Optimal. Leaf size=377 \[ -\frac{14 b^2 d^3 \text{PolyLog}\left (2,1-\frac{2}{1-c x}\right )}{15 c^3}+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{11 a b d^3 x}{6 c^2}+\frac{d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{60 c^3}-\frac{28 b d^3 \log \left (\frac{2}{1-c x}\right ) \left (a+b \tanh ^{-1}(c x)\right )}{15 c^3}+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{11}{18} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{14 b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{15 c}+\frac{113 b^2 d^3 \log \left (1-c^2 x^2\right )}{90 c^3}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{11 b^2 d^3 x \tanh ^{-1}(c x)}{6 c^2}-\frac{37 b^2 d^3 \tanh ^{-1}(c x)}{30 c^3}+\frac{1}{60} b^2 c d^3 x^4+\frac{61 b^2 d^3 x^2}{180 c}+\frac{1}{10} b^2 d^3 x^3 \]
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Rubi [A] time = 1.22981, antiderivative size = 377, normalized size of antiderivative = 1., number of steps used = 52, number of rules used = 15, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.682, Rules used = {5940, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 266, 43, 5910, 260, 5948, 302} \[ -\frac{14 b^2 d^3 \text{PolyLog}\left (2,1-\frac{2}{1-c x}\right )}{15 c^3}+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{11 a b d^3 x}{6 c^2}+\frac{d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{60 c^3}-\frac{28 b d^3 \log \left (\frac{2}{1-c x}\right ) \left (a+b \tanh ^{-1}(c x)\right )}{15 c^3}+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{11}{18} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{14 b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{15 c}+\frac{113 b^2 d^3 \log \left (1-c^2 x^2\right )}{90 c^3}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{11 b^2 d^3 x \tanh ^{-1}(c x)}{6 c^2}-\frac{37 b^2 d^3 \tanh ^{-1}(c x)}{30 c^3}+\frac{1}{60} b^2 c d^3 x^4+\frac{61 b^2 d^3 x^2}{180 c}+\frac{1}{10} b^2 d^3 x^3 \]
Antiderivative was successfully verified.
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Rule 5940
Rule 5916
Rule 5980
Rule 321
Rule 206
Rule 5984
Rule 5918
Rule 2402
Rule 2315
Rule 266
Rule 43
Rule 5910
Rule 260
Rule 5948
Rule 302
Rubi steps
\begin{align*} \int x^2 (d+c d x)^3 \left (a+b \tanh ^{-1}(c x)\right )^2 \, dx &=\int \left (d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )^2+3 c d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+3 c^2 d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+c^3 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2\right ) \, dx\\ &=d^3 \int x^2 \left (a+b \tanh ^{-1}(c x)\right )^2 \, dx+\left (3 c d^3\right ) \int x^3 \left (a+b \tanh ^{-1}(c x)\right )^2 \, dx+\left (3 c^2 d^3\right ) \int x^4 \left (a+b \tanh ^{-1}(c x)\right )^2 \, dx+\left (c^3 d^3\right ) \int x^5 \left (a+b \tanh ^{-1}(c x)\right )^2 \, dx\\ &=\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2-\frac{1}{3} \left (2 b c d^3\right ) \int \frac{x^3 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx-\frac{1}{2} \left (3 b c^2 d^3\right ) \int \frac{x^4 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx-\frac{1}{5} \left (6 b c^3 d^3\right ) \int \frac{x^5 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx-\frac{1}{3} \left (b c^4 d^3\right ) \int \frac{x^6 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx\\ &=\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{2} \left (3 b d^3\right ) \int x^2 \left (a+b \tanh ^{-1}(c x)\right ) \, dx-\frac{1}{2} \left (3 b d^3\right ) \int \frac{x^2 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx+\frac{\left (2 b d^3\right ) \int x \left (a+b \tanh ^{-1}(c x)\right ) \, dx}{3 c}-\frac{\left (2 b d^3\right ) \int \frac{x \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx}{3 c}+\frac{1}{5} \left (6 b c d^3\right ) \int x^3 \left (a+b \tanh ^{-1}(c x)\right ) \, dx-\frac{1}{5} \left (6 b c d^3\right ) \int \frac{x^3 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx+\frac{1}{3} \left (b c^2 d^3\right ) \int x^4 \left (a+b \tanh ^{-1}(c x)\right ) \, dx-\frac{1}{3} \left (b c^2 d^3\right ) \int \frac{x^4 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx\\ &=\frac{b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{3 c}+\frac{1}{2} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{3 c^3}+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{3} \left (b d^3\right ) \int x^2 \left (a+b \tanh ^{-1}(c x)\right ) \, dx-\frac{1}{3} \left (b d^3\right ) \int \frac{x^2 \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx-\frac{1}{3} \left (b^2 d^3\right ) \int \frac{x^2}{1-c^2 x^2} \, dx-\frac{\left (2 b d^3\right ) \int \frac{a+b \tanh ^{-1}(c x)}{1-c x} \, dx}{3 c^2}+\frac{\left (3 b d^3\right ) \int \left (a+b \tanh ^{-1}(c x)\right ) \, dx}{2 c^2}-\frac{\left (3 b d^3\right ) \int \frac{a+b \tanh ^{-1}(c x)}{1-c^2 x^2} \, dx}{2 c^2}+\frac{\left (6 b d^3\right ) \int x \left (a+b \tanh ^{-1}(c x)\right ) \, dx}{5 c}-\frac{\left (6 b d^3\right ) \int \frac{x \left (a+b \tanh ^{-1}(c x)\right )}{1-c^2 x^2} \, dx}{5 c}-\frac{1}{2} \left (b^2 c d^3\right ) \int \frac{x^3}{1-c^2 x^2} \, dx-\frac{1}{10} \left (3 b^2 c^2 d^3\right ) \int \frac{x^4}{1-c^2 x^2} \, dx-\frac{1}{15} \left (b^2 c^3 d^3\right ) \int \frac{x^5}{1-c^2 x^2} \, dx\\ &=\frac{3 a b d^3 x}{2 c^2}+\frac{b^2 d^3 x}{3 c^2}+\frac{14 b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{15 c}+\frac{11}{18} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{11 d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{60 c^3}+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2-\frac{2 b d^3 \left (a+b \tanh ^{-1}(c x)\right ) \log \left (\frac{2}{1-c x}\right )}{3 c^3}-\frac{1}{5} \left (3 b^2 d^3\right ) \int \frac{x^2}{1-c^2 x^2} \, dx+\frac{\left (b d^3\right ) \int \left (a+b \tanh ^{-1}(c x)\right ) \, dx}{3 c^2}-\frac{\left (b d^3\right ) \int \frac{a+b \tanh ^{-1}(c x)}{1-c^2 x^2} \, dx}{3 c^2}-\frac{\left (6 b d^3\right ) \int \frac{a+b \tanh ^{-1}(c x)}{1-c x} \, dx}{5 c^2}-\frac{\left (b^2 d^3\right ) \int \frac{1}{1-c^2 x^2} \, dx}{3 c^2}+\frac{\left (2 b^2 d^3\right ) \int \frac{\log \left (\frac{2}{1-c x}\right )}{1-c^2 x^2} \, dx}{3 c^2}+\frac{\left (3 b^2 d^3\right ) \int \tanh ^{-1}(c x) \, dx}{2 c^2}-\frac{1}{9} \left (b^2 c d^3\right ) \int \frac{x^3}{1-c^2 x^2} \, dx-\frac{1}{4} \left (b^2 c d^3\right ) \operatorname{Subst}\left (\int \frac{x}{1-c^2 x} \, dx,x,x^2\right )-\frac{1}{10} \left (3 b^2 c^2 d^3\right ) \int \left (-\frac{1}{c^4}-\frac{x^2}{c^2}+\frac{1}{c^4 \left (1-c^2 x^2\right )}\right ) \, dx-\frac{1}{30} \left (b^2 c^3 d^3\right ) \operatorname{Subst}\left (\int \frac{x^2}{1-c^2 x} \, dx,x,x^2\right )\\ &=\frac{11 a b d^3 x}{6 c^2}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{1}{10} b^2 d^3 x^3-\frac{b^2 d^3 \tanh ^{-1}(c x)}{3 c^3}+\frac{3 b^2 d^3 x \tanh ^{-1}(c x)}{2 c^2}+\frac{14 b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{15 c}+\frac{11}{18} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{60 c^3}+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2-\frac{28 b d^3 \left (a+b \tanh ^{-1}(c x)\right ) \log \left (\frac{2}{1-c x}\right )}{15 c^3}-\frac{\left (2 b^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (2 x)}{1-2 x} \, dx,x,\frac{1}{1-c x}\right )}{3 c^3}-\frac{\left (3 b^2 d^3\right ) \int \frac{1}{1-c^2 x^2} \, dx}{10 c^2}+\frac{\left (b^2 d^3\right ) \int \tanh ^{-1}(c x) \, dx}{3 c^2}-\frac{\left (3 b^2 d^3\right ) \int \frac{1}{1-c^2 x^2} \, dx}{5 c^2}+\frac{\left (6 b^2 d^3\right ) \int \frac{\log \left (\frac{2}{1-c x}\right )}{1-c^2 x^2} \, dx}{5 c^2}-\frac{\left (3 b^2 d^3\right ) \int \frac{x}{1-c^2 x^2} \, dx}{2 c}-\frac{1}{18} \left (b^2 c d^3\right ) \operatorname{Subst}\left (\int \frac{x}{1-c^2 x} \, dx,x,x^2\right )-\frac{1}{4} \left (b^2 c d^3\right ) \operatorname{Subst}\left (\int \left (-\frac{1}{c^2}-\frac{1}{c^2 \left (-1+c^2 x\right )}\right ) \, dx,x,x^2\right )-\frac{1}{30} \left (b^2 c^3 d^3\right ) \operatorname{Subst}\left (\int \left (-\frac{1}{c^4}-\frac{x}{c^2}-\frac{1}{c^4 \left (-1+c^2 x\right )}\right ) \, dx,x,x^2\right )\\ &=\frac{11 a b d^3 x}{6 c^2}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{17 b^2 d^3 x^2}{60 c}+\frac{1}{10} b^2 d^3 x^3+\frac{1}{60} b^2 c d^3 x^4-\frac{37 b^2 d^3 \tanh ^{-1}(c x)}{30 c^3}+\frac{11 b^2 d^3 x \tanh ^{-1}(c x)}{6 c^2}+\frac{14 b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{15 c}+\frac{11}{18} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{60 c^3}+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2-\frac{28 b d^3 \left (a+b \tanh ^{-1}(c x)\right ) \log \left (\frac{2}{1-c x}\right )}{15 c^3}+\frac{31 b^2 d^3 \log \left (1-c^2 x^2\right )}{30 c^3}-\frac{b^2 d^3 \text{Li}_2\left (1-\frac{2}{1-c x}\right )}{3 c^3}-\frac{\left (6 b^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (2 x)}{1-2 x} \, dx,x,\frac{1}{1-c x}\right )}{5 c^3}-\frac{\left (b^2 d^3\right ) \int \frac{x}{1-c^2 x^2} \, dx}{3 c}-\frac{1}{18} \left (b^2 c d^3\right ) \operatorname{Subst}\left (\int \left (-\frac{1}{c^2}-\frac{1}{c^2 \left (-1+c^2 x\right )}\right ) \, dx,x,x^2\right )\\ &=\frac{11 a b d^3 x}{6 c^2}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{61 b^2 d^3 x^2}{180 c}+\frac{1}{10} b^2 d^3 x^3+\frac{1}{60} b^2 c d^3 x^4-\frac{37 b^2 d^3 \tanh ^{-1}(c x)}{30 c^3}+\frac{11 b^2 d^3 x \tanh ^{-1}(c x)}{6 c^2}+\frac{14 b d^3 x^2 \left (a+b \tanh ^{-1}(c x)\right )}{15 c}+\frac{11}{18} b d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )+\frac{3}{10} b c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )+\frac{1}{15} b c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )+\frac{d^3 \left (a+b \tanh ^{-1}(c x)\right )^2}{60 c^3}+\frac{1}{3} d^3 x^3 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{4} c d^3 x^4 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{3}{5} c^2 d^3 x^5 \left (a+b \tanh ^{-1}(c x)\right )^2+\frac{1}{6} c^3 d^3 x^6 \left (a+b \tanh ^{-1}(c x)\right )^2-\frac{28 b d^3 \left (a+b \tanh ^{-1}(c x)\right ) \log \left (\frac{2}{1-c x}\right )}{15 c^3}+\frac{113 b^2 d^3 \log \left (1-c^2 x^2\right )}{90 c^3}-\frac{14 b^2 d^3 \text{Li}_2\left (1-\frac{2}{1-c x}\right )}{15 c^3}\\ \end{align*}
Mathematica [A] time = 1.28933, size = 356, normalized size = 0.94 \[ \frac{d^3 \left (168 b^2 \text{PolyLog}\left (2,-e^{-2 \tanh ^{-1}(c x)}\right )+30 a^2 c^6 x^6+108 a^2 c^5 x^5+135 a^2 c^4 x^4+60 a^2 c^3 x^3+12 a b c^5 x^5+54 a b c^4 x^4+110 a b c^3 x^3+168 a b c^2 x^2+168 a b \log \left (c^2 x^2-1\right )+2 b \tanh ^{-1}(c x) \left (3 a c^3 x^3 \left (10 c^3 x^3+36 c^2 x^2+45 c x+20\right )+b \left (6 c^5 x^5+27 c^4 x^4+55 c^3 x^3+84 c^2 x^2+165 c x-111\right )-168 b \log \left (e^{-2 \tanh ^{-1}(c x)}+1\right )\right )+330 a b c x+165 a b \log (1-c x)-165 a b \log (c x+1)-162 a b+3 b^2 c^4 x^4+18 b^2 c^3 x^3+61 b^2 c^2 x^2+226 b^2 \log \left (1-c^2 x^2\right )+3 b^2 \left (10 c^6 x^6+36 c^5 x^5+45 c^4 x^4+20 c^3 x^3-111\right ) \tanh ^{-1}(c x)^2+222 b^2 c x-64 b^2\right )}{180 c^3} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.055, size = 618, normalized size = 1.6 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 2.15919, size = 1046, normalized size = 2.77 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (a^{2} c^{3} d^{3} x^{5} + 3 \, a^{2} c^{2} d^{3} x^{4} + 3 \, a^{2} c d^{3} x^{3} + a^{2} d^{3} x^{2} +{\left (b^{2} c^{3} d^{3} x^{5} + 3 \, b^{2} c^{2} d^{3} x^{4} + 3 \, b^{2} c d^{3} x^{3} + b^{2} d^{3} x^{2}\right )} \operatorname{artanh}\left (c x\right )^{2} + 2 \,{\left (a b c^{3} d^{3} x^{5} + 3 \, a b c^{2} d^{3} x^{4} + 3 \, a b c d^{3} x^{3} + a b d^{3} x^{2}\right )} \operatorname{artanh}\left (c x\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} d^{3} \left (\int a^{2} x^{2}\, dx + \int 3 a^{2} c x^{3}\, dx + \int 3 a^{2} c^{2} x^{4}\, dx + \int a^{2} c^{3} x^{5}\, dx + \int b^{2} x^{2} \operatorname{atanh}^{2}{\left (c x \right )}\, dx + \int 2 a b x^{2} \operatorname{atanh}{\left (c x \right )}\, dx + \int 3 b^{2} c x^{3} \operatorname{atanh}^{2}{\left (c x \right )}\, dx + \int 3 b^{2} c^{2} x^{4} \operatorname{atanh}^{2}{\left (c x \right )}\, dx + \int b^{2} c^{3} x^{5} \operatorname{atanh}^{2}{\left (c x \right )}\, dx + \int 6 a b c x^{3} \operatorname{atanh}{\left (c x \right )}\, dx + \int 6 a b c^{2} x^{4} \operatorname{atanh}{\left (c x \right )}\, dx + \int 2 a b c^{3} x^{5} \operatorname{atanh}{\left (c x \right )}\, dx\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (c d x + d\right )}^{3}{\left (b \operatorname{artanh}\left (c x\right ) + a\right )}^{2} x^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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