Optimal. Leaf size=317 \[ \frac{B d n (a+b x)^2 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{2 g^3 (c+d x)^2 (b c-a d)^2}+\frac{b (a+b x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{g^3 (c+d x) (b c-a d)^2}-\frac{d (a+b x)^2 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{2 g^3 (c+d x)^2 (b c-a d)^2}-\frac{2 A b B n (a+b x)}{g^3 (c+d x) (b c-a d)^2}-\frac{2 b B^2 n (a+b x) \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{g^3 (c+d x) (b c-a d)^2}+\frac{2 b B^2 n^2 (a+b x)}{g^3 (c+d x) (b c-a d)^2}-\frac{B^2 d n^2 (a+b x)^2}{4 g^3 (c+d x)^2 (b c-a d)^2} \]
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Rubi [C] time = 0.915045, antiderivative size = 626, normalized size of antiderivative = 1.97, number of steps used = 28, number of rules used = 11, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.314, Rules used = {2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 44} \[ \frac{b^2 B^2 n^2 \text{PolyLog}\left (2,-\frac{d (a+b x)}{b c-a d}\right )}{d g^3 (b c-a d)^2}+\frac{b^2 B^2 n^2 \text{PolyLog}\left (2,\frac{b (c+d x)}{b c-a d}\right )}{d g^3 (b c-a d)^2}+\frac{b^2 B n \log (a+b x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{d g^3 (b c-a d)^2}-\frac{b^2 B n \log (c+d x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{d g^3 (b c-a d)^2}+\frac{b B n \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{d g^3 (c+d x) (b c-a d)}-\frac{\left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{2 d g^3 (c+d x)^2}+\frac{B n \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{2 d g^3 (c+d x)^2}-\frac{b^2 B^2 n^2 \log ^2(a+b x)}{2 d g^3 (b c-a d)^2}-\frac{b^2 B^2 n^2 \log ^2(c+d x)}{2 d g^3 (b c-a d)^2}-\frac{3 b^2 B^2 n^2 \log (a+b x)}{2 d g^3 (b c-a d)^2}+\frac{3 b^2 B^2 n^2 \log (c+d x)}{2 d g^3 (b c-a d)^2}+\frac{b^2 B^2 n^2 \log (c+d x) \log \left (-\frac{d (a+b x)}{b c-a d}\right )}{d g^3 (b c-a d)^2}+\frac{b^2 B^2 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{d g^3 (b c-a d)^2}-\frac{3 b B^2 n^2}{2 d g^3 (c+d x) (b c-a d)}-\frac{B^2 n^2}{4 d g^3 (c+d x)^2} \]
Antiderivative was successfully verified.
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Rule 2525
Rule 12
Rule 2528
Rule 2524
Rule 2418
Rule 2390
Rule 2301
Rule 2394
Rule 2393
Rule 2391
Rule 44
Rubi steps
\begin{align*} \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{(c g+d g x)^3} \, dx &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}+\frac{(B n) \int \frac{(b c-a d) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{g^2 (a+b x) (c+d x)^3} \, dx}{d g}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}+\frac{(B (b c-a d) n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)^3} \, dx}{d g^3}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}+\frac{(B (b c-a d) n) \int \left (\frac{b^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (a+b x)}-\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (c+d x)^3}-\frac{b d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (c+d x)^2}-\frac{b^2 d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{d g^3}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}-\frac{(B n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(c+d x)^3} \, dx}{g^3}-\frac{\left (b^2 B n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{(b c-a d)^2 g^3}+\frac{\left (b^3 B n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{d (b c-a d)^2 g^3}-\frac{(b B n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(c+d x)^2} \, dx}{(b c-a d) g^3}\\ &=\frac{B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{2 d g^3 (c+d x)^2}+\frac{b B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d) g^3 (c+d x)}+\frac{b^2 B n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d)^2 g^3}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}-\frac{b^2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{\left (B^2 n^2\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^3} \, dx}{2 d g^3}-\frac{\left (b^2 B^2 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{d (b c-a d)^2 g^3}+\frac{\left (b^2 B^2 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{d (b c-a d)^2 g^3}-\frac{\left (b B^2 n^2\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^2} \, dx}{d (b c-a d) g^3}\\ &=\frac{B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{2 d g^3 (c+d x)^2}+\frac{b B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d) g^3 (c+d x)}+\frac{b^2 B n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d)^2 g^3}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}-\frac{b^2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{\left (b B^2 n^2\right ) \int \frac{1}{(a+b x) (c+d x)^2} \, dx}{d g^3}-\frac{\left (b^2 B^2 n^2\right ) \int \left (\frac{b \log (a+b x)}{a+b x}-\frac{d \log (a+b x)}{c+d x}\right ) \, dx}{d (b c-a d)^2 g^3}+\frac{\left (b^2 B^2 n^2\right ) \int \left (\frac{b \log (c+d x)}{a+b x}-\frac{d \log (c+d x)}{c+d x}\right ) \, dx}{d (b c-a d)^2 g^3}-\frac{\left (B^2 (b c-a d) n^2\right ) \int \frac{1}{(a+b x) (c+d x)^3} \, dx}{2 d g^3}\\ &=\frac{B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{2 d g^3 (c+d x)^2}+\frac{b B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d) g^3 (c+d x)}+\frac{b^2 B n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d)^2 g^3}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}-\frac{b^2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{\left (b B^2 n^2\right ) \int \left (\frac{b^2}{(b c-a d)^2 (a+b x)}-\frac{d}{(b c-a d) (c+d x)^2}-\frac{b d}{(b c-a d)^2 (c+d x)}\right ) \, dx}{d g^3}+\frac{\left (b^2 B^2 n^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{(b c-a d)^2 g^3}-\frac{\left (b^2 B^2 n^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{(b c-a d)^2 g^3}-\frac{\left (b^3 B^2 n^2\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{d (b c-a d)^2 g^3}+\frac{\left (b^3 B^2 n^2\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{d (b c-a d)^2 g^3}-\frac{\left (B^2 (b c-a d) n^2\right ) \int \left (\frac{b^3}{(b c-a d)^3 (a+b x)}-\frac{d}{(b c-a d) (c+d x)^3}-\frac{b d}{(b c-a d)^2 (c+d x)^2}-\frac{b^2 d}{(b c-a d)^3 (c+d x)}\right ) \, dx}{2 d g^3}\\ &=-\frac{B^2 n^2}{4 d g^3 (c+d x)^2}-\frac{3 b B^2 n^2}{2 d (b c-a d) g^3 (c+d x)}-\frac{3 b^2 B^2 n^2 \log (a+b x)}{2 d (b c-a d)^2 g^3}+\frac{B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{2 d g^3 (c+d x)^2}+\frac{b B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d) g^3 (c+d x)}+\frac{b^2 B n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d)^2 g^3}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}+\frac{3 b^2 B^2 n^2 \log (c+d x)}{2 d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{b^2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{d (b c-a d)^2 g^3}-\frac{\left (b^2 B^2 n^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{(b c-a d)^2 g^3}-\frac{\left (b^2 B^2 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{d (b c-a d)^2 g^3}-\frac{\left (b^2 B^2 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{d (b c-a d)^2 g^3}-\frac{\left (b^3 B^2 n^2\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{d (b c-a d)^2 g^3}\\ &=-\frac{B^2 n^2}{4 d g^3 (c+d x)^2}-\frac{3 b B^2 n^2}{2 d (b c-a d) g^3 (c+d x)}-\frac{3 b^2 B^2 n^2 \log (a+b x)}{2 d (b c-a d)^2 g^3}-\frac{b^2 B^2 n^2 \log ^2(a+b x)}{2 d (b c-a d)^2 g^3}+\frac{B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{2 d g^3 (c+d x)^2}+\frac{b B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d) g^3 (c+d x)}+\frac{b^2 B n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d)^2 g^3}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}+\frac{3 b^2 B^2 n^2 \log (c+d x)}{2 d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{b^2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{b^2 B^2 n^2 \log ^2(c+d x)}{2 d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{d (b c-a d)^2 g^3}-\frac{\left (b^2 B^2 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{d (b c-a d)^2 g^3}-\frac{\left (b^2 B^2 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{d (b c-a d)^2 g^3}\\ &=-\frac{B^2 n^2}{4 d g^3 (c+d x)^2}-\frac{3 b B^2 n^2}{2 d (b c-a d) g^3 (c+d x)}-\frac{3 b^2 B^2 n^2 \log (a+b x)}{2 d (b c-a d)^2 g^3}-\frac{b^2 B^2 n^2 \log ^2(a+b x)}{2 d (b c-a d)^2 g^3}+\frac{B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{2 d g^3 (c+d x)^2}+\frac{b B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d) g^3 (c+d x)}+\frac{b^2 B n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{d (b c-a d)^2 g^3}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{2 d g^3 (c+d x)^2}+\frac{3 b^2 B^2 n^2 \log (c+d x)}{2 d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{b^2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{d (b c-a d)^2 g^3}-\frac{b^2 B^2 n^2 \log ^2(c+d x)}{2 d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{d (b c-a d)^2 g^3}+\frac{b^2 B^2 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{d (b c-a d)^2 g^3}\\ \end{align*}
Mathematica [C] time = 0.49214, size = 464, normalized size = 1.46 \[ \frac{\frac{B n \left (-2 b^2 B n (c+d x)^2 \left (\log (a+b x) \left (\log (a+b x)-2 \log \left (\frac{b (c+d x)}{b c-a d}\right )\right )-2 \text{PolyLog}\left (2,\frac{d (a+b x)}{a d-b c}\right )\right )+2 b^2 B n (c+d x)^2 \left (2 \text{PolyLog}\left (2,\frac{b (c+d x)}{b c-a d}\right )+\log (c+d x) \left (2 \log \left (\frac{d (a+b x)}{a d-b c}\right )-\log (c+d x)\right )\right )+4 b^2 (c+d x)^2 \log (a+b x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )-4 b^2 (c+d x)^2 \log (c+d x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )+2 (b c-a d)^2 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )+4 b (c+d x) (b c-a d) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )-B n \left (2 b^2 (c+d x)^2 \log (a+b x)+2 b (c+d x) (b c-a d)+(b c-a d)^2-2 b^2 (c+d x)^2 \log (c+d x)\right )-4 b B n (c+d x) (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)\right )}{(b c-a d)^2}-2 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{4 d g^3 (c+d x)^2} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.441, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dgx+cg \right ) ^{3}} \left ( A+B\ln \left ( e \left ({\frac{bx+a}{dx+c}} \right ) ^{n} \right ) \right ) ^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.38282, size = 1162, normalized size = 3.67 \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 [B] time = 0.969725, size = 1354, normalized size = 4.27 \begin{align*} -\frac{2 \, A^{2} b^{2} c^{2} - 4 \, A^{2} a b c d + 2 \, A^{2} a^{2} d^{2} +{\left (7 \, B^{2} b^{2} c^{2} - 8 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right )} n^{2} + 2 \,{\left (B^{2} b^{2} c^{2} - 2 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right )} \log \left (e\right )^{2} - 2 \,{\left (B^{2} b^{2} d^{2} n^{2} x^{2} + 2 \, B^{2} b^{2} c d n^{2} x +{\left (2 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right )} n^{2}\right )} \log \left (\frac{b x + a}{d x + c}\right )^{2} - 2 \,{\left (3 \, A B b^{2} c^{2} - 4 \, A B a b c d + A B a^{2} d^{2}\right )} n + 2 \,{\left (3 \,{\left (B^{2} b^{2} c d - B^{2} a b d^{2}\right )} n^{2} - 2 \,{\left (A B b^{2} c d - A B a b d^{2}\right )} n\right )} x + 2 \,{\left (2 \, A B b^{2} c^{2} - 4 \, A B a b c d + 2 \, A B a^{2} d^{2} - 2 \,{\left (B^{2} b^{2} c d - B^{2} a b d^{2}\right )} n x -{\left (3 \, B^{2} b^{2} c^{2} - 4 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right )} n - 2 \,{\left (B^{2} b^{2} d^{2} n x^{2} + 2 \, B^{2} b^{2} c d n x +{\left (2 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right )} n\right )} \log \left (\frac{b x + a}{d x + c}\right )\right )} \log \left (e\right ) + 2 \,{\left ({\left (4 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right )} n^{2} +{\left (3 \, B^{2} b^{2} d^{2} n^{2} - 2 \, A B b^{2} d^{2} n\right )} x^{2} - 2 \,{\left (2 \, A B a b c d - A B a^{2} d^{2}\right )} n - 2 \,{\left (2 \, A B b^{2} c d n -{\left (2 \, B^{2} b^{2} c d + B^{2} a b d^{2}\right )} n^{2}\right )} x\right )} \log \left (\frac{b x + a}{d x + c}\right )}{4 \,{\left ({\left (b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right )} g^{3} x^{2} + 2 \,{\left (b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right )} g^{3} x +{\left (b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right )} g^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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 \frac{{\left (B \log \left (e \left (\frac{b x + a}{d x + c}\right )^{n}\right ) + A\right )}^{2}}{{\left (d g x + c g\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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