Optimal. Leaf size=764 \[ \frac{2 d^3 p q r^2 \text{PolyLog}\left (2,\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \text{PolyLog}\left (2,-\frac{d (a+b x)}{b c-a d}\right )}{3 b (b c-a d)^3}+\frac{2 d^3 q r \log (a+b x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}+\frac{2 d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x) (b c-a d)^2}+\frac{8 d^2 p q r^2}{9 b (a+b x) (b c-a d)^2}-\frac{d^3 p q r^2 \log ^2(a+b x)}{3 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (c+d x) \log \left (-\frac{d (a+b x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{d^2 q^2 r^2}{3 b (a+b x) (b c-a d)^2}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 b (b c-a d)^3}-\frac{d^3 q^2 r^2 \log (a+b x)}{b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log (c+d x)}{b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}-\frac{d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^2 (b c-a d)}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (a+b x)^2 (b c-a d)}-\frac{2 p^2 r^2}{27 b (a+b x)^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.606462, antiderivative size = 764, normalized size of antiderivative = 1., number of steps used = 28, number of rules used = 13, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.419, Rules used = {2498, 2495, 32, 44, 2514, 36, 31, 2494, 2390, 2301, 2394, 2393, 2391} \[ \frac{2 d^3 p q r^2 \text{PolyLog}\left (2,\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \text{PolyLog}\left (2,-\frac{d (a+b x)}{b c-a d}\right )}{3 b (b c-a d)^3}+\frac{2 d^3 q r \log (a+b x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}+\frac{2 d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x) (b c-a d)^2}+\frac{8 d^2 p q r^2}{9 b (a+b x) (b c-a d)^2}-\frac{d^3 p q r^2 \log ^2(a+b x)}{3 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (c+d x) \log \left (-\frac{d (a+b x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{d^2 q^2 r^2}{3 b (a+b x) (b c-a d)^2}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 b (b c-a d)^3}-\frac{d^3 q^2 r^2 \log (a+b x)}{b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log (c+d x)}{b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}-\frac{d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^2 (b c-a d)}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (a+b x)^2 (b c-a d)}-\frac{2 p^2 r^2}{27 b (a+b x)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2498
Rule 2495
Rule 32
Rule 44
Rule 2514
Rule 36
Rule 31
Rule 2494
Rule 2390
Rule 2301
Rule 2394
Rule 2393
Rule 2391
Rubi steps
\begin{align*} \int \frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^4} \, dx &=-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}+\frac{1}{3} (2 p r) \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^4} \, dx+\frac{(2 d q r) \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^3 (c+d x)} \, dx}{3 b}\\ &=-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}+\frac{(2 d q r) \int \left (\frac{b \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(b c-a d) (a+b x)^3}-\frac{b d \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2 \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(b c-a d)^3 (a+b x)}-\frac{d^3 \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{3 b}+\frac{1}{9} \left (2 p^2 r^2\right ) \int \frac{1}{(a+b x)^4} \, dx+\frac{\left (2 d p q r^2\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{9 b}\\ &=-\frac{2 p^2 r^2}{27 b (a+b x)^3}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}+\frac{\left (2 d^3 q r\right ) \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{a+b x} \, dx}{3 (b c-a d)^3}-\frac{\left (2 d^4 q r\right ) \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{c+d x} \, dx}{3 b (b c-a d)^3}-\frac{\left (2 d^2 q r\right ) \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^2} \, dx}{3 (b c-a d)^2}+\frac{(2 d q r) \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^3} \, dx}{3 (b c-a d)}+\frac{\left (2 d p q r^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{9 b}\\ &=-\frac{2 p^2 r^2}{27 b (a+b x)^3}-\frac{d p q r^2}{9 b (b c-a d) (a+b x)^2}+\frac{2 d^2 p q r^2}{9 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d) (a+b x)^2}+\frac{2 d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 q r \log (a+b x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}-\frac{\left (2 d^3 p q r^2\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{3 (b c-a d)^3}+\frac{\left (2 d^3 p q r^2\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{3 (b c-a d)^3}-\frac{\left (2 d^2 p q r^2\right ) \int \frac{1}{(a+b x)^2} \, dx}{3 (b c-a d)^2}+\frac{\left (d p q r^2\right ) \int \frac{1}{(a+b x)^3} \, dx}{3 (b c-a d)}-\frac{\left (2 d^4 q^2 r^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{3 b (b c-a d)^3}+\frac{\left (2 d^4 q^2 r^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{3 b (b c-a d)^3}-\frac{\left (2 d^3 q^2 r^2\right ) \int \frac{1}{(a+b x) (c+d x)} \, dx}{3 b (b c-a d)^2}+\frac{\left (d^2 q^2 r^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{3 b (b c-a d)}\\ &=-\frac{2 p^2 r^2}{27 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (b c-a d) (a+b x)^2}+\frac{8 d^2 p q r^2}{9 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d) (a+b x)^2}+\frac{2 d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 q r \log (a+b x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}-\frac{\left (2 d^3 p q r^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{3 b (b c-a d)^3}-\frac{\left (2 d^4 p q r^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3 b (b c-a d)^3}-\frac{\left (2 d^3 q^2 r^2\right ) \int \frac{1}{a+b x} \, dx}{3 (b c-a d)^3}+\frac{\left (2 d^3 q^2 r^2\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3 (b c-a d)^3}+\frac{\left (2 d^3 q^2 r^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{3 b (b c-a d)^3}+\frac{\left (2 d^4 q^2 r^2\right ) \int \frac{1}{c+d x} \, dx}{3 b (b c-a d)^3}+\frac{\left (d^2 q^2 r^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{3 b (b c-a d)}\\ &=-\frac{2 p^2 r^2}{27 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (b c-a d) (a+b x)^2}+\frac{8 d^2 p q r^2}{9 b (b c-a d)^2 (a+b x)}-\frac{d^2 q^2 r^2}{3 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{d^3 q^2 r^2 \log (a+b x)}{b (b c-a d)^3}-\frac{d^3 p q r^2 \log ^2(a+b x)}{3 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log (c+d x)}{b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d) (a+b x)^2}+\frac{2 d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 q r \log (a+b x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}-\frac{\left (2 d^3 p q r^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 )}{3 b (b c-a d)^3}+\frac{\left (2 d^3 q^2 r^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 )}{3 b (b c-a d)^3}\\ &=-\frac{2 p^2 r^2}{27 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (b c-a d) (a+b x)^2}+\frac{8 d^2 p q r^2}{9 b (b c-a d)^2 (a+b x)}-\frac{d^2 q^2 r^2}{3 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{d^3 q^2 r^2 \log (a+b x)}{b (b c-a d)^3}-\frac{d^3 p q r^2 \log ^2(a+b x)}{3 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log (c+d x)}{b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}-\frac{2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{9 b (a+b x)^3}-\frac{d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d) (a+b x)^2}+\frac{2 d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^2 (a+b x)}+\frac{2 d^3 q r \log (a+b x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (b c-a d)^3}-\frac{\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 b (a+b x)^3}-\frac{2 d^3 q^2 r^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{3 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{3 b (b c-a d)^3}\\ \end{align*}
Mathematica [A] time = 2.73125, size = 1407, normalized size = 1.84 \[ -\frac{4 c^3 p^2 r^2 b^3+18 c d^2 q^2 r^2 x^2 b^3-48 c d^2 p q r^2 x^2 b^3-18 d^3 q^2 r^2 x^3 \log ^2(c+d x) b^3+18 c^3 \log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^3+15 c^2 d p q r^2 x b^3-54 d^3 q^2 r^2 x^3 \log (c+d x) b^3+12 d^3 p q r^2 x^3 \log (c+d x) b^3-36 c d^2 q r x^2 \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^3+12 c^3 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^3+18 c^2 d q r x \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^3+36 d^3 q r x^3 \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^3-12 a c^2 d p^2 r^2 b^2+15 a c^2 d p q r^2 b^2-18 a d^3 q^2 r^2 x^2 b^2+48 a d^3 p q r^2 x^2 b^2-54 a d^3 q^2 r^2 x^2 \log ^2(c+d x) b^2-54 a c^2 d \log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^2+36 a c d^2 q^2 r^2 x b^2-126 a c d^2 p q r^2 x b^2-162 a d^3 q^2 r^2 x^2 \log (c+d x) b^2+36 a d^3 p q r^2 x^2 \log (c+d x) b^2+36 a d^3 q r x^2 \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^2-36 a c^2 d p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^2+18 a c^2 d q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^2-108 a c d^2 q r x \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^2+108 a d^3 q r x^2 \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b^2+12 a^2 c d^2 p^2 r^2 b+18 a^2 c d^2 q^2 r^2 b-78 a^2 c d^2 p q r^2 b-54 a^2 d^3 q^2 r^2 x \log ^2(c+d x) b+54 a^2 c d^2 \log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b-36 a^2 d^3 q^2 r^2 x b+111 a^2 d^3 p q r^2 x b-162 a^2 d^3 q^2 r^2 x \log (c+d x) b+36 a^2 d^3 p q r^2 x \log (c+d x) b+36 a^2 c d^2 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b-72 a^2 c d^2 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b+90 a^2 d^3 q r x \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b+108 a^2 d^3 q r x \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right ) b-4 a^3 d^3 p^2 r^2-18 a^3 d^3 q^2 r^2+63 a^3 d^3 p q r^2+18 d^3 p q r^2 (a+b x)^3 \log ^2(a+b x)-18 a^3 d^3 q^2 r^2 \log ^2(c+d x)-18 a^3 d^3 \log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )-54 a^3 d^3 q^2 r^2 \log (c+d x)+12 a^3 d^3 p q r^2 \log (c+d x)-12 a^3 d^3 p r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )+54 a^3 d^3 q r \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )+36 a^3 d^3 q r \log (c+d x) \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )-6 d^3 q r (a+b x)^3 \log (a+b x) \left (2 p r-9 q r+6 p \log (c+d x) r-6 (p+q) \log \left (\frac{b (c+d x)}{b c-a d}\right ) r+6 \log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )+36 d^3 q (p+q) r^2 (a+b x)^3 \text{PolyLog}\left (2,\frac{d (a+b x)}{a d-b c}\right )}{54 b (b c-a d)^3 (a+b x)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.414, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \ln \left ( e \left ( f \left ( bx+a \right ) ^{p} \left ( dx+c \right ) ^{q} \right ) ^{r} \right ) \right ) ^{2}}{ \left ( bx+a \right ) ^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.76099, size = 1690, normalized size = 2.21 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (\left ({\left (b x + a\right )}^{p}{\left (d x + c\right )}^{q} f\right )^{r} e\right )^{2}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (\left ({\left (b x + a\right )}^{p}{\left (d x + c\right )}^{q} f\right )^{r} e\right )^{2}}{{\left (b x + a\right )}^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]