Optimal. Leaf size=661 \[ \frac {53 b x}{192 c^3}+\frac {11 a x}{27 c^2}+\frac {49 (3 b+4 a c) x}{432 c^3}+\frac {29 b x^2}{384 c^2}+\frac {5 a x^2}{54 c}+\frac {13 (3 b+4 a c) x^2}{864 c^2}+\frac {2 a x^3}{81}+\frac {17 b x^3}{576 c}+\frac {(3 b+4 a c) x^3}{324 c}+\frac {3 b x^4}{256}+\frac {29 b \log (1-c x)}{192 c^4}+\frac {5 a \log (1-c x)}{27 c^3}+\frac {13 (3 b+4 a c) \log (1-c x)}{432 c^4}-\frac {b x^2 \log (1-c x)}{16 c^2}-\frac {a x^2 \log (1-c x)}{9 c}-\frac {(3 b+4 a c) x^2 \log (1-c x)}{48 c^2}-\frac {2}{27} a x^3 \log (1-c x)-\frac {b x^3 \log (1-c x)}{24 c}-\frac {(3 b+4 a c) x^3 \log (1-c x)}{108 c}-\frac {3}{64} b x^4 \log (1-c x)+\frac {b (1-c x) \log (1-c x)}{8 c^4}+\frac {2 a (1-c x) \log (1-c x)}{9 c^3}+\frac {(3 b+4 a c) (1-c x) \log (1-c x)}{12 c^4}-\frac {b \log ^2(1-c x)}{16 c^4}-\frac {a \log ^2(1-c x)}{9 c^3}+\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) \log (c x) \log ^2(1-c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {PolyLog}(2,c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {PolyLog}(2,c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {PolyLog}(2,c x)}{36 c}-\frac {1}{16} b x^4 \text {PolyLog}(2,c x)-\frac {(3 b+4 a c) \log (1-c x) \text {PolyLog}(2,c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {PolyLog}(2,c x)-\frac {(3 b+4 a c) \log (1-c x) \text {PolyLog}(2,1-c x)}{6 c^4}+\frac {(3 b+4 a c) \text {PolyLog}(3,1-c x)}{6 c^4} \]
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Rubi [A]
time = 0.64, antiderivative size = 661, normalized size of antiderivative = 1.00, number of steps
used = 52, number of rules used = 17, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.810, Rules used = {6874, 6726,
2442, 45, 6739, 2445, 2457, 2436, 2332, 2437, 2338, 6721, 6731, 2443, 2481, 2421, 6724}
\begin {gather*} \frac {(4 a c+3 b) \text {Li}_3(1-c x)}{6 c^4}-\frac {(4 a c+3 b) \text {Li}_2(c x) \log (1-c x)}{12 c^4}-\frac {(4 a c+3 b) \text {Li}_2(1-c x) \log (1-c x)}{6 c^4}-\frac {(4 a c+3 b) \log (c x) \log ^2(1-c x)}{12 c^4}+\frac {13 (4 a c+3 b) \log (1-c x)}{432 c^4}+\frac {(1-c x) (4 a c+3 b) \log (1-c x)}{12 c^4}-\frac {x (4 a c+3 b) \text {Li}_2(c x)}{12 c^3}+\frac {49 x (4 a c+3 b)}{432 c^3}-\frac {x^2 (4 a c+3 b) \text {Li}_2(c x)}{24 c^2}+\frac {13 x^2 (4 a c+3 b)}{864 c^2}-\frac {x^2 (4 a c+3 b) \log (1-c x)}{48 c^2}-\frac {x^3 (4 a c+3 b) \text {Li}_2(c x)}{36 c}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \text {Li}_2(c x) \log (1-c x)+\frac {x^3 (4 a c+3 b)}{324 c}-\frac {x^3 (4 a c+3 b) \log (1-c x)}{108 c}-\frac {a \log ^2(1-c x)}{9 c^3}+\frac {2 a (1-c x) \log (1-c x)}{9 c^3}+\frac {5 a \log (1-c x)}{27 c^3}+\frac {11 a x}{27 c^2}+\frac {1}{9} a x^3 \log ^2(1-c x)-\frac {2}{27} a x^3 \log (1-c x)+\frac {5 a x^2}{54 c}-\frac {a x^2 \log (1-c x)}{9 c}+\frac {2 a x^3}{81}-\frac {b \log ^2(1-c x)}{16 c^4}+\frac {b (1-c x) \log (1-c x)}{8 c^4}+\frac {29 b \log (1-c x)}{192 c^4}+\frac {53 b x}{192 c^3}+\frac {29 b x^2}{384 c^2}-\frac {b x^2 \log (1-c x)}{16 c^2}-\frac {1}{16} b x^4 \text {Li}_2(c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {3}{64} b x^4 \log (1-c x)+\frac {17 b x^3}{576 c}-\frac {b x^3 \log (1-c x)}{24 c}+\frac {3 b x^4}{256} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 2332
Rule 2338
Rule 2421
Rule 2436
Rule 2437
Rule 2442
Rule 2443
Rule 2445
Rule 2457
Rule 2481
Rule 6721
Rule 6724
Rule 6726
Rule 6731
Rule 6739
Rule 6874
Rubi steps
\begin {align*} \int x^2 (a+b x) \log (1-c x) \text {Li}_2(c x) \, dx &=\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)+c \int \left (\frac {(-3 b-4 a c) \text {Li}_2(c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{12 c^2}-\frac {b x^3 \text {Li}_2(c x)}{4 c}+\frac {(-3 b-4 a c) \text {Li}_2(c x)}{12 c^4 (-1+c x)}\right ) \, dx+\int \left (\frac {1}{3} a x^2 \log ^2(1-c x)+\frac {1}{4} b x^3 \log ^2(1-c x)\right ) \, dx\\ &=\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)+\frac {1}{3} a \int x^2 \log ^2(1-c x) \, dx+\frac {1}{4} b \int x^3 \log ^2(1-c x) \, dx-\frac {1}{4} b \int x^3 \text {Li}_2(c x) \, dx-\frac {(3 b+4 a c) \int \text {Li}_2(c x) \, dx}{12 c^3}-\frac {(3 b+4 a c) \int \frac {\text {Li}_2(c x)}{-1+c x} \, dx}{12 c^3}-\frac {(3 b+4 a c) \int x \text {Li}_2(c x) \, dx}{12 c^2}-\frac {(3 b+4 a c) \int x^2 \text {Li}_2(c x) \, dx}{12 c}\\ &=\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {Li}_2(c x)}{36 c}-\frac {1}{16} b x^4 \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)-\frac {1}{16} b \int x^3 \log (1-c x) \, dx+\frac {1}{9} (2 a c) \int \frac {x^3 \log (1-c x)}{1-c x} \, dx+\frac {1}{8} (b c) \int \frac {x^4 \log (1-c x)}{1-c x} \, dx-\frac {(3 b+4 a c) \int \frac {\log ^2(1-c x)}{x} \, dx}{12 c^4}-\frac {(3 b+4 a c) \int \log (1-c x) \, dx}{12 c^3}-\frac {(3 b+4 a c) \int x \log (1-c x) \, dx}{24 c^2}-\frac {(3 b+4 a c) \int x^2 \log (1-c x) \, dx}{36 c}\\ &=-\frac {(3 b+4 a c) x^2 \log (1-c x)}{48 c^2}-\frac {(3 b+4 a c) x^3 \log (1-c x)}{108 c}-\frac {1}{64} b x^4 \log (1-c x)+\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) \log (c x) \log ^2(1-c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {Li}_2(c x)}{36 c}-\frac {1}{16} b x^4 \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)+\frac {1}{9} (2 a c) \int \left (-\frac {\log (1-c x)}{c^3}-\frac {x \log (1-c x)}{c^2}-\frac {x^2 \log (1-c x)}{c}-\frac {\log (1-c x)}{c^3 (-1+c x)}\right ) \, dx-\frac {1}{64} (b c) \int \frac {x^4}{1-c x} \, dx+\frac {1}{8} (b c) \int \left (-\frac {\log (1-c x)}{c^4}-\frac {x \log (1-c x)}{c^3}-\frac {x^2 \log (1-c x)}{c^2}-\frac {x^3 \log (1-c x)}{c}-\frac {\log (1-c x)}{c^4 (-1+c x)}\right ) \, dx-\frac {1}{108} (3 b+4 a c) \int \frac {x^3}{1-c x} \, dx+\frac {(3 b+4 a c) \text {Subst}(\int \log (x) \, dx,x,1-c x)}{12 c^4}-\frac {(3 b+4 a c) \int \frac {\log (c x) \log (1-c x)}{1-c x} \, dx}{6 c^3}-\frac {(3 b+4 a c) \int \frac {x^2}{1-c x} \, dx}{48 c}\\ &=\frac {(3 b+4 a c) x}{12 c^3}-\frac {(3 b+4 a c) x^2 \log (1-c x)}{48 c^2}-\frac {(3 b+4 a c) x^3 \log (1-c x)}{108 c}-\frac {1}{64} b x^4 \log (1-c x)+\frac {(3 b+4 a c) (1-c x) \log (1-c x)}{12 c^4}+\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) \log (c x) \log ^2(1-c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {Li}_2(c x)}{36 c}-\frac {1}{16} b x^4 \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)-\frac {1}{9} (2 a) \int x^2 \log (1-c x) \, dx-\frac {1}{8} b \int x^3 \log (1-c x) \, dx-\frac {b \int \log (1-c x) \, dx}{8 c^3}-\frac {b \int \frac {\log (1-c x)}{-1+c x} \, dx}{8 c^3}-\frac {(2 a) \int \log (1-c x) \, dx}{9 c^2}-\frac {(2 a) \int \frac {\log (1-c x)}{-1+c x} \, dx}{9 c^2}-\frac {b \int x \log (1-c x) \, dx}{8 c^2}-\frac {(2 a) \int x \log (1-c x) \, dx}{9 c}-\frac {b \int x^2 \log (1-c x) \, dx}{8 c}-\frac {1}{64} (b c) \int \left (-\frac {1}{c^4}-\frac {x}{c^3}-\frac {x^2}{c^2}-\frac {x^3}{c}-\frac {1}{c^4 (-1+c x)}\right ) \, dx-\frac {1}{108} (3 b+4 a c) \int \left (-\frac {1}{c^3}-\frac {x}{c^2}-\frac {x^2}{c}-\frac {1}{c^3 (-1+c x)}\right ) \, dx+\frac {(3 b+4 a c) \text {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 )}{6 c^4}-\frac {(3 b+4 a c) \int \left (-\frac {1}{c^2}-\frac {x}{c}-\frac {1}{c^2 (-1+c x)}\right ) \, dx}{48 c}\\ &=\frac {b x}{64 c^3}+\frac {49 (3 b+4 a c) x}{432 c^3}+\frac {b x^2}{128 c^2}+\frac {13 (3 b+4 a c) x^2}{864 c^2}+\frac {b x^3}{192 c}+\frac {(3 b+4 a c) x^3}{324 c}+\frac {b x^4}{256}+\frac {b \log (1-c x)}{64 c^4}+\frac {13 (3 b+4 a c) \log (1-c x)}{432 c^4}-\frac {b x^2 \log (1-c x)}{16 c^2}-\frac {a x^2 \log (1-c x)}{9 c}-\frac {(3 b+4 a c) x^2 \log (1-c x)}{48 c^2}-\frac {2}{27} a x^3 \log (1-c x)-\frac {b x^3 \log (1-c x)}{24 c}-\frac {(3 b+4 a c) x^3 \log (1-c x)}{108 c}-\frac {3}{64} b x^4 \log (1-c x)+\frac {(3 b+4 a c) (1-c x) \log (1-c x)}{12 c^4}+\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) \log (c x) \log ^2(1-c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {Li}_2(c x)}{36 c}-\frac {1}{16} b x^4 \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(1-c x)}{6 c^4}-\frac {1}{9} a \int \frac {x^2}{1-c x} \, dx-\frac {1}{24} b \int \frac {x^3}{1-c x} \, dx+\frac {b \text {Subst}(\int \log (x) \, dx,x,1-c x)}{8 c^4}-\frac {b \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1-c x\right )}{8 c^4}+\frac {(2 a) \text {Subst}(\int \log (x) \, dx,x,1-c x)}{9 c^3}-\frac {(2 a) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1-c x\right )}{9 c^3}-\frac {b \int \frac {x^2}{1-c x} \, dx}{16 c}-\frac {1}{27} (2 a c) \int \frac {x^3}{1-c x} \, dx-\frac {1}{32} (b c) \int \frac {x^4}{1-c x} \, dx+\frac {(3 b+4 a c) \text {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,1-c x\right )}{6 c^4}\\ &=\frac {9 b x}{64 c^3}+\frac {2 a x}{9 c^2}+\frac {49 (3 b+4 a c) x}{432 c^3}+\frac {b x^2}{128 c^2}+\frac {13 (3 b+4 a c) x^2}{864 c^2}+\frac {b x^3}{192 c}+\frac {(3 b+4 a c) x^3}{324 c}+\frac {b x^4}{256}+\frac {b \log (1-c x)}{64 c^4}+\frac {13 (3 b+4 a c) \log (1-c x)}{432 c^4}-\frac {b x^2 \log (1-c x)}{16 c^2}-\frac {a x^2 \log (1-c x)}{9 c}-\frac {(3 b+4 a c) x^2 \log (1-c x)}{48 c^2}-\frac {2}{27} a x^3 \log (1-c x)-\frac {b x^3 \log (1-c x)}{24 c}-\frac {(3 b+4 a c) x^3 \log (1-c x)}{108 c}-\frac {3}{64} b x^4 \log (1-c x)+\frac {b (1-c x) \log (1-c x)}{8 c^4}+\frac {2 a (1-c x) \log (1-c x)}{9 c^3}+\frac {(3 b+4 a c) (1-c x) \log (1-c x)}{12 c^4}-\frac {b \log ^2(1-c x)}{16 c^4}-\frac {a \log ^2(1-c x)}{9 c^3}+\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) \log (c x) \log ^2(1-c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {Li}_2(c x)}{36 c}-\frac {1}{16} b x^4 \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(1-c x)}{6 c^4}+\frac {(3 b+4 a c) \text {Li}_3(1-c x)}{6 c^4}-\frac {1}{9} a \int \left (-\frac {1}{c^2}-\frac {x}{c}-\frac {1}{c^2 (-1+c x)}\right ) \, dx-\frac {1}{24} b \int \left (-\frac {1}{c^3}-\frac {x}{c^2}-\frac {x^2}{c}-\frac {1}{c^3 (-1+c x)}\right ) \, dx-\frac {b \int \left (-\frac {1}{c^2}-\frac {x}{c}-\frac {1}{c^2 (-1+c x)}\right ) \, dx}{16 c}-\frac {1}{27} (2 a c) \int \left (-\frac {1}{c^3}-\frac {x}{c^2}-\frac {x^2}{c}-\frac {1}{c^3 (-1+c x)}\right ) \, dx-\frac {1}{32} (b c) \int \left (-\frac {1}{c^4}-\frac {x}{c^3}-\frac {x^2}{c^2}-\frac {x^3}{c}-\frac {1}{c^4 (-1+c x)}\right ) \, dx\\ &=\frac {53 b x}{192 c^3}+\frac {11 a x}{27 c^2}+\frac {49 (3 b+4 a c) x}{432 c^3}+\frac {29 b x^2}{384 c^2}+\frac {5 a x^2}{54 c}+\frac {13 (3 b+4 a c) x^2}{864 c^2}+\frac {2 a x^3}{81}+\frac {17 b x^3}{576 c}+\frac {(3 b+4 a c) x^3}{324 c}+\frac {3 b x^4}{256}+\frac {29 b \log (1-c x)}{192 c^4}+\frac {5 a \log (1-c x)}{27 c^3}+\frac {13 (3 b+4 a c) \log (1-c x)}{432 c^4}-\frac {b x^2 \log (1-c x)}{16 c^2}-\frac {a x^2 \log (1-c x)}{9 c}-\frac {(3 b+4 a c) x^2 \log (1-c x)}{48 c^2}-\frac {2}{27} a x^3 \log (1-c x)-\frac {b x^3 \log (1-c x)}{24 c}-\frac {(3 b+4 a c) x^3 \log (1-c x)}{108 c}-\frac {3}{64} b x^4 \log (1-c x)+\frac {b (1-c x) \log (1-c x)}{8 c^4}+\frac {2 a (1-c x) \log (1-c x)}{9 c^3}+\frac {(3 b+4 a c) (1-c x) \log (1-c x)}{12 c^4}-\frac {b \log ^2(1-c x)}{16 c^4}-\frac {a \log ^2(1-c x)}{9 c^3}+\frac {1}{9} a x^3 \log ^2(1-c x)+\frac {1}{16} b x^4 \log ^2(1-c x)-\frac {(3 b+4 a c) \log (c x) \log ^2(1-c x)}{12 c^4}-\frac {(3 b+4 a c) x \text {Li}_2(c x)}{12 c^3}-\frac {(3 b+4 a c) x^2 \text {Li}_2(c x)}{24 c^2}-\frac {(3 b+4 a c) x^3 \text {Li}_2(c x)}{36 c}-\frac {1}{16} b x^4 \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(c x)}{12 c^4}+\frac {1}{12} \left (4 a x^3+3 b x^4\right ) \log (1-c x) \text {Li}_2(c x)-\frac {(3 b+4 a c) \log (1-c x) \text {Li}_2(1-c x)}{6 c^4}+\frac {(3 b+4 a c) \text {Li}_3(1-c x)}{6 c^4}\\ \end {align*}
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Mathematica [A]
time = 0.53, size = 425, normalized size = 0.64 \begin {gather*} \frac {4260 b c x+5952 a c^2 x+834 b c^2 x^2+1056 a c^3 x^2+268 b c^3 x^3+256 a c^4 x^3+81 b c^4 x^4+4260 b \log (1-c x)+5952 a c \log (1-c x)-2592 b c x \log (1-c x)-3840 a c^2 x \log (1-c x)-864 b c^2 x^2 \log (1-c x)-1344 a c^3 x^2 \log (1-c x)-480 b c^3 x^3 \log (1-c x)-768 a c^4 x^3 \log (1-c x)-324 b c^4 x^4 \log (1-c x)-432 b \log ^2(1-c x)-768 a c \log ^2(1-c x)+768 a c^4 x^3 \log ^2(1-c x)+432 b c^4 x^4 \log ^2(1-c x)-1728 b \log (c x) \log ^2(1-c x)-2304 a c \log (c x) \log ^2(1-c x)+48 \left (-c x \left (8 a c \left (6+3 c x+2 c^2 x^2\right )+3 b \left (12+6 c x+4 c^2 x^2+3 c^3 x^3\right )\right )+12 \left (4 a c \left (-1+c^3 x^3\right )+3 b \left (-1+c^4 x^4\right )\right ) \log (1-c x)\right ) \text {PolyLog}(2,c x)-1152 (3 b+4 a c) \log (1-c x) \text {PolyLog}(2,1-c x)+3456 b \text {PolyLog}(3,1-c x)+4608 a c \text {PolyLog}(3,1-c x)}{6912 c^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int x^{2} \left (b x +a \right ) \ln \left (-c x +1\right ) \polylog \left (2, c x \right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 415, normalized size = 0.63 \begin {gather*} -\frac {1}{6912} \, c {\left (\frac {576 \, {\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 )} {\left (4 \, a c + 3 \, b\right )}}{c^{5}} - \frac {81 \, b c^{4} x^{4} + 4 \, {\left (64 \, a c^{4} + 67 \, b c^{3}\right )} x^{3} + 6 \, {\left (176 \, a c^{3} + 139 \, b c^{2}\right )} x^{2} + 12 \, {\left (496 \, a c^{2} + 355 \, b c\right )} x - 48 \, {\left (9 \, b c^{4} x^{4} + 4 \, {\left (4 \, a c^{4} + 3 \, b c^{3}\right )} x^{3} + 6 \, {\left (4 \, a c^{3} + 3 \, b c^{2}\right )} x^{2} + 12 \, {\left (4 \, a c^{2} + 3 \, b c\right )} x + 12 \, {\left (4 \, a c + 3 \, b\right )} \log \left (-c x + 1\right )\right )} {\rm Li}_2\left (c x\right ) - 4 \, {\left (54 \, b c^{4} x^{4} + 4 \, {\left (32 \, a c^{4} + 21 \, b c^{3}\right )} x^{3} + 6 \, {\left (40 \, a c^{3} + 27 \, b c^{2}\right )} x^{2} - 1488 \, a c + 12 \, {\left (64 \, a c^{2} + 45 \, b c\right )} x - 1065 \, b\right )} \log \left (-c x + 1\right )}{c^{5}}\right )} + \frac {1}{1728} \, {\left (\frac {32 \, {\left (18 \, c^{3} x^{3} {\rm Li}_2\left (c x\right ) - 2 \, c^{3} x^{3} - 3 \, c^{2} x^{2} - 6 \, c x + 6 \, {\left (c^{3} x^{3} - 1\right )} \log \left (-c x + 1\right )\right )} a}{c^{3}} + \frac {9 \, {\left (48 \, c^{4} x^{4} {\rm Li}_2\left (c x\right ) - 3 \, c^{4} x^{4} - 4 \, c^{3} x^{3} - 6 \, c^{2} x^{2} - 12 \, c x + 12 \, {\left (c^{4} x^{4} - 1\right )} \log \left (-c x + 1\right )\right )} b}{c^{4}}\right )} \log \left (-c x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int x^2\,\ln \left (1-c\,x\right )\,\mathrm {polylog}\left (2,c\,x\right )\,\left (a+b\,x\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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