+400 x^3\right )\right ) \log (4)+\left (24 x+42 x^2+2 x^3+2 x^5+2 x^6+e \left (4 x^2+8 x^3\right )\right ) \log ^2(4)\right ) \log (x)+\left (-1250 x^2-2500 x^3+\left (-100 x^2-200 x^3\right ) \log (4)+\left (-2 x^2-4 x^3\right ) \log ^2(4)\right ) \log ^2(x)}{x^5+3 x^6+3 x^7+x^8} \, dx=x^2\,{\left (\ln \left (4\right )+25\right )}^2+\frac {16\,{\left (\ln \left (4\right )+25\right )}^2}{x^4}-\frac {2\,{\left (\ln \left (4\right )+25\right )}^2\,\left ({\mathrm {e}}^2-12\,\mathrm {e}+12\,\ln \left (x\right )+{\ln \left (x\right )}^2-2\,\mathrm {e}\,\ln \left (x\right )+28\right )}{x}+\frac {{\left (\ln \left (4\right )+25\right )}^2\,\left ({\mathrm {e}}^2-16\,\mathrm {e}+16\,\ln \left (x\right )+{\ln \left (x\right )}^2-2\,\mathrm {e}\,\ln \left (x\right )+48\right )}{x^2}+\frac {{\left (\ln \left (4\right )+25\right )}^2\,{\left (\ln \left (x\right )-\mathrm {e}+4\right )}^2}{{\left (x+1\right )}^2}-\frac {8\,{\left (\ln \left (4\right )+25\right )}^2\,\left (\ln \left (x\right )-\mathrm {e}+4\right )}{x^3}+\frac {2\,{\left (\ln \left (4\right )+25\right )}^2\,\left ({\mathrm {e}}^2-11\,\mathrm {e}+11\,\ln \left (x\right )+{\ln \left (x\right )}^2-2\,\mathrm {e}\,\ln \left (x\right )+28\right )}{x+1} \]
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