Optimal. Leaf size=659 \[ \frac{6 b^2 f p^2 q^2 \text{PolyLog}\left (2,-\frac{j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(f i-e j) (h i-g j)}-\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left (3,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(h i-g j)^2}+\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left (3,-\frac{j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(h i-g j)^2}+\frac{3 b h p q \text{PolyLog}\left (2,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(h i-g j)^2}-\frac{3 b h p q \text{PolyLog}\left (2,-\frac{j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(h i-g j)^2}-\frac{6 b^3 f p^3 q^3 \text{PolyLog}\left (3,-\frac{j (e+f x)}{f i-e j}\right )}{(f i-e j) (h i-g j)}+\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left (4,-\frac{h (e+f x)}{f g-e h}\right )}{(h i-g j)^2}-\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left (4,-\frac{j (e+f x)}{f i-e j}\right )}{(h i-g j)^2}+\frac{3 b f p q \log \left (\frac{f (i+j x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(f i-e j) (h i-g j)}-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(i+j x) (f i-e j) (h i-g j)}+\frac{h \log \left (\frac{f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(h i-g j)^2}-\frac{h \log \left (\frac{f (i+j x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(h i-g j)^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 1.71566, antiderivative size = 659, normalized size of antiderivative = 1., number of steps used = 18, number of rules used = 8, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.229, Rules used = {2418, 2396, 2433, 2374, 2383, 6589, 2397, 2445} \[ \frac{6 b^2 f p^2 q^2 \text{PolyLog}\left (2,-\frac{j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(f i-e j) (h i-g j)}-\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left (3,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(h i-g j)^2}+\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left (3,-\frac{j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(h i-g j)^2}+\frac{3 b h p q \text{PolyLog}\left (2,-\frac{h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(h i-g j)^2}-\frac{3 b h p q \text{PolyLog}\left (2,-\frac{j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(h i-g j)^2}-\frac{6 b^3 f p^3 q^3 \text{PolyLog}\left (3,-\frac{j (e+f x)}{f i-e j}\right )}{(f i-e j) (h i-g j)}+\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left (4,-\frac{h (e+f x)}{f g-e h}\right )}{(h i-g j)^2}-\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left (4,-\frac{j (e+f x)}{f i-e j}\right )}{(h i-g j)^2}+\frac{3 b f p q \log \left (\frac{f (i+j x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(f i-e j) (h i-g j)}-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(i+j x) (f i-e j) (h i-g j)}+\frac{h \log \left (\frac{f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(h i-g j)^2}-\frac{h \log \left (\frac{f (i+j x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(h i-g j)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2418
Rule 2396
Rule 2433
Rule 2374
Rule 2383
Rule 6589
Rule 2397
Rule 2445
Rubi steps
\begin{align*} \int \frac{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(g+h x) (539+j x)^2} \, dx &=\operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{(g+h x) (539+j x)^2} \, 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{h^2 \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{(539 h-g j)^2 (g+h x)}-\frac{j \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{(539 h-g j) (539+j x)^2}-\frac{h j \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{(539 h-g j)^2 (539+j x)}\right ) \, dx,c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=\operatorname{Subst}\left (\frac{h^2 \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{g+h x} \, dx}{(539 h-g j)^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{(h j) \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{539+j x} \, dx}{(539 h-g j)^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )-\operatorname{Subst}\left (\frac{j \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^3}{(539+j x)^2} \, dx}{539 h-g j},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(539 f-e j) (539 h-g j) (539+j x)}+\frac{h \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 )}{(539 h-g j)^2}-\frac{h \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 h-g j)^2}-\operatorname{Subst}\left (\frac{(3 b f h p q) \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}{(539 h-g j)^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(3 b f h p q) \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{e+f x} \, dx}{(539 h-g j)^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(3 b f j p q) \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{539+j x} \, dx}{(539 f-e j) (539 h-g j)},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(539 f-e j) (539 h-g j) (539+j x)}+\frac{h \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 )}{(539 h-g j)^2}+\frac{3 b f p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}-\frac{h \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 h-g j)^2}-\operatorname{Subst}\left (\frac{(3 b h p q) \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 )}{(539 h-g j)^2},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )+\operatorname{Subst}\left (\frac{(3 b h p q) \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{539 f-e j}{f}+\frac{j x}{f}\right )}{539 f-e j}\right )}{x} \, dx,x,e+f x\right )}{(539 h-g j)^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 f^2 p^2 q^2\right ) \int \frac{\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right ) \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{e+f x} \, dx}{(539 f-e j) (539 h-g j)},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(539 f-e j) (539 h-g j) (539+j x)}+\frac{h \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 )}{(539 h-g j)^2}+\frac{3 b f p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}-\frac{h \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 h-g j)^2}+\frac{3 b h 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 )}{(539 h-g j)^2}-\frac{3 b h p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 h-g j)^2}-\operatorname{Subst}\left (\frac{\left (6 b^2 h 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 )}{(539 h-g j)^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 h 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{j x}{539 f-e j}\right )}{x} \, dx,x,e+f x\right )}{(539 h-g j)^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 f p^2 q^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c d^q x^{p q}\right )\right ) \log \left (\frac{f \left (\frac{539 f-e j}{f}+\frac{j x}{f}\right )}{539 f-e j}\right )}{x} \, dx,x,e+f x\right )}{(539 f-e j) (539 h-g j)},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(539 f-e j) (539 h-g j) (539+j x)}+\frac{h \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 )}{(539 h-g j)^2}+\frac{3 b f p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}-\frac{h \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 h-g j)^2}+\frac{3 b h 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 )}{(539 h-g j)^2}+\frac{6 b^2 f p^2 q^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text{Li}_2\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}-\frac{3 b h p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 h-g j)^2}-\frac{6 b^2 h 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 )}{(539 h-g j)^2}+\frac{6 b^2 h 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{j (e+f x)}{539 f-e j}\right )}{(539 h-g j)^2}+\operatorname{Subst}\left (\frac{\left (6 b^3 h 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 )}{(539 h-g j)^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 h p^3 q^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_3\left (-\frac{j x}{539 f-e j}\right )}{x} \, dx,x,e+f x\right )}{(539 h-g j)^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 f p^3 q^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{j x}{539 f-e j}\right )}{x} \, dx,x,e+f x\right )}{(539 f-e j) (539 h-g j)},c d^q (e+f x)^{p q},c \left (d (e+f x)^p\right )^q\right )\\ &=-\frac{j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(539 f-e j) (539 h-g j) (539+j x)}+\frac{h \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 )}{(539 h-g j)^2}+\frac{3 b f p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}-\frac{h \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log \left (\frac{f (539+j x)}{539 f-e j}\right )}{(539 h-g j)^2}+\frac{3 b h 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 )}{(539 h-g j)^2}+\frac{6 b^2 f p^2 q^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text{Li}_2\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}-\frac{3 b h p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \text{Li}_2\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 h-g j)^2}-\frac{6 b^2 h 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 )}{(539 h-g j)^2}-\frac{6 b^3 f p^3 q^3 \text{Li}_3\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 f-e j) (539 h-g j)}+\frac{6 b^2 h 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{j (e+f x)}{539 f-e j}\right )}{(539 h-g j)^2}+\frac{6 b^3 h p^3 q^3 \text{Li}_4\left (-\frac{h (e+f x)}{f g-e h}\right )}{(539 h-g j)^2}-\frac{6 b^3 h p^3 q^3 \text{Li}_4\left (-\frac{j (e+f x)}{539 f-e j}\right )}{(539 h-g j)^2}\\ \end{align*}
Mathematica [A] time = 1.83126, size = 1057, normalized size = 1.6 \[ \frac{-b^3 p^3 \left ((h i-g j) \left (\left (j (e+f x) \log (e+f x)-3 f (i+j x) \log \left (\frac{f (i+j x)}{f i-e j}\right )\right ) \log ^2(e+f x)-6 f (i+j x) \text{PolyLog}\left (2,\frac{j (e+f x)}{e j-f i}\right ) \log (e+f x)+6 f (i+j x) \text{PolyLog}\left (3,\frac{j (e+f x)}{e j-f i}\right )\right )-h (f i-e j) (i+j x) \left (\log \left (\frac{f (g+h x)}{f g-e h}\right ) \log ^3(e+f x)+3 \text{PolyLog}\left (2,\frac{h (e+f x)}{e h-f g}\right ) \log ^2(e+f x)-6 \text{PolyLog}\left (3,\frac{h (e+f x)}{e h-f g}\right ) \log (e+f x)+6 \text{PolyLog}\left (4,\frac{h (e+f x)}{e h-f g}\right )\right )+h (f i-e j) (i+j x) \left (\log \left (\frac{f (i+j x)}{f i-e j}\right ) \log ^3(e+f x)+3 \text{PolyLog}\left (2,\frac{j (e+f x)}{e j-f i}\right ) \log ^2(e+f x)-6 \text{PolyLog}\left (3,\frac{j (e+f x)}{e j-f i}\right ) \log (e+f x)+6 \text{PolyLog}\left (4,\frac{j (e+f x)}{e j-f i}\right )\right )\right ) q^3-3 b^2 p^2 \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \left ((h i-g j) \left (\log (e+f x) \left (j (e+f x) \log (e+f x)-2 f (i+j x) \log \left (\frac{f (i+j x)}{f i-e j}\right )\right )-2 f (i+j x) \text{PolyLog}\left (2,\frac{j (e+f x)}{e j-f i}\right )\right )-h (f i-e j) (i+j x) \left (\log \left (\frac{f (g+h x)}{f g-e h}\right ) \log ^2(e+f x)+2 \text{PolyLog}\left (2,\frac{h (e+f x)}{e h-f g}\right ) \log (e+f x)-2 \text{PolyLog}\left (3,\frac{h (e+f x)}{e h-f g}\right )\right )+h (f i-e j) (i+j x) \left (\log \left (\frac{f (i+j x)}{f i-e j}\right ) \log ^2(e+f x)+2 \text{PolyLog}\left (2,\frac{j (e+f x)}{e j-f i}\right ) \log (e+f x)-2 \text{PolyLog}\left (3,\frac{j (e+f x)}{e j-f i}\right )\right )\right ) q^2-3 b p \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \left ((h i-g j) (j (e+f x) \log (e+f x)-f (i+j x) \log (i+j x))-h (f i-e j) (i+j x) \left (\log (e+f x) \log \left (\frac{f (g+h x)}{f g-e h}\right )+\text{PolyLog}\left (2,\frac{h (e+f x)}{e h-f g}\right )\right )+h (f i-e j) (i+j x) \left (\log (e+f x) \log \left (\frac{f (i+j x)}{f i-e j}\right )+\text{PolyLog}\left (2,\frac{j (e+f x)}{e j-f i}\right )\right )\right ) q+(f i-e j) (h i-g j) \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3+h (f i-e j) (i+j x) \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log (g+h x)-h (f i-e j) (i+j x) \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3 \log (i+j x)}{(f i-e j) (h i-g j)^2 (i+j x)} \]
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 1.011, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\ln \left ( c \left ( d \left ( fx+e \right ) ^{p} \right ) ^{q} \right ) \right ) ^{3}}{ \left ( hx+g \right ) \left ( jx+i \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} a^{3}{\left (\frac{h \log \left (h x + g\right )}{h^{2} i^{2} - 2 \, g h i j + g^{2} j^{2}} - \frac{h \log \left (j x + i\right )}{h^{2} i^{2} - 2 \, g h i j + g^{2} j^{2}} + \frac{1}{h i^{2} - g i j +{\left (h i j - g j^{2}\right )} x}\right )} + \int \frac{b^{3} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )^{3} + 3 \,{\left (\log \left (c\right )^{2} + 2 \, \log \left (c\right ) \log \left (d^{q}\right ) + \log \left (d^{q}\right )^{2}\right )} a b^{2} +{\left (\log \left (c\right )^{3} + 3 \, \log \left (c\right )^{2} \log \left (d^{q}\right ) + 3 \, \log \left (c\right ) \log \left (d^{q}\right )^{2} + \log \left (d^{q}\right )^{3}\right )} b^{3} + 3 \, a^{2} b{\left (\log \left (c\right ) + \log \left (d^{q}\right )\right )} + 3 \,{\left (b^{3}{\left (\log \left (c\right ) + \log \left (d^{q}\right )\right )} + a b^{2}\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )^{2} + 3 \,{\left ({\left (\log \left (c\right )^{2} + 2 \, \log \left (c\right ) \log \left (d^{q}\right ) + \log \left (d^{q}\right )^{2}\right )} b^{3} + 2 \, a b^{2}{\left (\log \left (c\right ) + \log \left (d^{q}\right )\right )} + a^{2} b\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )}{h j^{2} x^{3} + g i^{2} +{\left (2 \, h i j + g j^{2}\right )} x^{2} +{\left (h i^{2} + 2 \, g i j\right )} x}\,{d x} \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{b^{3} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{3} + 3 \, a b^{2} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 3 \, a^{2} b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a^{3}}{h j^{2} x^{3} + g i^{2} +{\left (2 \, h i j + g j^{2}\right )} x^{2} +{\left (h i^{2} + 2 \, g i j\right )} x}, 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{{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{3}}{{\left (h x + g\right )}{\left (j x + i\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]