Optimal. Leaf size=742 \[ -\frac{6 b^2 p^2 q^2 (h i-g j)^2 \text{PolyLog}\left (3,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{h^3}+\frac{3 b p q (h i-g j)^2 \text{PolyLog}\left (2,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{h^3}+\frac{6 b^3 p^3 q^3 (h i-g j)^2 \text{PolyLog}\left (4,-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\frac{3 b^2 j^2 p^2 q^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{4 f^2 h}+\frac{6 a b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac{6 a b^2 j p^2 q^2 x (h i-g j)}{h^2}-\frac{3 b j p q (e+f x) (f i-e j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}+\frac{j (e+f x) (f i-e j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f^2 h}-\frac{3 b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{4 f^2 h}+\frac{j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{2 f^2 h}-\frac{3 b j p q (e+f x) (h i-g j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac{j (e+f x) (h i-g j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{(h i-g j)^2 \log \left (\frac{f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{h^3}+\frac{6 b^3 j p^2 q^2 (e+f x) (f i-e j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f^2 h}+\frac{6 b^3 j p^2 q^2 (e+f x) (h i-g j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}-\frac{3 b^3 j^2 p^3 q^3 (e+f x)^2}{8 f^2 h}-\frac{6 b^3 j p^3 q^3 x (f i-e j)}{f h}-\frac{6 b^3 j p^3 q^3 x (h i-g j)}{h^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 1.83124, antiderivative size = 742, normalized size of antiderivative = 1., number of steps used = 24, number of rules used = 14, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4, Rules used = {2418, 2389, 2296, 2295, 2396, 2433, 2374, 2383, 6589, 2401, 2390, 2305, 2304, 2445} \[ -\frac{6 b^2 p^2 q^2 (h i-g j)^2 \text{PolyLog}\left (3,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{h^3}+\frac{3 b p q (h i-g j)^2 \text{PolyLog}\left (2,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{h^3}+\frac{6 b^3 p^3 q^3 (h i-g j)^2 \text{PolyLog}\left (4,-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\frac{3 b^2 j^2 p^2 q^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{4 f^2 h}+\frac{6 a b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac{6 a b^2 j p^2 q^2 x (h i-g j)}{h^2}-\frac{3 b j p q (e+f x) (f i-e j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}+\frac{j (e+f x) (f i-e j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f^2 h}-\frac{3 b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{4 f^2 h}+\frac{j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{2 f^2 h}-\frac{3 b j p q (e+f x) (h i-g j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac{j (e+f x) (h i-g j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{(h i-g j)^2 \log \left (\frac{f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{h^3}+\frac{6 b^3 j p^2 q^2 (e+f x) (f i-e j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f^2 h}+\frac{6 b^3 j p^2 q^2 (e+f x) (h i-g j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}-\frac{3 b^3 j^2 p^3 q^3 (e+f x)^2}{8 f^2 h}-\frac{6 b^3 j p^3 q^3 x (f i-e j)}{f h}-\frac{6 b^3 j p^3 q^3 x (h i-g j)}{h^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2418
Rule 2389
Rule 2296
Rule 2295
Rule 2396
Rule 2433
Rule 2374
Rule 2383
Rule 6589
Rule 2401
Rule 2390
Rule 2305
Rule 2304
Rule 2445
Rubi steps
\begin{align*} \int \frac{(535+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{g+h x} \, dx &=\operatorname{Subst}\left (\int \frac{(535+j x)^2 \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{g+h x} \, dx,c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\operatorname{Subst}\left (\int \left (\frac{j (535 h-g j) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{h^2}+\frac{(535 h-g j)^2 \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{h^2 (g+h x)}+\frac{j (535+j x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{h}\right ) \, dx,c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\operatorname{Subst}\left (\frac{j \int (535+j x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3 \, dx}{h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(j (535 h-g j)) \int \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3 \, dx}{h^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(535 h-g j)^2 \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{g+h x} \, dx}{h^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\operatorname{Subst}\left (\frac{j \int \left (\frac{(535 f-e j) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{f}+\frac{j (e+f x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{f}\right ) \, dx}{h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(j (535 h-g j)) \operatorname{Subst}\left (\int \left (a+b \log \left (c d^q x^{p q}\right )\right )^3 \, dx,x,e+f x\right )}{f h^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{\left (3 b f (535 h-g j)^2 p q\right ) \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{e+f x} \, dx}{h^3},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\frac{j (535 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\operatorname{Subst}\left (\frac{j^2 \int (e+f x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3 \, dx}{f h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(j (535 f-e j)) \int \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3 \, dx}{f h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{(3 b j (535 h-g j) p q) \operatorname{Subst}\left (\int \left (a+b \log \left (c d^q x^{p q}\right )\right )^2 \, dx,x,e+f x\right )}{f h^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{\left (3 b (535 h-g j)^2 p q\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c d^q x^{p q}\right )\right )^2 \log \left (\frac{f \left (\frac{f g-e h}{f}+\frac{h x}{f}\right )}{f g-e h}\right )}{x} \, dx,x,e+f x\right )}{h^3},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=-\frac{3 b j (535 h-g j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac{j (535 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\frac{3 b (535 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\operatorname{Subst}\left (\frac{j^2 \operatorname{Subst}\left (\int x \left (a+b \log \left (c d^q x^{p q}\right )\right )^3 \, dx,x,e+f x\right )}{f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(j (535 f-e j)) \operatorname{Subst}\left (\int \left (a+b \log \left (c d^q x^{p q}\right )\right )^3 \, dx,x,e+f x\right )}{f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{\left (6 b^2 j (535 h-g j) p^2 q^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c d^q x^{p q}\right )\right ) \, dx,x,e+f x\right )}{f h^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{\left (6 b^2 (535 h-g j)^2 p^2 q^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c d^q x^{p q}\right )\right ) \text{Li}_2\left (-\frac{h x}{f g-e h}\right )}{x} \, dx,x,e+f x\right )}{h^3},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\frac{6 a b^2 j (535 h-g j) p^2 q^2 x}{h^2}-\frac{3 b j (535 h-g j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac{j (535 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f^2 h}+\frac{j (535 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{2 f^2 h}+\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\frac{3 b (535 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}-\frac{6 b^2 (535 h-g j)^2 p^2 q^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text{Li}_3\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}-\operatorname{Subst}\left (\frac{\left (3 b j^2 p q\right ) \operatorname{Subst}\left (\int x \left (a+b \log \left (c d^q x^{p q}\right )\right )^2 \, dx,x,e+f x\right )}{2 f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{(3 b j (535 f-e j) p q) \operatorname{Subst}\left (\int \left (a+b \log \left (c d^q x^{p q}\right )\right )^2 \, dx,x,e+f x\right )}{f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{\left (6 b^3 j (535 h-g j) p^2 q^2\right ) \operatorname{Subst}\left (\int \log \left (c d^q x^{p q}\right ) \, dx,x,e+f x\right )}{f h^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{\left (6 b^3 (535 h-g j)^2 p^3 q^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_3\left (-\frac{h x}{f g-e h}\right )}{x} \, dx,x,e+f x\right )}{h^3},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\frac{6 a b^2 j (535 h-g j) p^2 q^2 x}{h^2}-\frac{6 b^3 j (535 h-g j) p^3 q^3 x}{h^2}+\frac{6 b^3 j (535 h-g j) p^2 q^2 (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}-\frac{3 b j (535 f-e j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}-\frac{3 b j (535 h-g j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}-\frac{3 b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{4 f^2 h}+\frac{j (535 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f^2 h}+\frac{j (535 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{2 f^2 h}+\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\frac{3 b (535 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}-\frac{6 b^2 (535 h-g j)^2 p^2 q^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text{Li}_3\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\frac{6 b^3 (535 h-g j)^2 p^3 q^3 \text{Li}_4\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\operatorname{Subst}\left (\frac{\left (3 b^2 j^2 p^2 q^2\right ) \operatorname{Subst}\left (\int x \left (a+b \log \left (c d^q x^{p q}\right )\right ) \, dx,x,e+f x\right )}{2 f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{\left (6 b^2 j (535 f-e j) p^2 q^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c d^q x^{p q}\right )\right ) \, dx,x,e+f x\right )}{f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\frac{6 a b^2 j (535 f-e j) p^2 q^2 x}{f h}+\frac{6 a b^2 j (535 h-g j) p^2 q^2 x}{h^2}-\frac{6 b^3 j (535 h-g j) p^3 q^3 x}{h^2}-\frac{3 b^3 j^2 p^3 q^3 (e+f x)^2}{8 f^2 h}+\frac{6 b^3 j (535 h-g j) p^2 q^2 (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}+\frac{3 b^2 j^2 p^2 q^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{4 f^2 h}-\frac{3 b j (535 f-e j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}-\frac{3 b j (535 h-g j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}-\frac{3 b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{4 f^2 h}+\frac{j (535 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f^2 h}+\frac{j (535 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{2 f^2 h}+\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\frac{3 b (535 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}-\frac{6 b^2 (535 h-g j)^2 p^2 q^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text{Li}_3\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\frac{6 b^3 (535 h-g j)^2 p^3 q^3 \text{Li}_4\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\operatorname{Subst}\left (\frac{\left (6 b^3 j (535 f-e j) p^2 q^2\right ) \operatorname{Subst}\left (\int \log \left (c d^q x^{p q}\right ) \, dx,x,e+f x\right )}{f^2 h},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\frac{6 a b^2 j (535 f-e j) p^2 q^2 x}{f h}+\frac{6 a b^2 j (535 h-g j) p^2 q^2 x}{h^2}-\frac{6 b^3 j (535 f-e j) p^3 q^3 x}{f h}-\frac{6 b^3 j (535 h-g j) p^3 q^3 x}{h^2}-\frac{3 b^3 j^2 p^3 q^3 (e+f x)^2}{8 f^2 h}+\frac{6 b^3 j (535 f-e j) p^2 q^2 (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f^2 h}+\frac{6 b^3 j (535 h-g j) p^2 q^2 (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}+\frac{3 b^2 j^2 p^2 q^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{4 f^2 h}-\frac{3 b j (535 f-e j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}-\frac{3 b j (535 h-g j) p q (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}-\frac{3 b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{4 f^2 h}+\frac{j (535 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f^2 h}+\frac{j (535 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{f h^2}+\frac{j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{2 f^2 h}+\frac{(535 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (g+h x)}{f g-e h}\right )}{h^3}+\frac{3 b (535 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}-\frac{6 b^2 (535 h-g j)^2 p^2 q^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text{Li}_3\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}+\frac{6 b^3 (535 h-g j)^2 p^3 q^3 \text{Li}_4\left (-\frac{h (e+f x)}{f g-e h}\right )}{h^3}\\ \end{align*}
Mathematica [B] time = 1.45203, size = 4056, normalized size = 5.47 \[ \text{Result too large to show} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.841, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( jx+i \right ) ^{2} \left ( a+b\ln \left ( c \left ( d \left ( fx+e \right ) ^{p} \right ) ^{q} \right ) \right ) ^{3}}{hx+g}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \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 (\frac{a^{3} j^{2} x^{2} + 2 \, a^{3} i j x + a^{3} i^{2} +{\left (b^{3} j^{2} x^{2} + 2 \, b^{3} i j x + b^{3} i^{2}\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{3} + 3 \,{\left (a b^{2} j^{2} x^{2} + 2 \, a b^{2} i j x + a b^{2} i^{2}\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 3 \,{\left (a^{2} b j^{2} x^{2} + 2 \, a^{2} b i j x + a^{2} b i^{2}\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )}{h x + g}, x\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 (j x + i\right )}^{2}{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{3}}{h x + g}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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