Optimal. Leaf size=1957 \[ -\frac {b^2 p^2 r^2}{3 h (b g-a h)^2 (g+h x)}-\frac {2 b d p q r^2}{3 h (b g-a h) (d g-c h) (g+h x)}-\frac {d^2 q^2 r^2}{3 h (d g-c h)^2 (g+h x)}-\frac {b^3 p^2 r^2 \log (a+b x)}{3 h (b g-a h)^3}-\frac {2 b d^2 p q r^2 \log (a+b x)}{3 h (b g-a h) (d g-c h)^2}-\frac {b^2 d p q r^2 \log (a+b x)}{3 h (b g-a h)^2 (d g-c h)}+\frac {b p^2 r^2 \log (a+b x)}{3 h (b g-a h) (g+h x)^2}+\frac {d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^2 p^2 r^2 (a+b x) \log (a+b x)}{3 (b g-a h)^3 (g+h x)}-\frac {b d^2 p q r^2 \log (c+d x)}{3 h (b g-a h) (d g-c h)^2}-\frac {2 b^2 d p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (d g-c h)}-\frac {d^3 q^2 r^2 \log (c+d x)}{3 h (d g-c h)^3}+\frac {b p q r^2 \log (c+d x)}{3 h (b g-a h) (g+h x)^2}+\frac {d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 b^2 p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac {2 b^3 p q r^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 h (b g-a h)^3}+\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h) (g+h x)^2}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}-\frac {2 b^2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^3 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {b^3 p^2 r^2 \log (g+h x)}{h (b g-a h)^3}+\frac {b d^2 p q r^2 \log (g+h x)}{h (b g-a h) (d g-c h)^2}+\frac {b^2 d p q r^2 \log (g+h x)}{h (b g-a h)^2 (d g-c h)}+\frac {d^3 q^2 r^2 \log (g+h x)}{h (d g-c h)^3}+\frac {2 b^3 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (b g-a h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (d g-c h)^3}-\frac {2 b^3 p q r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (b g-a h)^3}-\frac {2 b^3 p^2 r^2 \log (a+b x) \log \left (1+\frac {b g-a h}{h (a+b x)}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q^2 r^2 \log (c+d x) \log \left (1+\frac {d g-c h}{h (c+d x)}\right )}{3 h (d g-c h)^3}+\frac {2 b^3 p^2 r^2 \text {Li}_2\left (-\frac {b g-a h}{h (a+b x)}\right )}{3 h (b g-a h)^3}+\frac {2 d^3 p q r^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \text {Li}_2\left (-\frac {h (a+b x)}{b g-a h}\right )}{3 h (d g-c h)^3}+\frac {2 d^3 q^2 r^2 \text {Li}_2\left (-\frac {d g-c h}{h (c+d x)}\right )}{3 h (d g-c h)^3}+\frac {2 b^3 p q r^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (b g-a h)^3}-\frac {2 b^3 p q r^2 \text {Li}_2\left (-\frac {h (c+d x)}{d g-c h}\right )}{3 h (b g-a h)^3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 1.43, antiderivative size = 1957, normalized size of antiderivative = 1.00, number of steps
used = 57, number of rules used = 15, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.484, Rules used =
{2584, 2593, 2458, 2389, 2379, 2438, 2351, 31, 2356, 46, 2465, 2441, 2440, 2442, 36}
\begin {gather*} -\frac {p^2 r^2 \log (a+b x) b^3}{3 h (b g-a h)^3}+\frac {2 p q r^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x) b^3}{3 h (b g-a h)^3}-\frac {2 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) b^3}{3 h (b g-a h)^3}+\frac {p^2 r^2 \log (g+h x) b^3}{h (b g-a h)^3}+\frac {2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x) b^3}{3 h (b g-a h)^3}-\frac {2 p q r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right ) b^3}{3 h (b g-a h)^3}-\frac {2 p^2 r^2 \log (a+b x) \log \left (\frac {b g-a h}{h (a+b x)}+1\right ) b^3}{3 h (b g-a h)^3}+\frac {2 p^2 r^2 \text {PolyLog}\left (2,-\frac {b g-a h}{h (a+b x)}\right ) b^3}{3 h (b g-a h)^3}+\frac {2 p q r^2 \text {PolyLog}\left (2,\frac {b (c+d x)}{b c-a d}\right ) b^3}{3 h (b g-a h)^3}-\frac {2 p q r^2 \text {PolyLog}\left (2,-\frac {h (c+d x)}{d g-c h}\right ) b^3}{3 h (b g-a h)^3}-\frac {d p q r^2 \log (a+b x) b^2}{3 h (b g-a h)^2 (d g-c h)}-\frac {2 p^2 r^2 (a+b x) \log (a+b x) b^2}{3 (b g-a h)^3 (g+h x)}-\frac {2 d p q r^2 \log (c+d x) b^2}{3 h (b g-a h)^2 (d g-c h)}+\frac {2 p q r^2 \log (c+d x) b^2}{3 h (b g-a h)^2 (g+h x)}-\frac {2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) b^2}{3 h (b g-a h)^2 (g+h x)}+\frac {d p q r^2 \log (g+h x) b^2}{h (b g-a h)^2 (d g-c h)}-\frac {p^2 r^2 b^2}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 p q r^2 \log (a+b x) b}{3 h (b g-a h) (d g-c h)^2}+\frac {p^2 r^2 \log (a+b x) b}{3 h (b g-a h) (g+h x)^2}-\frac {d^2 p q r^2 \log (c+d x) b}{3 h (b g-a h) (d g-c h)^2}+\frac {p q r^2 \log (c+d x) b}{3 h (b g-a h) (g+h x)^2}-\frac {p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) b}{3 h (b g-a h) (g+h x)^2}+\frac {d^2 p q r^2 \log (g+h x) b}{h (b g-a h) (d g-c h)^2}-\frac {2 d p q r^2 b}{3 h (b g-a h) (d g-c h) (g+h x)}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}+\frac {d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}-\frac {d^3 q^2 r^2 \log (c+d x)}{3 h (d g-c h)^3}-\frac {2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac {d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}+\frac {d^3 q^2 r^2 \log (g+h x)}{h (d g-c h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (d g-c h)^3}-\frac {2 d^3 q^2 r^2 \log (c+d x) \log \left (\frac {d g-c h}{h (c+d x)}+1\right )}{3 h (d g-c h)^3}+\frac {2 d^3 p q r^2 \text {PolyLog}\left (2,-\frac {d (a+b x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \text {PolyLog}\left (2,-\frac {h (a+b x)}{b g-a h}\right )}{3 h (d g-c h)^3}+\frac {2 d^3 q^2 r^2 \text {PolyLog}\left (2,-\frac {d g-c h}{h (c+d x)}\right )}{3 h (d g-c h)^3}-\frac {d^2 q^2 r^2}{3 h (d g-c h)^2 (g+h x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 36
Rule 46
Rule 2351
Rule 2356
Rule 2379
Rule 2389
Rule 2438
Rule 2440
Rule 2441
Rule 2442
Rule 2458
Rule 2465
Rule 2584
Rule 2593
Rubi steps
\begin {align*} \int \frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(g+h x)^4} \, dx &=-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {(2 b p r) \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x) (g+h x)^3} \, dx}{3 h}+\frac {(2 d q r) \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(c+d x) (g+h x)^3} \, dx}{3 h}\\ &=-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {\left (2 b p^2 r^2\right ) \int \frac {\log (a+b x)}{(a+b x) (g+h x)^3} \, dx}{3 h}+\frac {\left (2 b p q r^2\right ) \int \frac {\log (c+d x)}{(a+b x) (g+h x)^3} \, dx}{3 h}+\frac {\left (2 d p q r^2\right ) \int \frac {\log (a+b x)}{(c+d x) (g+h x)^3} \, dx}{3 h}+\frac {\left (2 d q^2 r^2\right ) \int \frac {\log (c+d x)}{(c+d x) (g+h x)^3} \, dx}{3 h}-\frac {\left (2 b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )\right ) \int \frac {1}{(a+b x) (g+h x)^3} \, dx}{3 h}-\frac {\left (2 d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )\right ) \int \frac {1}{(c+d x) (g+h x)^3} \, dx}{3 h}\\ &=-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {\left (2 p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {b g-a h}{b}+\frac {h x}{b}\right )^3} \, dx,x,a+b x\right )}{3 h}+\frac {\left (2 b p q r^2\right ) \int \left (\frac {b^3 \log (c+d x)}{(b g-a h)^3 (a+b x)}-\frac {h \log (c+d x)}{(b g-a h) (g+h x)^3}-\frac {b h \log (c+d x)}{(b g-a h)^2 (g+h x)^2}-\frac {b^2 h \log (c+d x)}{(b g-a h)^3 (g+h x)}\right ) \, dx}{3 h}+\frac {\left (2 d p q r^2\right ) \int \left (\frac {d^3 \log (a+b x)}{(d g-c h)^3 (c+d x)}-\frac {h \log (a+b x)}{(d g-c h) (g+h x)^3}-\frac {d h \log (a+b x)}{(d g-c h)^2 (g+h x)^2}-\frac {d^2 h \log (a+b x)}{(d g-c h)^3 (g+h x)}\right ) \, dx}{3 h}+\frac {\left (2 q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {d g-c h}{d}+\frac {h x}{d}\right )^3} \, dx,x,c+d x\right )}{3 h}-\frac {\left (2 b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )\right ) \int \left (\frac {b^3}{(b g-a h)^3 (a+b x)}-\frac {h}{(b g-a h) (g+h x)^3}-\frac {b h}{(b g-a h)^2 (g+h x)^2}-\frac {b^2 h}{(b g-a h)^3 (g+h x)}\right ) \, dx}{3 h}-\frac {\left (2 d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )\right ) \int \left (\frac {d^3}{(d g-c h)^3 (c+d x)}-\frac {h}{(d g-c h) (g+h x)^3}-\frac {d h}{(d g-c h)^2 (g+h x)^2}-\frac {d^2 h}{(d g-c h)^3 (g+h x)}\right ) \, dx}{3 h}\\ &=-\frac {b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h) (g+h x)^2}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}-\frac {2 b^2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^3 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {2 b^3 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (b g-a h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {\left (2 p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{\left (\frac {b g-a h}{b}+\frac {h x}{b}\right )^3} \, dx,x,a+b x\right )}{3 (b g-a h)}+\frac {\left (2 b p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {b g-a h}{b}+\frac {h x}{b}\right )^2} \, dx,x,a+b x\right )}{3 h (b g-a h)}-\frac {\left (2 b^3 p q r^2\right ) \int \frac {\log (c+d x)}{g+h x} \, dx}{3 (b g-a h)^3}+\frac {\left (2 b^4 p q r^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{3 h (b g-a h)^3}-\frac {\left (2 b^2 p q r^2\right ) \int \frac {\log (c+d x)}{(g+h x)^2} \, dx}{3 (b g-a h)^2}-\frac {\left (2 b p q r^2\right ) \int \frac {\log (c+d x)}{(g+h x)^3} \, dx}{3 (b g-a h)}-\frac {\left (2 d^3 p q r^2\right ) \int \frac {\log (a+b x)}{g+h x} \, dx}{3 (d g-c h)^3}+\frac {\left (2 d^4 p q r^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{3 h (d g-c h)^3}-\frac {\left (2 d^2 p q r^2\right ) \int \frac {\log (a+b x)}{(g+h x)^2} \, dx}{3 (d g-c h)^2}-\frac {\left (2 d p q r^2\right ) \int \frac {\log (a+b x)}{(g+h x)^3} \, dx}{3 (d g-c h)}-\frac {\left (2 q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{\left (\frac {d g-c h}{d}+\frac {h x}{d}\right )^3} \, dx,x,c+d x\right )}{3 (d g-c h)}+\frac {\left (2 d q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {d g-c h}{d}+\frac {h x}{d}\right )^2} \, dx,x,c+d x\right )}{3 h (d g-c h)}\\ &=\frac {b p^2 r^2 \log (a+b x)}{3 h (b g-a h) (g+h x)^2}+\frac {d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}+\frac {b p q r^2 \log (c+d x)}{3 h (b g-a h) (g+h x)^2}+\frac {d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 b^2 p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (g+h x)}+\frac {2 b^3 p q r^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 h (b g-a h)^3}+\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h) (g+h x)^2}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}-\frac {2 b^2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^3 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {2 b^3 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (b g-a h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (d g-c h)^3}-\frac {2 b^3 p q r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (b g-a h)^3}-\frac {\left (2 b p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{\left (\frac {b g-a h}{b}+\frac {h x}{b}\right )^2} \, dx,x,a+b x\right )}{3 (b g-a h)^2}+\frac {\left (2 b^2 p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {b g-a h}{b}+\frac {h x}{b}\right )} \, dx,x,a+b x\right )}{3 h (b g-a h)^2}-\frac {\left (b p^2 r^2\right ) \text {Subst}\left (\int \frac {1}{x \left (\frac {b g-a h}{b}+\frac {h x}{b}\right )^2} \, dx,x,a+b x\right )}{3 h (b g-a h)}-\frac {\left (2 b^3 d p q r^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3 h (b g-a h)^3}+\frac {\left (2 b^3 d p q r^2\right ) \int \frac {\log \left (\frac {d (g+h x)}{d g-c h}\right )}{c+d x} \, dx}{3 h (b g-a h)^3}-\frac {\left (2 b^2 d p q r^2\right ) \int \frac {1}{(c+d x) (g+h x)} \, dx}{3 h (b g-a h)^2}-\frac {\left (b d p q r^2\right ) \int \frac {1}{(c+d x) (g+h x)^2} \, dx}{3 h (b g-a h)}-\frac {\left (2 b d^3 p q r^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3 h (d g-c h)^3}+\frac {\left (2 b d^3 p q r^2\right ) \int \frac {\log \left (\frac {b (g+h x)}{b g-a h}\right )}{a+b x} \, dx}{3 h (d g-c h)^3}-\frac {\left (2 b d^2 p q r^2\right ) \int \frac {1}{(a+b x) (g+h x)} \, dx}{3 h (d g-c h)^2}-\frac {\left (b d p q r^2\right ) \int \frac {1}{(a+b x) (g+h x)^2} \, dx}{3 h (d g-c h)}-\frac {\left (2 d q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{\left (\frac {d g-c h}{d}+\frac {h x}{d}\right )^2} \, dx,x,c+d x\right )}{3 (d g-c h)^2}+\frac {\left (2 d^2 q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {d g-c h}{d}+\frac {h x}{d}\right )} \, dx,x,c+d x\right )}{3 h (d g-c h)^2}-\frac {\left (d q^2 r^2\right ) \text {Subst}\left (\int \frac {1}{x \left (\frac {d g-c h}{d}+\frac {h x}{d}\right )^2} \, dx,x,c+d x\right )}{3 h (d g-c h)}\\ &=\frac {b p^2 r^2 \log (a+b x)}{3 h (b g-a h) (g+h x)^2}+\frac {d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^2 p^2 r^2 (a+b x) \log (a+b x)}{3 (b g-a h)^3 (g+h x)}+\frac {b p q r^2 \log (c+d x)}{3 h (b g-a h) (g+h x)^2}+\frac {d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 b^2 p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac {2 b^3 p q r^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 h (b g-a h)^3}+\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h) (g+h x)^2}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}-\frac {2 b^2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^3 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {2 b^3 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (b g-a h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (d g-c h)^3}-\frac {2 b^3 p q r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (b g-a h)^3}+\frac {\left (2 b^2 p^2 r^2\right ) \text {Subst}\left (\int \frac {1}{\frac {b g-a h}{b}+\frac {h x}{b}} \, dx,x,a+b x\right )}{3 (b g-a h)^3}-\frac {\left (2 b^2 p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{\frac {b g-a h}{b}+\frac {h x}{b}} \, dx,x,a+b x\right )}{3 (b g-a h)^3}+\frac {\left (2 b^3 p^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{3 h (b g-a h)^3}-\frac {\left (b p^2 r^2\right ) \text {Subst}\left (\int \left (\frac {b^2}{(b g-a h)^2 x}-\frac {b^2 h}{(b g-a h) (b g-a h+h x)^2}-\frac {b^2 h}{(b g-a h)^2 (b g-a h+h x)}\right ) \, dx,x,a+b x\right )}{3 h (b g-a h)}-\frac {\left (2 b^3 p q r^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{3 h (b g-a h)^3}+\frac {\left (2 b^3 p q r^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {h x}{d g-c h}\right )}{x} \, dx,x,c+d x\right )}{3 h (b g-a h)^3}-\frac {\left (b d p q r^2\right ) \int \left (\frac {d^2}{(d g-c h)^2 (c+d x)}-\frac {h}{(d g-c h) (g+h x)^2}-\frac {d h}{(d g-c h)^2 (g+h x)}\right ) \, dx}{3 h (b g-a h)}-\frac {\left (2 d^3 p q r^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{3 h (d g-c h)^3}+\frac {\left (2 d^3 p q r^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {h x}{b g-a h}\right )}{x} \, dx,x,a+b x\right )}{3 h (d g-c h)^3}+\frac {\left (2 b d^2 p q r^2\right ) \int \frac {1}{g+h x} \, dx}{3 (b g-a h) (d g-c h)^2}-\frac {\left (2 b^2 d^2 p q r^2\right ) \int \frac {1}{a+b x} \, dx}{3 h (b g-a h) (d g-c h)^2}-\frac {\left (b d p q r^2\right ) \int \left (\frac {b^2}{(b g-a h)^2 (a+b x)}-\frac {h}{(b g-a h) (g+h x)^2}-\frac {b h}{(b g-a h)^2 (g+h x)}\right ) \, dx}{3 h (d g-c h)}+\frac {\left (2 b^2 d p q r^2\right ) \int \frac {1}{g+h x} \, dx}{3 (b g-a h)^2 (d g-c h)}-\frac {\left (2 b^2 d^2 p q r^2\right ) \int \frac {1}{c+d x} \, dx}{3 h (b g-a h)^2 (d g-c h)}+\frac {\left (2 d^2 q^2 r^2\right ) \text {Subst}\left (\int \frac {1}{\frac {d g-c h}{d}+\frac {h x}{d}} \, dx,x,c+d x\right )}{3 (d g-c h)^3}-\frac {\left (2 d^2 q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{\frac {d g-c h}{d}+\frac {h x}{d}} \, dx,x,c+d x\right )}{3 (d g-c h)^3}+\frac {\left (2 d^3 q^2 r^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{3 h (d g-c h)^3}-\frac {\left (d q^2 r^2\right ) \text {Subst}\left (\int \left (\frac {d^2}{(d g-c h)^2 x}-\frac {d^2 h}{(d g-c h) (d g-c h+h x)^2}-\frac {d^2 h}{(d g-c h)^2 (d g-c h+h x)}\right ) \, dx,x,c+d x\right )}{3 h (d g-c h)}\\ &=-\frac {b^2 p^2 r^2}{3 h (b g-a h)^2 (g+h x)}-\frac {2 b d p q r^2}{3 h (b g-a h) (d g-c h) (g+h x)}-\frac {d^2 q^2 r^2}{3 h (d g-c h)^2 (g+h x)}-\frac {b^3 p^2 r^2 \log (a+b x)}{3 h (b g-a h)^3}-\frac {2 b d^2 p q r^2 \log (a+b x)}{3 h (b g-a h) (d g-c h)^2}-\frac {b^2 d p q r^2 \log (a+b x)}{3 h (b g-a h)^2 (d g-c h)}+\frac {b p^2 r^2 \log (a+b x)}{3 h (b g-a h) (g+h x)^2}+\frac {d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^2 p^2 r^2 (a+b x) \log (a+b x)}{3 (b g-a h)^3 (g+h x)}+\frac {b^3 p^2 r^2 \log ^2(a+b x)}{3 h (b g-a h)^3}-\frac {b d^2 p q r^2 \log (c+d x)}{3 h (b g-a h) (d g-c h)^2}-\frac {2 b^2 d p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (d g-c h)}-\frac {d^3 q^2 r^2 \log (c+d x)}{3 h (d g-c h)^3}+\frac {b p q r^2 \log (c+d x)}{3 h (b g-a h) (g+h x)^2}+\frac {d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 b^2 p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac {2 b^3 p q r^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 h (b g-a h)^3}+\frac {d^3 q^2 r^2 \log ^2(c+d x)}{3 h (d g-c h)^3}+\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h) (g+h x)^2}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}-\frac {2 b^2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^3 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {b^3 p^2 r^2 \log (g+h x)}{h (b g-a h)^3}+\frac {b d^2 p q r^2 \log (g+h x)}{h (b g-a h) (d g-c h)^2}+\frac {b^2 d p q r^2 \log (g+h x)}{h (b g-a h)^2 (d g-c h)}+\frac {d^3 q^2 r^2 \log (g+h x)}{h (d g-c h)^3}+\frac {2 b^3 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (b g-a h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {2 b^3 p^2 r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (d g-c h)^3}-\frac {2 b^3 p q r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q^2 r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (d g-c h)^3}+\frac {2 d^3 p q r^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {2 d^3 p q r^2 \text {Li}_2\left (-\frac {h (a+b x)}{b g-a h}\right )}{3 h (d g-c h)^3}+\frac {2 b^3 p q r^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (b g-a h)^3}-\frac {2 b^3 p q r^2 \text {Li}_2\left (-\frac {h (c+d x)}{d g-c h}\right )}{3 h (b g-a h)^3}+\frac {\left (2 b^3 p^2 r^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {h x}{b g-a h}\right )}{x} \, dx,x,a+b x\right )}{3 h (b g-a h)^3}+\frac {\left (2 d^3 q^2 r^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {h x}{d g-c h}\right )}{x} \, dx,x,c+d x\right )}{3 h (d g-c h)^3}\\ &=-\frac {b^2 p^2 r^2}{3 h (b g-a h)^2 (g+h x)}-\frac {2 b d p q r^2}{3 h (b g-a h) (d g-c h) (g+h x)}-\frac {d^2 q^2 r^2}{3 h (d g-c h)^2 (g+h x)}-\frac {b^3 p^2 r^2 \log (a+b x)}{3 h (b g-a h)^3}-\frac {2 b d^2 p q r^2 \log (a+b x)}{3 h (b g-a h) (d g-c h)^2}-\frac {b^2 d p q r^2 \log (a+b x)}{3 h (b g-a h)^2 (d g-c h)}+\frac {b p^2 r^2 \log (a+b x)}{3 h (b g-a h) (g+h x)^2}+\frac {d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^2 p^2 r^2 (a+b x) \log (a+b x)}{3 (b g-a h)^3 (g+h x)}+\frac {b^3 p^2 r^2 \log ^2(a+b x)}{3 h (b g-a h)^3}-\frac {b d^2 p q r^2 \log (c+d x)}{3 h (b g-a h) (d g-c h)^2}-\frac {2 b^2 d p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (d g-c h)}-\frac {d^3 q^2 r^2 \log (c+d x)}{3 h (d g-c h)^3}+\frac {b p q r^2 \log (c+d x)}{3 h (b g-a h) (g+h x)^2}+\frac {d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac {2 b^2 p q r^2 \log (c+d x)}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac {2 b^3 p q r^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{3 h (b g-a h)^3}+\frac {d^3 q^2 r^2 \log ^2(c+d x)}{3 h (d g-c h)^3}+\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {b p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h) (g+h x)^2}-\frac {d q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h) (g+h x)^2}-\frac {2 b^2 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^2 (g+h x)}-\frac {2 d^2 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^2 (g+h x)}-\frac {2 b^3 p r \log (a+b x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q r \log (c+d x) \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right )}{3 h (d g-c h)^3}-\frac {\log ^2\left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{3 h (g+h x)^3}+\frac {b^3 p^2 r^2 \log (g+h x)}{h (b g-a h)^3}+\frac {b d^2 p q r^2 \log (g+h x)}{h (b g-a h) (d g-c h)^2}+\frac {b^2 d p q r^2 \log (g+h x)}{h (b g-a h)^2 (d g-c h)}+\frac {d^3 q^2 r^2 \log (g+h x)}{h (d g-c h)^3}+\frac {2 b^3 p r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (b g-a h)^3}+\frac {2 d^3 q r \left (p r \log (a+b x)+q r \log (c+d x)-\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )\right ) \log (g+h x)}{3 h (d g-c h)^3}-\frac {2 b^3 p^2 r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 p q r^2 \log (a+b x) \log \left (\frac {b (g+h x)}{b g-a h}\right )}{3 h (d g-c h)^3}-\frac {2 b^3 p q r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q^2 r^2 \log (c+d x) \log \left (\frac {d (g+h x)}{d g-c h}\right )}{3 h (d g-c h)^3}+\frac {2 d^3 p q r^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 h (d g-c h)^3}-\frac {2 b^3 p^2 r^2 \text {Li}_2\left (-\frac {h (a+b x)}{b g-a h}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 p q r^2 \text {Li}_2\left (-\frac {h (a+b x)}{b g-a h}\right )}{3 h (d g-c h)^3}+\frac {2 b^3 p q r^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{3 h (b g-a h)^3}-\frac {2 b^3 p q r^2 \text {Li}_2\left (-\frac {h (c+d x)}{d g-c h}\right )}{3 h (b g-a h)^3}-\frac {2 d^3 q^2 r^2 \text {Li}_2\left (-\frac {h (c+d x)}{d g-c h}\right )}{3 h (d g-c h)^3}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(47127\) vs. \(2(1957)=3914\).
time = 6.33, size = 47127, normalized size = 24.08 \begin {gather*} \text {Result too large to show} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.18, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (e \left (f \left (b x +a \right )^{p} \left (d x +c \right )^{q}\right )^{r}\right )^{2}}{\left (h x +g \right )^{4}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 4734 vs.
\(2 (1884) = 3768\).
time = 1.20, size = 4734, normalized size = 2.42 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {{\ln \left (e\,{\left (f\,{\left (a+b\,x\right )}^p\,{\left (c+d\,x\right )}^q\right )}^r\right )}^2}{{\left (g+h\,x\right )}^4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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