Optimal. Leaf size=659 \[ \frac {6 b^2 f p^2 q^2 \text {Li}_2\left (-\frac {j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(f i-e j) (h i-g j)}-\frac {6 b^2 h p^2 q^2 \text {Li}_3\left (-\frac {h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(h i-g j)^2}+\frac {6 b^2 h p^2 q^2 \text {Li}_3\left (-\frac {j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{(h i-g j)^2}+\frac {3 b h p q \text {Li}_2\left (-\frac {h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(h i-g j)^2}-\frac {3 b h p q \text {Li}_2\left (-\frac {j (e+f x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(h i-g j)^2}+\frac {3 b f p q \log \left (\frac {f (i+j x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{(f i-e j) (h i-g j)}-\frac {j (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(i+j x) (f i-e j) (h i-g j)}+\frac {h \log \left (\frac {f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(h i-g j)^2}-\frac {h \log \left (\frac {f (i+j x)}{f i-e j}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3}{(h i-g j)^2}-\frac {6 b^3 f p^3 q^3 \text {Li}_3\left (-\frac {j (e+f x)}{f i-e j}\right )}{(f i-e j) (h i-g j)}+\frac {6 b^3 h p^3 q^3 \text {Li}_4\left (-\frac {h (e+f x)}{f g-e h}\right )}{(h i-g j)^2}-\frac {6 b^3 h p^3 q^3 \text {Li}_4\left (-\frac {j (e+f x)}{f i-e j}\right )}{(h i-g j)^2} \]
[Out]
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Rubi [A] time = 1.72, antiderivative size = 659, normalized size of antiderivative = 1.00, 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 2374
Rule 2383
Rule 2396
Rule 2397
Rule 2418
Rule 2433
Rule 2445
Rule 6589
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*}
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Mathematica [A] time = 1.69, size = 1057, normalized size = 1.60 \[ \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 {Li}_2\left (\frac {j (e+f x)}{e j-f i}\right ) \log (e+f x)+6 f (i+j x) \text {Li}_3\left (\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 {Li}_2\left (\frac {h (e+f x)}{e h-f g}\right ) \log ^2(e+f x)-6 \text {Li}_3\left (\frac {h (e+f x)}{e h-f g}\right ) \log (e+f x)+6 \text {Li}_4\left (\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 {Li}_2\left (\frac {j (e+f x)}{e j-f i}\right ) \log ^2(e+f x)-6 \text {Li}_3\left (\frac {j (e+f x)}{e j-f i}\right ) \log (e+f x)+6 \text {Li}_4\left (\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 {Li}_2\left (\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 {Li}_2\left (\frac {h (e+f x)}{e h-f g}\right ) \log (e+f x)-2 \text {Li}_3\left (\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 {Li}_2\left (\frac {j (e+f x)}{e j-f i}\right ) \log (e+f x)-2 \text {Li}_3\left (\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 {Li}_2\left (\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 {Li}_2\left (\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)} \]
Antiderivative was successfully verified.
[In]
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fricas [F] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b^{3} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{3} + 3 \, a b^{2} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 3 \, a^{2} b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a^{3}}{h j^{2} x^{3} + g i^{2} + {\left (2 \, h i j + g j^{2}\right )} x^{2} + {\left (h i^{2} + 2 \, g i j\right )} x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{3}}{{\left (h x + g\right )} {\left (j x + i\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.54, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a \right )^{3}}{\left (h x +g \right ) \left (j x +i \right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ a^{3} {\left (\frac {h \log \left (h x + g\right )}{h^{2} i^{2} - 2 \, g h i j + g^{2} j^{2}} - \frac {h \log \left (j x + i\right )}{h^{2} i^{2} - 2 \, g h i j + g^{2} j^{2}} + \frac {1}{h i^{2} - g i j + {\left (h i j - g j^{2}\right )} x}\right )} + \int \frac {b^{3} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )^{3} + 3 \, {\left (q \log \relax (d) + \log \relax (c)\right )} a^{2} b + 3 \, {\left (q^{2} \log \relax (d)^{2} + 2 \, q \log \relax (c) \log \relax (d) + \log \relax (c)^{2}\right )} a b^{2} + {\left (q^{3} \log \relax (d)^{3} + 3 \, q^{2} \log \relax (c) \log \relax (d)^{2} + 3 \, q \log \relax (c)^{2} \log \relax (d) + \log \relax (c)^{3}\right )} b^{3} + 3 \, {\left ({\left (q \log \relax (d) + \log \relax (c)\right )} b^{3} + a b^{2}\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )^{2} + 3 \, {\left (2 \, {\left (q \log \relax (d) + \log \relax (c)\right )} a b^{2} + {\left (q^{2} \log \relax (d)^{2} + 2 \, q \log \relax (c) \log \relax (d) + \log \relax (c)^{2}\right )} b^{3} + a^{2} b\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )}{h j^{2} x^{3} + g i^{2} + {\left (2 \, h i j + g j^{2}\right )} x^{2} + {\left (h i^{2} + 2 \, g i j\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^3}{\left (g+h\,x\right )\,{\left (i+j\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right )^{3}}{\left (g + h x\right ) \left (i + j x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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