Optimal. Leaf size=519 \[ \frac {j (e+f x) (f i-e j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}-\frac {b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{2 f^2 h}+\frac {j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{2 f^2 h}+\frac {2 b p q (h i-g j)^2 \text {Li}_2\left (-\frac {h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{h^3}+\frac {(h i-g j)^2 \log \left (\frac {f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{h^3}+\frac {j (e+f x) (h i-g j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}-\frac {2 a b j p q x (f i-e j)}{f h}-\frac {2 a b j p q x (h i-g j)}{h^2}-\frac {2 b^2 j p q (e+f x) (f i-e j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f^2 h}-\frac {2 b^2 j p q (e+f x) (h i-g j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}+\frac {b^2 j^2 p^2 q^2 (e+f x)^2}{4 f^2 h}-\frac {2 b^2 p^2 q^2 (h i-g j)^2 \text {Li}_3\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}+\frac {2 b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac {2 b^2 j p^2 q^2 x (h i-g j)}{h^2} \]
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Rubi [A] time = 1.34, antiderivative size = 519, normalized size of antiderivative = 1.00, number of steps used = 20, number of rules used = 13, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.371, Rules used = {2418, 2389, 2296, 2295, 2396, 2433, 2374, 6589, 2401, 2390, 2305, 2304, 2445} \[ \frac {2 b p q (h i-g j)^2 \text {PolyLog}\left (2,-\frac {h (e+f x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{h^3}-\frac {2 b^2 p^2 q^2 (h i-g j)^2 \text {PolyLog}\left (3,-\frac {h (e+f x)}{f g-e h}\right )}{h^3}+\frac {j (e+f x) (f i-e j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}-\frac {b j^2 p q (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )}{2 f^2 h}+\frac {j^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{2 f^2 h}+\frac {j (e+f x) (h i-g j) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac {(h i-g j)^2 \log \left (\frac {f (g+h x)}{f g-e h}\right ) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{h^3}-\frac {2 a b j p q x (f i-e j)}{f h}-\frac {2 a b j p q x (h i-g j)}{h^2}-\frac {2 b^2 j p q (e+f x) (f i-e j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f^2 h}-\frac {2 b^2 j p q (e+f x) (h i-g j) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}+\frac {b^2 j^2 p^2 q^2 (e+f x)^2}{4 f^2 h}+\frac {2 b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac {2 b^2 j p^2 q^2 x (h i-g j)}{h^2} \]
Antiderivative was successfully verified.
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Rule 2295
Rule 2296
Rule 2304
Rule 2305
Rule 2374
Rule 2389
Rule 2390
Rule 2396
Rule 2401
Rule 2418
Rule 2433
Rule 2445
Rule 6589
Rubi steps
\begin {align*} \int \frac {(530+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{g+h x} \, dx &=\operatorname {Subst}\left (\int \frac {(530+j x)^2 \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{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 (530 h-g j) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{h^2}+\frac {(530 h-g j)^2 \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{h^2 (g+h x)}+\frac {j (530+j x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{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 (530+j x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2 \, 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 (530 h-g j)) \int \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2 \, 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 {(530 h-g j)^2 \int \frac {\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{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 {(530 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac {f (g+h x)}{f g-e h}\right )}{h^3}+\operatorname {Subst}\left (\frac {j \int \left (\frac {(530 f-e j) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{f}+\frac {j (e+f x) \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2}{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 (530 h-g j)) \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 (2 b f (530 h-g j)^2 p q\right ) \int \frac {\left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right ) \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 (530 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac {(530 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \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 )^2 \, 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 (530 f-e j)) \int \left (a+b \log \left (c d^q (e+f x)^{p q}\right )\right )^2 \, 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 {(2 b j (530 h-g j) p q) \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 (2 b (530 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 ) \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 {2 a b j (530 h-g j) p q x}{h^2}+\frac {j (530 h-g j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f h^2}+\frac {(530 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac {f (g+h x)}{f g-e h}\right )}{h^3}+\frac {2 b (530 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \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 )^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 {(j (530 f-e j)) \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 (2 b^2 j (530 h-g j) p q\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 (2 b^2 (530 h-g j)^2 p^2 q^2\right ) \operatorname {Subst}\left (\int \frac {\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 {2 a b j (530 h-g j) p q x}{h^2}+\frac {2 b^2 j (530 h-g j) p^2 q^2 x}{h^2}-\frac {2 b^2 j (530 h-g j) p q (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}+\frac {j (530 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}+\frac {j (530 h-g j) (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^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{2 f^2 h}+\frac {(530 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac {f (g+h x)}{f g-e h}\right )}{h^3}+\frac {2 b (530 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text {Li}_2\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}-\frac {2 b^2 (530 h-g j)^2 p^2 q^2 \text {Li}_3\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}-\operatorname {Subst}\left (\frac {\left (b j^2 p q\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 )}{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 {(2 b j (530 f-e j) p q) \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 {2 a b j (530 f-e j) p q x}{f h}-\frac {2 a b j (530 h-g j) p q x}{h^2}+\frac {2 b^2 j (530 h-g j) p^2 q^2 x}{h^2}+\frac {b^2 j^2 p^2 q^2 (e+f x)^2}{4 f^2 h}-\frac {2 b^2 j (530 h-g j) p q (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}-\frac {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 f^2 h}+\frac {j (530 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}+\frac {j (530 h-g j) (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^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{2 f^2 h}+\frac {(530 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac {f (g+h x)}{f g-e h}\right )}{h^3}+\frac {2 b (530 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text {Li}_2\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}-\frac {2 b^2 (530 h-g j)^2 p^2 q^2 \text {Li}_3\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}-\operatorname {Subst}\left (\frac {\left (2 b^2 j (530 f-e j) p q\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 {2 a b j (530 f-e j) p q x}{f h}-\frac {2 a b j (530 h-g j) p q x}{h^2}+\frac {2 b^2 j (530 f-e j) p^2 q^2 x}{f h}+\frac {2 b^2 j (530 h-g j) p^2 q^2 x}{h^2}+\frac {b^2 j^2 p^2 q^2 (e+f x)^2}{4 f^2 h}-\frac {2 b^2 j (530 f-e j) p q (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f^2 h}-\frac {2 b^2 j (530 h-g j) p q (e+f x) \log \left (c \left (d (e+f x)^p\right )^q\right )}{f h^2}-\frac {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 f^2 h}+\frac {j (530 f-e j) (e+f x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{f^2 h}+\frac {j (530 h-g j) (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^2 (e+f x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2}{2 f^2 h}+\frac {(530 h-g j)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log \left (\frac {f (g+h x)}{f g-e h}\right )}{h^3}+\frac {2 b (530 h-g j)^2 p q \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \text {Li}_2\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}-\frac {2 b^2 (530 h-g j)^2 p^2 q^2 \text {Li}_3\left (-\frac {h (e+f x)}{f g-e h}\right )}{h^3}\\ \end {align*}
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Mathematica [A] time = 0.75, size = 927, normalized size = 1.79 \[ \frac {-8 b f^2 h^2 p q \left (-a+b p q \log (e+f x)-b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \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 ) i^2+4 b^2 f^2 h^2 p^2 q^2 \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 ) i^2-16 b f h j p q \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 (e+f x)+\log (e+f x) \left (e h+f x h-f g \log \left (\frac {f (g+h x)}{f g-e h}\right )\right )-f g \text {Li}_2\left (\frac {h (e+f x)}{e h-f g}\right )\right ) i+8 b^2 f h j p^2 q^2 \left (h \left ((e+f x) \log ^2(e+f x)-2 (e+f x) \log (e+f x)+2 f x\right )-f g \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 )\right ) i+2 f^2 h^2 j^2 x^2 \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2+4 f^2 h j (2 h i-g 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 )^2+4 f^2 (h i-g j)^2 \left (a-b p q \log (e+f x)+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2 \log (g+h x)+2 b j^2 p q \left (-a+b p q \log (e+f x)-b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \left (-4 f^2 \text {Li}_2\left (\frac {h (e+f x)}{e h-f g}\right ) g^2+f h (f x (h x-4 g)-2 e (2 g+h x))+2 \log (e+f x) \left (h (e+f x) (2 f g+e h-f h x)-2 f^2 g^2 \log \left (\frac {f (g+h x)}{f g-e h}\right )\right )\right )-b^2 j^2 p^2 q^2 \left (-4 f^2 \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 ) g^2+4 f h \left ((e+f x) \log ^2(e+f x)-2 (e+f x) \log (e+f x)+2 f x\right ) g+h^2 \left (2 \left (e^2-f^2 x^2\right ) \log ^2(e+f x)+\left (-6 e^2-4 f x e+2 f^2 x^2\right ) \log (e+f x)+f x (6 e-f x)\right )\right )}{4 f^2 h^3} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {a^{2} j^{2} x^{2} + 2 \, a^{2} i j x + a^{2} i^{2} + {\left (b^{2} j^{2} x^{2} + 2 \, b^{2} i j x + b^{2} i^{2}\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 2 \, {\left (a b j^{2} x^{2} + 2 \, a b i j x + a b i^{2}\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )}{h x + g}, x\right ) \]
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 \[ \int \frac {{\left (j x + i\right )}^{2} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}}{h x + g}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.52, size = 0, normalized size = 0.00 \[ \int \frac {\left (j x +i \right )^{2} \left (b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a \right )^{2}}{h x +g}\, dx \]
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 \[ 2 \, a^{2} i j {\left (\frac {x}{h} - \frac {g \log \left (h x + g\right )}{h^{2}}\right )} + \frac {1}{2} \, a^{2} j^{2} {\left (\frac {2 \, g^{2} \log \left (h x + g\right )}{h^{3}} + \frac {h x^{2} - 2 \, g x}{h^{2}}\right )} + \frac {a^{2} i^{2} \log \left (h x + g\right )}{h} + \int \frac {2 \, {\left (i^{2} q \log \relax (d) + i^{2} \log \relax (c)\right )} a b + {\left (i^{2} q^{2} \log \relax (d)^{2} + 2 \, i^{2} q \log \relax (c) \log \relax (d) + i^{2} \log \relax (c)^{2}\right )} b^{2} + {\left (2 \, {\left (j^{2} q \log \relax (d) + j^{2} \log \relax (c)\right )} a b + {\left (j^{2} q^{2} \log \relax (d)^{2} + 2 \, j^{2} q \log \relax (c) \log \relax (d) + j^{2} \log \relax (c)^{2}\right )} b^{2}\right )} x^{2} + {\left (b^{2} j^{2} x^{2} + 2 \, b^{2} i j x + b^{2} i^{2}\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )^{2} + 2 \, {\left (2 \, {\left (i j q \log \relax (d) + i j \log \relax (c)\right )} a b + {\left (i j q^{2} \log \relax (d)^{2} + 2 \, i j q \log \relax (c) \log \relax (d) + i j \log \relax (c)^{2}\right )} b^{2}\right )} x + 2 \, {\left (a b i^{2} + {\left (i^{2} q \log \relax (d) + i^{2} \log \relax (c)\right )} b^{2} + {\left (a b j^{2} + {\left (j^{2} q \log \relax (d) + j^{2} \log \relax (c)\right )} b^{2}\right )} x^{2} + 2 \, {\left (a b i j + {\left (i j q \log \relax (d) + i j \log \relax (c)\right )} b^{2}\right )} x\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )}{h x + g}\,{d x} \]
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 \[ \int \frac {{\left (i+j\,x\right )}^2\,{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^2}{g+h\,x} \,d x \]
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 \[ \int \frac {\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right )^{2} \left (i + j x\right )^{2}}{g + h x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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