Optimal. Leaf size=584 \[ -\frac {1}{12} c^3 (3 a c+4 b) \text {Li}_3(c x)-\frac {1}{6} c^3 (3 a c+4 b) \text {Li}_3(1-c x)+\frac {1}{12} c^3 (3 a c+4 b) \text {Li}_2(c x) \log (1-c x)+\frac {1}{6} c^3 (3 a c+4 b) \text {Li}_2(1-c x) \log (1-c x)+\frac {1}{12} c^3 (3 a c+4 b) \log (c x) \log ^2(1-c x)-\frac {5}{48} c^3 \log (x) (3 a c+4 b)+\frac {5}{48} c^3 (3 a c+4 b) \log (1-c x)+\frac {c^2 (3 a c+4 b) \text {Li}_2(c x)}{12 x}+\frac {c^2 (3 a c+4 b)}{48 x}-\frac {c^2 (3 a c+4 b) \log (1-c x)}{12 x}+\frac {c (3 a c+4 b) \text {Li}_2(c x)}{24 x^2}-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \text {Li}_2(c x) \log (1-c x)-\frac {c (3 a c+4 b) \log (1-c x)}{48 x^2}-\frac {1}{8} a c^4 \text {Li}_2(c x)-\frac {1}{16} a c^4 \log ^2(1-c x)-\frac {37}{144} a c^4 \log (x)+\frac {37}{144} a c^4 \log (1-c x)+\frac {19 a c^3}{144 x}-\frac {a c^3 \log (1-c x)}{8 x}+\frac {5 a c^2}{144 x^2}-\frac {a c^2 \log (1-c x)}{16 x^2}+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {a \log ^2(1-c x)}{16 x^4}-\frac {5 a c \log (1-c x)}{72 x^3}-\frac {2}{9} b c^3 \text {Li}_2(c x)-\frac {1}{9} b c^3 \log ^2(1-c x)-\frac {1}{3} b c^3 \log (x)+\frac {1}{3} b c^3 \log (1-c x)+\frac {b c^2}{9 x}-\frac {2 b c^2 \log (1-c x)}{9 x}+\frac {b \log ^2(1-c x)}{9 x^3}-\frac {b c \log (1-c x)}{9 x^2} \]
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Rubi [A] time = 0.84, antiderivative size = 584, normalized size of antiderivative = 1.00, number of steps used = 51, number of rules used = 19, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.905, Rules used = {6742, 6591, 2395, 44, 43, 6606, 2398, 2410, 36, 29, 31, 2391, 2390, 2301, 6589, 6596, 2396, 2433, 2374} \[ -\frac {1}{12} c^3 (3 a c+4 b) \text {PolyLog}(3,c x)-\frac {1}{6} c^3 (3 a c+4 b) \text {PolyLog}(3,1-c x)+\frac {c^2 (3 a c+4 b) \text {PolyLog}(2,c x)}{12 x}+\frac {1}{12} c^3 (3 a c+4 b) \log (1-c x) \text {PolyLog}(2,c x)+\frac {1}{6} c^3 (3 a c+4 b) \log (1-c x) \text {PolyLog}(2,1-c x)+\frac {c (3 a c+4 b) \text {PolyLog}(2,c x)}{24 x^2}-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {PolyLog}(2,c x)-\frac {1}{8} a c^4 \text {PolyLog}(2,c x)+\frac {a c \text {PolyLog}(2,c x)}{12 x^3}-\frac {2}{9} b c^3 \text {PolyLog}(2,c x)+\frac {c^2 (3 a c+4 b)}{48 x}+\frac {1}{12} c^3 (3 a c+4 b) \log (c x) \log ^2(1-c x)-\frac {5}{48} c^3 \log (x) (3 a c+4 b)+\frac {5}{48} c^3 (3 a c+4 b) \log (1-c x)-\frac {c^2 (3 a c+4 b) \log (1-c x)}{12 x}-\frac {c (3 a c+4 b) \log (1-c x)}{48 x^2}+\frac {5 a c^2}{144 x^2}-\frac {a c^2 \log (1-c x)}{16 x^2}+\frac {19 a c^3}{144 x}-\frac {1}{16} a c^4 \log ^2(1-c x)-\frac {37}{144} a c^4 \log (x)+\frac {37}{144} a c^4 \log (1-c x)-\frac {a c^3 \log (1-c x)}{8 x}+\frac {a \log ^2(1-c x)}{16 x^4}-\frac {5 a c \log (1-c x)}{72 x^3}+\frac {b c^2}{9 x}-\frac {1}{9} b c^3 \log ^2(1-c x)-\frac {1}{3} b c^3 \log (x)+\frac {1}{3} b c^3 \log (1-c x)-\frac {2 b c^2 \log (1-c x)}{9 x}+\frac {b \log ^2(1-c x)}{9 x^3}-\frac {b c \log (1-c x)}{9 x^2} \]
Antiderivative was successfully verified.
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Rule 29
Rule 31
Rule 36
Rule 43
Rule 44
Rule 2301
Rule 2374
Rule 2390
Rule 2391
Rule 2395
Rule 2396
Rule 2398
Rule 2410
Rule 2433
Rule 6589
Rule 6591
Rule 6596
Rule 6606
Rule 6742
Rubi steps
\begin {align*} \int \frac {(a+b x) \log (1-c x) \text {Li}_2(c x)}{x^5} \, dx &=-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)+c \int \left (-\frac {a \text {Li}_2(c x)}{4 x^4}+\frac {(-4 b-3 a c) \text {Li}_2(c x)}{12 x^3}-\frac {c (4 b+3 a c) \text {Li}_2(c x)}{12 x^2}-\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {c^3 (4 b+3 a c) \text {Li}_2(c x)}{12 (-1+c x)}\right ) \, dx+\int \left (-\frac {a \log ^2(1-c x)}{4 x^5}-\frac {b \log ^2(1-c x)}{3 x^4}\right ) \, dx\\ &=-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)-\frac {1}{4} a \int \frac {\log ^2(1-c x)}{x^5} \, dx-\frac {1}{3} b \int \frac {\log ^2(1-c x)}{x^4} \, dx-\frac {1}{4} (a c) \int \frac {\text {Li}_2(c x)}{x^4} \, dx-\frac {1}{12} (c (4 b+3 a c)) \int \frac {\text {Li}_2(c x)}{x^3} \, dx-\frac {1}{12} \left (c^2 (4 b+3 a c)\right ) \int \frac {\text {Li}_2(c x)}{x^2} \, dx-\frac {1}{12} \left (c^3 (4 b+3 a c)\right ) \int \frac {\text {Li}_2(c x)}{x} \, dx+\frac {1}{12} \left (c^4 (4 b+3 a c)\right ) \int \frac {\text {Li}_2(c x)}{-1+c x} \, dx\\ &=\frac {a \log ^2(1-c x)}{16 x^4}+\frac {b \log ^2(1-c x)}{9 x^3}+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {c (4 b+3 a c) \text {Li}_2(c x)}{24 x^2}+\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {1}{12} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} c^3 (4 b+3 a c) \text {Li}_3(c x)+\frac {1}{12} (a c) \int \frac {\log (1-c x)}{x^4} \, dx+\frac {1}{8} (a c) \int \frac {\log (1-c x)}{x^4 (1-c x)} \, dx+\frac {1}{9} (2 b c) \int \frac {\log (1-c x)}{x^3 (1-c x)} \, dx+\frac {1}{24} (c (4 b+3 a c)) \int \frac {\log (1-c x)}{x^3} \, dx+\frac {1}{12} \left (c^2 (4 b+3 a c)\right ) \int \frac {\log (1-c x)}{x^2} \, dx+\frac {1}{12} \left (c^3 (4 b+3 a c)\right ) \int \frac {\log ^2(1-c x)}{x} \, dx\\ &=-\frac {a c \log (1-c x)}{36 x^3}-\frac {c (4 b+3 a c) \log (1-c x)}{48 x^2}-\frac {c^2 (4 b+3 a c) \log (1-c x)}{12 x}+\frac {a \log ^2(1-c x)}{16 x^4}+\frac {b \log ^2(1-c x)}{9 x^3}+\frac {1}{12} c^3 (4 b+3 a c) \log (c x) \log ^2(1-c x)+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {c (4 b+3 a c) \text {Li}_2(c x)}{24 x^2}+\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {1}{12} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} c^3 (4 b+3 a c) \text {Li}_3(c x)+\frac {1}{8} (a c) \int \left (\frac {\log (1-c x)}{x^4}+\frac {c \log (1-c x)}{x^3}+\frac {c^2 \log (1-c x)}{x^2}+\frac {c^3 \log (1-c x)}{x}-\frac {c^4 \log (1-c x)}{-1+c x}\right ) \, dx+\frac {1}{9} (2 b c) \int \left (\frac {\log (1-c x)}{x^3}+\frac {c \log (1-c x)}{x^2}+\frac {c^2 \log (1-c x)}{x}-\frac {c^3 \log (1-c x)}{-1+c x}\right ) \, dx-\frac {1}{36} \left (a c^2\right ) \int \frac {1}{x^3 (1-c x)} \, dx-\frac {1}{48} \left (c^2 (4 b+3 a c)\right ) \int \frac {1}{x^2 (1-c x)} \, dx-\frac {1}{12} \left (c^3 (4 b+3 a c)\right ) \int \frac {1}{x (1-c x)} \, dx+\frac {1}{6} \left (c^4 (4 b+3 a c)\right ) \int \frac {\log (c x) \log (1-c x)}{1-c x} \, dx\\ &=-\frac {a c \log (1-c x)}{36 x^3}-\frac {c (4 b+3 a c) \log (1-c x)}{48 x^2}-\frac {c^2 (4 b+3 a c) \log (1-c x)}{12 x}+\frac {a \log ^2(1-c x)}{16 x^4}+\frac {b \log ^2(1-c x)}{9 x^3}+\frac {1}{12} c^3 (4 b+3 a c) \log (c x) \log ^2(1-c x)+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {c (4 b+3 a c) \text {Li}_2(c x)}{24 x^2}+\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {1}{12} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} c^3 (4 b+3 a c) \text {Li}_3(c x)+\frac {1}{8} (a c) \int \frac {\log (1-c x)}{x^4} \, dx+\frac {1}{9} (2 b c) \int \frac {\log (1-c x)}{x^3} \, dx-\frac {1}{36} \left (a c^2\right ) \int \left (\frac {1}{x^3}+\frac {c}{x^2}+\frac {c^2}{x}-\frac {c^3}{-1+c x}\right ) \, dx+\frac {1}{8} \left (a c^2\right ) \int \frac {\log (1-c x)}{x^3} \, dx+\frac {1}{9} \left (2 b c^2\right ) \int \frac {\log (1-c x)}{x^2} \, dx+\frac {1}{8} \left (a c^3\right ) \int \frac {\log (1-c x)}{x^2} \, dx+\frac {1}{9} \left (2 b c^3\right ) \int \frac {\log (1-c x)}{x} \, dx+\frac {1}{8} \left (a c^4\right ) \int \frac {\log (1-c x)}{x} \, dx-\frac {1}{9} \left (2 b c^4\right ) \int \frac {\log (1-c x)}{-1+c x} \, dx-\frac {1}{8} \left (a c^5\right ) \int \frac {\log (1-c x)}{-1+c x} \, dx-\frac {1}{48} \left (c^2 (4 b+3 a c)\right ) \int \left (\frac {1}{x^2}+\frac {c}{x}-\frac {c^2}{-1+c x}\right ) \, dx-\frac {1}{12} \left (c^3 (4 b+3 a c)\right ) \int \frac {1}{x} \, dx-\frac {1}{6} \left (c^3 (4 b+3 a c)\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (c \left (\frac {1}{c}-\frac {x}{c}\right )\right )}{x} \, dx,x,1-c x\right )-\frac {1}{12} \left (c^4 (4 b+3 a c)\right ) \int \frac {1}{1-c x} \, dx\\ &=\frac {a c^2}{72 x^2}+\frac {a c^3}{36 x}+\frac {c^2 (4 b+3 a c)}{48 x}-\frac {1}{36} a c^4 \log (x)-\frac {5}{48} c^3 (4 b+3 a c) \log (x)+\frac {1}{36} a c^4 \log (1-c x)+\frac {5}{48} c^3 (4 b+3 a c) \log (1-c x)-\frac {5 a c \log (1-c x)}{72 x^3}-\frac {b c \log (1-c x)}{9 x^2}-\frac {a c^2 \log (1-c x)}{16 x^2}-\frac {c (4 b+3 a c) \log (1-c x)}{48 x^2}-\frac {2 b c^2 \log (1-c x)}{9 x}-\frac {a c^3 \log (1-c x)}{8 x}-\frac {c^2 (4 b+3 a c) \log (1-c x)}{12 x}+\frac {a \log ^2(1-c x)}{16 x^4}+\frac {b \log ^2(1-c x)}{9 x^3}+\frac {1}{12} c^3 (4 b+3 a c) \log (c x) \log ^2(1-c x)-\frac {2}{9} b c^3 \text {Li}_2(c x)-\frac {1}{8} a c^4 \text {Li}_2(c x)+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {c (4 b+3 a c) \text {Li}_2(c x)}{24 x^2}+\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {1}{12} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)+\frac {1}{6} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(1-c x)-\frac {1}{12} c^3 (4 b+3 a c) \text {Li}_3(c x)-\frac {1}{24} \left (a c^2\right ) \int \frac {1}{x^3 (1-c x)} \, dx-\frac {1}{9} \left (b c^2\right ) \int \frac {1}{x^2 (1-c x)} \, dx-\frac {1}{16} \left (a c^3\right ) \int \frac {1}{x^2 (1-c x)} \, dx-\frac {1}{9} \left (2 b c^3\right ) \int \frac {1}{x (1-c x)} \, dx-\frac {1}{9} \left (2 b c^3\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1-c x\right )-\frac {1}{8} \left (a c^4\right ) \int \frac {1}{x (1-c x)} \, dx-\frac {1}{8} \left (a c^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1-c x\right )-\frac {1}{6} \left (c^3 (4 b+3 a c)\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,1-c x\right )\\ &=\frac {a c^2}{72 x^2}+\frac {a c^3}{36 x}+\frac {c^2 (4 b+3 a c)}{48 x}-\frac {1}{36} a c^4 \log (x)-\frac {5}{48} c^3 (4 b+3 a c) \log (x)+\frac {1}{36} a c^4 \log (1-c x)+\frac {5}{48} c^3 (4 b+3 a c) \log (1-c x)-\frac {5 a c \log (1-c x)}{72 x^3}-\frac {b c \log (1-c x)}{9 x^2}-\frac {a c^2 \log (1-c x)}{16 x^2}-\frac {c (4 b+3 a c) \log (1-c x)}{48 x^2}-\frac {2 b c^2 \log (1-c x)}{9 x}-\frac {a c^3 \log (1-c x)}{8 x}-\frac {c^2 (4 b+3 a c) \log (1-c x)}{12 x}-\frac {1}{9} b c^3 \log ^2(1-c x)-\frac {1}{16} a c^4 \log ^2(1-c x)+\frac {a \log ^2(1-c x)}{16 x^4}+\frac {b \log ^2(1-c x)}{9 x^3}+\frac {1}{12} c^3 (4 b+3 a c) \log (c x) \log ^2(1-c x)-\frac {2}{9} b c^3 \text {Li}_2(c x)-\frac {1}{8} a c^4 \text {Li}_2(c x)+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {c (4 b+3 a c) \text {Li}_2(c x)}{24 x^2}+\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {1}{12} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)+\frac {1}{6} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(1-c x)-\frac {1}{12} c^3 (4 b+3 a c) \text {Li}_3(c x)-\frac {1}{6} c^3 (4 b+3 a c) \text {Li}_3(1-c x)-\frac {1}{24} \left (a c^2\right ) \int \left (\frac {1}{x^3}+\frac {c}{x^2}+\frac {c^2}{x}-\frac {c^3}{-1+c x}\right ) \, dx-\frac {1}{9} \left (b c^2\right ) \int \left (\frac {1}{x^2}+\frac {c}{x}-\frac {c^2}{-1+c x}\right ) \, dx-\frac {1}{16} \left (a c^3\right ) \int \left (\frac {1}{x^2}+\frac {c}{x}-\frac {c^2}{-1+c x}\right ) \, dx-\frac {1}{9} \left (2 b c^3\right ) \int \frac {1}{x} \, dx-\frac {1}{8} \left (a c^4\right ) \int \frac {1}{x} \, dx-\frac {1}{9} \left (2 b c^4\right ) \int \frac {1}{1-c x} \, dx-\frac {1}{8} \left (a c^5\right ) \int \frac {1}{1-c x} \, dx\\ &=\frac {5 a c^2}{144 x^2}+\frac {b c^2}{9 x}+\frac {19 a c^3}{144 x}+\frac {c^2 (4 b+3 a c)}{48 x}-\frac {1}{3} b c^3 \log (x)-\frac {37}{144} a c^4 \log (x)-\frac {5}{48} c^3 (4 b+3 a c) \log (x)+\frac {1}{3} b c^3 \log (1-c x)+\frac {37}{144} a c^4 \log (1-c x)+\frac {5}{48} c^3 (4 b+3 a c) \log (1-c x)-\frac {5 a c \log (1-c x)}{72 x^3}-\frac {b c \log (1-c x)}{9 x^2}-\frac {a c^2 \log (1-c x)}{16 x^2}-\frac {c (4 b+3 a c) \log (1-c x)}{48 x^2}-\frac {2 b c^2 \log (1-c x)}{9 x}-\frac {a c^3 \log (1-c x)}{8 x}-\frac {c^2 (4 b+3 a c) \log (1-c x)}{12 x}-\frac {1}{9} b c^3 \log ^2(1-c x)-\frac {1}{16} a c^4 \log ^2(1-c x)+\frac {a \log ^2(1-c x)}{16 x^4}+\frac {b \log ^2(1-c x)}{9 x^3}+\frac {1}{12} c^3 (4 b+3 a c) \log (c x) \log ^2(1-c x)-\frac {2}{9} b c^3 \text {Li}_2(c x)-\frac {1}{8} a c^4 \text {Li}_2(c x)+\frac {a c \text {Li}_2(c x)}{12 x^3}+\frac {c (4 b+3 a c) \text {Li}_2(c x)}{24 x^2}+\frac {c^2 (4 b+3 a c) \text {Li}_2(c x)}{12 x}+\frac {1}{12} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(c x)-\frac {1}{12} \left (\frac {3 a}{x^4}+\frac {4 b}{x^3}\right ) \log (1-c x) \text {Li}_2(c x)+\frac {1}{6} c^3 (4 b+3 a c) \log (1-c x) \text {Li}_2(1-c x)-\frac {1}{12} c^3 (4 b+3 a c) \text {Li}_3(c x)-\frac {1}{6} c^3 (4 b+3 a c) \text {Li}_3(1-c x)\\ \end {align*}
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Mathematica [A] time = 1.47, size = 505, normalized size = 0.86 \[ -\frac {-2 c^3 x^4 \text {Li}_2(1-c x) (12 (3 a c+4 b) \log (1-c x)+9 a c+16 b)-6 \text {Li}_2(c x) \left (c x \left (a \left (6 c^2 x^2+3 c x+2\right )+4 b x (2 c x+1)\right )+\log (1-c x) \left (6 a \left (c^4 x^4-1\right )+8 b x \left (c^3 x^3-1\right )\right )\right )+36 a c^4 x^4 \text {Li}_3(c x)+72 a c^4 x^4 \text {Li}_3(1-c x)+33 a c^4 x^4+9 a c^4 x^4 \log ^2(1-c x)-36 a c^4 x^4 \log (c x) \log ^2(1-c x)+82 a c^4 x^4 \log (c x)-82 a c^4 x^4 \log (1-c x)-18 a c^4 x^4 \log (c x) \log (1-c x)-28 a c^3 x^3+54 a c^3 x^3 \log (1-c x)-5 a c^2 x^2+18 a c^2 x^2 \log (1-c x)-9 a \log ^2(1-c x)+10 a c x \log (1-c x)+48 b c^3 x^4 \text {Li}_3(c x)+96 b c^3 x^4 \text {Li}_3(1-c x)+28 b c^3 x^4+16 b c^3 x^4 \log ^2(1-c x)-48 b c^3 x^4 \log (c x) \log ^2(1-c x)+108 b c^3 x^4 \log (c x)-108 b c^3 x^4 \log (1-c x)-32 b c^3 x^4 \log (c x) \log (1-c x)-28 b c^2 x^3+80 b c^2 x^3 \log (1-c x)+28 b c x^2 \log (1-c x)-16 b x \log ^2(1-c x)}{144 x^4} \]
Antiderivative was successfully verified.
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fricas [F] time = 2.50, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b x + a\right )} {\rm Li}_2\left (c x\right ) \log \left (-c x + 1\right )}{x^{5}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x + a\right )} {\rm Li}_2\left (c x\right ) \log \left (-c x + 1\right )}{x^{5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.01, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x +a \right ) \ln \left (-c x +1\right ) \polylog \left (2, c x \right )}{x^{5}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 341, normalized size = 0.58 \[ \frac {1}{12} \, {\left (3 \, a c^{4} + 4 \, b c^{3}\right )} {\left (\log \left (c x\right ) \log \left (-c x + 1\right )^{2} + 2 \, {\rm Li}_2\left (-c x + 1\right ) \log \left (-c x + 1\right ) - 2 \, {\rm Li}_{3}(-c x + 1)\right )} + \frac {1}{72} \, {\left (9 \, a c^{4} + 16 \, b c^{3}\right )} {\left (\log \left (c x\right ) \log \left (-c x + 1\right ) + {\rm Li}_2\left (-c x + 1\right )\right )} - \frac {1}{72} \, {\left (41 \, a c^{4} + 54 \, b c^{3}\right )} \log \relax (x) - \frac {1}{12} \, {\left (3 \, a c^{4} + 4 \, b c^{3}\right )} {\rm Li}_{3}(c x) + \frac {5 \, a c^{2} x^{2} + 28 \, {\left (a c^{3} + b c^{2}\right )} x^{3} - {\left ({\left (9 \, a c^{4} + 16 \, b c^{3}\right )} x^{4} - 16 \, b x - 9 \, a\right )} \log \left (-c x + 1\right )^{2} + 6 \, {\left (2 \, {\left (3 \, a c^{3} + 4 \, b c^{2}\right )} x^{3} + 2 \, a c x + {\left (3 \, a c^{2} + 4 \, b c\right )} x^{2} + 2 \, {\left ({\left (3 \, a c^{4} + 4 \, b c^{3}\right )} x^{4} - 4 \, b x - 3 \, a\right )} \log \left (-c x + 1\right )\right )} {\rm Li}_2\left (c x\right ) + 2 \, {\left ({\left (41 \, a c^{4} + 54 \, b c^{3}\right )} x^{4} - {\left (27 \, a c^{3} + 40 \, b c^{2}\right )} x^{3} - 5 \, a c x - {\left (9 \, a c^{2} + 14 \, b c\right )} x^{2}\right )} \log \left (-c x + 1\right )}{144 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {\ln \left (1-c\,x\right )\,\mathrm {polylog}\left (2,c\,x\right )\,\left (a+b\,x\right )}{x^5} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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