Optimal. Leaf size=742 \[ \frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (i+j x)^m\right )\right )-\frac {g i^4 m \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 j^4}-\frac {g i^2 m x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 j^2}+\frac {g i m x^3 \left (a+b \log \left (c (d+e x)^n\right )\right )}{12 j}-\frac {1}{16} g m x^4 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac {a g i^3 m x}{4 j^3}+\frac {b g i^3 m (d+e x) \log \left (c (d+e x)^n\right )}{4 e j^3}-\frac {b d^4 n \log \left (-\frac {j (d+e x)}{e i-d j}\right ) \left (f+g \log \left (h (i+j x)^m\right )\right )}{4 e^4}-\frac {b d^4 g m n \text {Li}_2\left (\frac {e (i+j x)}{e i-d j}\right )}{4 e^4}+\frac {b d^4 g m n \log (d+e x)}{16 e^4}+\frac {b d^3 f n x}{4 e^3}+\frac {b d^3 g n (i+j x) \log \left (h (i+j x)^m\right )}{4 e^3 j}+\frac {b d^3 g i m n \log (d+e x)}{12 e^3 j}-\frac {5 b d^3 g m n x}{16 e^3}-\frac {b d^2 n x^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{8 e^2}+\frac {b d^2 g i^2 m n \log (d+e x)}{8 e^2 j^2}+\frac {b d^2 g i^2 m n \log (i+j x)}{8 e^2 j^2}-\frac {5 b d^2 g i m n x}{24 e^2 j}+\frac {3 b d^2 g m n x^2}{32 e^2}+\frac {b d n x^3 \left (f+g \log \left (h (i+j x)^m\right )\right )}{12 e}-\frac {b g i^4 m n \text {Li}_2\left (-\frac {j (d+e x)}{e i-d j}\right )}{4 j^4}+\frac {b d g i^3 m n \log (i+j x)}{12 e j^3}-\frac {5 b d g i^2 m n x}{24 e j^2}+\frac {b d g i m n x^2}{12 e j}-\frac {7 b d g m n x^3}{144 e}-\frac {1}{16} b n x^4 \left (f+g \log \left (h (i+j x)^m\right )\right )+\frac {b g i^4 m n \log (i+j x)}{16 j^4}-\frac {5 b g i^3 m n x}{16 j^3}+\frac {3 b g i^2 m n x^2}{32 j^2}-\frac {7 b g i m n x^3}{144 j}+\frac {1}{32} b g m n x^4 \]
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Rubi [A] time = 0.87, antiderivative size = 742, normalized size of antiderivative = 1.00, number of steps used = 35, number of rules used = 9, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.281, Rules used = {2439, 43, 2416, 2389, 2295, 2395, 2394, 2393, 2391} \[ -\frac {b d^4 g m n \text {PolyLog}\left (2,\frac {e (i+j x)}{e i-d j}\right )}{4 e^4}-\frac {b g i^4 m n \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right )}{4 j^4}+\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (i+j x)^m\right )\right )-\frac {g i^2 m x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 j^2}-\frac {g i^4 m \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 j^4}+\frac {g i m x^3 \left (a+b \log \left (c (d+e x)^n\right )\right )}{12 j}-\frac {1}{16} g m x^4 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac {a g i^3 m x}{4 j^3}+\frac {b g i^3 m (d+e x) \log \left (c (d+e x)^n\right )}{4 e j^3}-\frac {b d^2 n x^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{8 e^2}-\frac {b d^4 n \log \left (-\frac {j (d+e x)}{e i-d j}\right ) \left (f+g \log \left (h (i+j x)^m\right )\right )}{4 e^4}+\frac {b d^3 f n x}{4 e^3}+\frac {b d^3 g n (i+j x) \log \left (h (i+j x)^m\right )}{4 e^3 j}+\frac {b d^2 g i^2 m n \log (d+e x)}{8 e^2 j^2}+\frac {b d^2 g i^2 m n \log (i+j x)}{8 e^2 j^2}-\frac {5 b d^2 g i m n x}{24 e^2 j}+\frac {b d^3 g i m n \log (d+e x)}{12 e^3 j}+\frac {3 b d^2 g m n x^2}{32 e^2}-\frac {5 b d^3 g m n x}{16 e^3}+\frac {b d^4 g m n \log (d+e x)}{16 e^4}+\frac {b d n x^3 \left (f+g \log \left (h (i+j x)^m\right )\right )}{12 e}-\frac {5 b d g i^2 m n x}{24 e j^2}+\frac {b d g i^3 m n \log (i+j x)}{12 e j^3}+\frac {b d g i m n x^2}{12 e j}-\frac {7 b d g m n x^3}{144 e}-\frac {1}{16} b n x^4 \left (f+g \log \left (h (i+j x)^m\right )\right )+\frac {3 b g i^2 m n x^2}{32 j^2}-\frac {5 b g i^3 m n x}{16 j^3}+\frac {b g i^4 m n \log (i+j x)}{16 j^4}-\frac {7 b g i m n x^3}{144 j}+\frac {1}{32} b g m n x^4 \]
Antiderivative was successfully verified.
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Rule 43
Rule 2295
Rule 2389
Rule 2391
Rule 2393
Rule 2394
Rule 2395
Rule 2416
Rule 2439
Rubi steps
\begin {align*} \int x^3 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right ) \, dx &=\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {1}{4} (g j m) \int \frac {x^4 \left (a+b \log \left (c (d+e x)^n\right )\right )}{386+j x} \, dx-\frac {1}{4} (b e n) \int \frac {x^4 \left (f+g \log \left (h (386+j x)^m\right )\right )}{d+e x} \, dx\\ &=\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {1}{4} (g j m) \int \left (-\frac {57512456 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^4}+\frac {148996 x \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^3}-\frac {386 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2}+\frac {x^3 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j}+\frac {22199808016 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^4 (386+j x)}\right ) \, dx-\frac {1}{4} (b e n) \int \left (-\frac {d^3 \left (f+g \log \left (h (386+j x)^m\right )\right )}{e^4}+\frac {d^2 x \left (f+g \log \left (h (386+j x)^m\right )\right )}{e^3}-\frac {d x^2 \left (f+g \log \left (h (386+j x)^m\right )\right )}{e^2}+\frac {x^3 \left (f+g \log \left (h (386+j x)^m\right )\right )}{e}+\frac {d^4 \left (f+g \log \left (h (386+j x)^m\right )\right )}{e^4 (d+e x)}\right ) \, dx\\ &=\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {1}{4} (g m) \int x^3 \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx+\frac {(14378114 g m) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{j^3}-\frac {(5549952004 g m) \int \frac {a+b \log \left (c (d+e x)^n\right )}{386+j x} \, dx}{j^3}-\frac {(37249 g m) \int x \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{j^2}+\frac {(193 g m) \int x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{2 j}-\frac {1}{4} (b n) \int x^3 \left (f+g \log \left (h (386+j x)^m\right )\right ) \, dx+\frac {\left (b d^3 n\right ) \int \left (f+g \log \left (h (386+j x)^m\right )\right ) \, dx}{4 e^3}-\frac {\left (b d^4 n\right ) \int \frac {f+g \log \left (h (386+j x)^m\right )}{d+e x} \, dx}{4 e^3}-\frac {\left (b d^2 n\right ) \int x \left (f+g \log \left (h (386+j x)^m\right )\right ) \, dx}{4 e^2}+\frac {(b d n) \int x^2 \left (f+g \log \left (h (386+j x)^m\right )\right ) \, dx}{4 e}\\ &=\frac {14378114 a g m x}{j^3}+\frac {b d^3 f n x}{4 e^3}-\frac {37249 g m x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{2 j^2}+\frac {193 g m x^3 \left (a+b \log \left (c (d+e x)^n\right )\right )}{6 j}-\frac {1}{16} g m x^4 \left (a+b \log \left (c (d+e x)^n\right )\right )-\frac {5549952004 g m \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (386+j x)}{386 e-d j}\right )}{j^4}-\frac {b d^2 n x^2 \left (f+g \log \left (h (386+j x)^m\right )\right )}{8 e^2}+\frac {b d n x^3 \left (f+g \log \left (h (386+j x)^m\right )\right )}{12 e}-\frac {1}{16} b n x^4 \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {b d^4 n \log \left (-\frac {j (d+e x)}{386 e-d j}\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )}{4 e^4}+\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )+\frac {(14378114 b g m) \int \log \left (c (d+e x)^n\right ) \, dx}{j^3}+\frac {\left (b d^3 g n\right ) \int \log \left (h (386+j x)^m\right ) \, dx}{4 e^3}+\frac {1}{16} (b e g m n) \int \frac {x^4}{d+e x} \, dx+\frac {(5549952004 b e g m n) \int \frac {\log \left (\frac {e (386+j x)}{386 e-d j}\right )}{d+e x} \, dx}{j^4}+\frac {(37249 b e g m n) \int \frac {x^2}{d+e x} \, dx}{2 j^2}-\frac {(193 b e g m n) \int \frac {x^3}{d+e x} \, dx}{6 j}+\frac {1}{16} (b g j m n) \int \frac {x^4}{386+j x} \, dx+\frac {\left (b d^4 g j m n\right ) \int \frac {\log \left (\frac {j (d+e x)}{-386 e+d j}\right )}{386+j x} \, dx}{4 e^4}+\frac {\left (b d^2 g j m n\right ) \int \frac {x^2}{386+j x} \, dx}{8 e^2}-\frac {(b d g j m n) \int \frac {x^3}{386+j x} \, dx}{12 e}\\ &=\frac {14378114 a g m x}{j^3}+\frac {b d^3 f n x}{4 e^3}-\frac {37249 g m x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{2 j^2}+\frac {193 g m x^3 \left (a+b \log \left (c (d+e x)^n\right )\right )}{6 j}-\frac {1}{16} g m x^4 \left (a+b \log \left (c (d+e x)^n\right )\right )-\frac {5549952004 g m \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (386+j x)}{386 e-d j}\right )}{j^4}-\frac {b d^2 n x^2 \left (f+g \log \left (h (386+j x)^m\right )\right )}{8 e^2}+\frac {b d n x^3 \left (f+g \log \left (h (386+j x)^m\right )\right )}{12 e}-\frac {1}{16} b n x^4 \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {b d^4 n \log \left (-\frac {j (d+e x)}{386 e-d j}\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )}{4 e^4}+\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )+\frac {(14378114 b g m) \operatorname {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e j^3}+\frac {\left (b d^3 g n\right ) \operatorname {Subst}\left (\int \log \left (h x^m\right ) \, dx,x,386+j x\right )}{4 e^3 j}+\frac {\left (b d^4 g m n\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {e x}{-386 e+d j}\right )}{x} \, dx,x,386+j x\right )}{4 e^4}+\frac {1}{16} (b e g m n) \int \left (-\frac {d^3}{e^4}+\frac {d^2 x}{e^3}-\frac {d x^2}{e^2}+\frac {x^3}{e}+\frac {d^4}{e^4 (d+e x)}\right ) \, dx+\frac {(5549952004 b g m n) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {j x}{386 e-d j}\right )}{x} \, dx,x,d+e x\right )}{j^4}+\frac {(37249 b e g m n) \int \left (-\frac {d}{e^2}+\frac {x}{e}+\frac {d^2}{e^2 (d+e x)}\right ) \, dx}{2 j^2}-\frac {(193 b e g m n) \int \left (\frac {d^2}{e^3}-\frac {d x}{e^2}+\frac {x^2}{e}-\frac {d^3}{e^3 (d+e x)}\right ) \, dx}{6 j}+\frac {1}{16} (b g j m n) \int \left (-\frac {57512456}{j^4}+\frac {148996 x}{j^3}-\frac {386 x^2}{j^2}+\frac {x^3}{j}+\frac {22199808016}{j^4 (386+j x)}\right ) \, dx+\frac {\left (b d^2 g j m n\right ) \int \left (-\frac {386}{j^2}+\frac {x}{j}+\frac {148996}{j^2 (386+j x)}\right ) \, dx}{8 e^2}-\frac {(b d g j m n) \int \left (\frac {148996}{j^3}-\frac {386 x}{j^2}+\frac {x^2}{j}-\frac {57512456}{j^3 (386+j x)}\right ) \, dx}{12 e}\\ &=\frac {14378114 a g m x}{j^3}+\frac {b d^3 f n x}{4 e^3}-\frac {5 b d^3 g m n x}{16 e^3}-\frac {35945285 b g m n x}{2 j^3}-\frac {186245 b d g m n x}{6 e j^2}-\frac {965 b d^2 g m n x}{12 e^2 j}+\frac {3 b d^2 g m n x^2}{32 e^2}+\frac {111747 b g m n x^2}{8 j^2}+\frac {193 b d g m n x^2}{6 e j}-\frac {7 b d g m n x^3}{144 e}-\frac {1351 b g m n x^3}{72 j}+\frac {1}{32} b g m n x^4+\frac {b d^4 g m n \log (d+e x)}{16 e^4}+\frac {37249 b d^2 g m n \log (d+e x)}{2 e^2 j^2}+\frac {193 b d^3 g m n \log (d+e x)}{6 e^3 j}+\frac {14378114 b g m (d+e x) \log \left (c (d+e x)^n\right )}{e j^3}-\frac {37249 g m x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{2 j^2}+\frac {193 g m x^3 \left (a+b \log \left (c (d+e x)^n\right )\right )}{6 j}-\frac {1}{16} g m x^4 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac {1387488001 b g m n \log (386+j x)}{j^4}+\frac {14378114 b d g m n \log (386+j x)}{3 e j^3}+\frac {37249 b d^2 g m n \log (386+j x)}{2 e^2 j^2}-\frac {5549952004 g m \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (386+j x)}{386 e-d j}\right )}{j^4}+\frac {b d^3 g n (386+j x) \log \left (h (386+j x)^m\right )}{4 e^3 j}-\frac {b d^2 n x^2 \left (f+g \log \left (h (386+j x)^m\right )\right )}{8 e^2}+\frac {b d n x^3 \left (f+g \log \left (h (386+j x)^m\right )\right )}{12 e}-\frac {1}{16} b n x^4 \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {b d^4 n \log \left (-\frac {j (d+e x)}{386 e-d j}\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )}{4 e^4}+\frac {1}{4} x^4 \left (a+b \log \left (c (d+e x)^n\right )\right ) \left (f+g \log \left (h (386+j x)^m\right )\right )-\frac {5549952004 b g m n \text {Li}_2\left (-\frac {j (d+e x)}{386 e-d j}\right )}{j^4}-\frac {b d^4 g m n \text {Li}_2\left (\frac {e (386+j x)}{386 e-d j}\right )}{4 e^4}\\ \end {align*}
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Mathematica [A] time = 1.20, size = 605, normalized size = 0.82 \[ \frac {e \left (j \left (-6 g j^3 x \left (b n \left (-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right )-12 a e^3 x^3\right ) \log \left (h (i+j x)^m\right )+6 a e^3 x \left (12 f j^3 x^3+g m \left (12 i^3-6 i^2 j x+4 i j^2 x^2-3 j^3 x^3\right )\right )-b n \left (18 d^3 j^3 x (5 g m-4 f)+3 d^2 e j^2 x (12 f j x+g m (20 i-9 j x))+2 d e^2 \left (g m \left (36 i^3+30 i^2 j x-12 i j^2 x^2+7 j^3 x^3\right )-12 f j^3 x^3\right )+e^3 x \left (18 f j^3 x^3+g m \left (90 i^3-27 i^2 j x+14 i j^2 x^2-9 j^3 x^3\right )\right )\right )\right )+6 g i m \log (i+j x) \left (b n \left (12 d^3 j^3+6 d^2 e i j^2+4 d e^2 i^2 j+3 e^3 i^3\right )-12 a e^3 i^3\right )-6 b e^3 \log \left (c (d+e x)^n\right ) \left (-12 f j^4 x^4-12 g j^4 x^4 \log \left (h (i+j x)^m\right )+12 g i^4 m \log (i+j x)+g j m x \left (-12 i^3+6 i^2 j x-4 i j^2 x^2+3 j^3 x^3\right )\right )\right )-72 b g m n \left (e^4 i^4-d^4 j^4\right ) \text {Li}_2\left (\frac {j (d+e x)}{d j-e i}\right )+6 b n \log (d+e x) \left (-12 g m \left (e^4 i^4-d^4 j^4\right ) \log \left (\frac {e (i+j x)}{e i-d j}\right )+d j \left (3 d^3 j^3 (g m-4 f)-12 d^3 g j^3 \log \left (h (i+j x)^m\right )+4 d^2 e g i j^2 m+6 d e^2 g i^2 j m+12 e^3 g i^3 m\right )+12 e^4 g i^4 m \log (i+j x)\right )}{288 e^4 j^4} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (b f x^{3} \log \left ({\left (e x + d\right )}^{n} c\right ) + a f x^{3} + {\left (b g x^{3} \log \left ({\left (e x + d\right )}^{n} c\right ) + a g x^{3}\right )} \log \left ({\left (j x + i\right )}^{m} h\right ), x\right ) \]
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 \[ \int {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )} {\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )} x^{3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 2.21, size = 4217, normalized size = 5.68 \[ \text {output too large to display} \]
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 \[ \frac {1}{4} \, b f x^{4} \log \left ({\left (e x + d\right )}^{n} c\right ) + \frac {1}{4} \, a g x^{4} \log \left ({\left (j x + i\right )}^{m} h\right ) + \frac {1}{4} \, a f x^{4} - \frac {1}{48} \, b e f n {\left (\frac {12 \, d^{4} \log \left (e x + d\right )}{e^{5}} + \frac {3 \, e^{3} x^{4} - 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} - 12 \, d^{3} x}{e^{4}}\right )} - \frac {1}{48} \, a g j m {\left (\frac {12 \, i^{4} \log \left (j x + i\right )}{j^{5}} + \frac {3 \, j^{3} x^{4} - 4 \, i j^{2} x^{3} + 6 \, i^{2} j x^{2} - 12 \, i^{3} x}{j^{4}}\right )} + \frac {1}{48} \, b g {\left (\frac {12 \, e^{4} i^{4} m n \log \left (e x + d\right ) \log \left (j x + i\right ) + {\left (4 \, e^{4} i j^{3} m x^{3} - 6 \, e^{4} i^{2} j^{2} m x^{2} + 12 \, e^{4} i^{3} j m x - 12 \, e^{4} i^{4} m \log \left (j x + i\right ) - 3 \, {\left (j^{4} m - 4 \, j^{4} \log \relax (h)\right )} e^{4} x^{4}\right )} \log \left ({\left (e x + d\right )}^{n}\right ) + {\left (12 \, e^{4} j^{4} x^{4} \log \left ({\left (e x + d\right )}^{n}\right ) + 4 \, d e^{3} j^{4} n x^{3} - 6 \, d^{2} e^{2} j^{4} n x^{2} + 12 \, d^{3} e j^{4} n x - 12 \, d^{4} j^{4} n \log \left (e x + d\right ) - 3 \, {\left (e^{4} j^{4} n - 4 \, e^{4} j^{4} \log \relax (c)\right )} x^{4}\right )} \log \left ({\left (j x + i\right )}^{m}\right )}{e^{4} j^{4}} + 48 \, \int -\frac {6 \, {\left (2 \, {\left (j^{4} m - 4 \, j^{4} \log \relax (h)\right )} e^{5} \log \relax (c) - {\left (j^{4} m n - 2 \, j^{4} n \log \relax (h)\right )} e^{5}\right )} x^{5} + {\left (d e^{4} j^{4} m n + {\left (i j^{3} m n + 12 \, i j^{3} n \log \relax (h)\right )} e^{5} - 12 \, {\left (4 \, e^{5} i j^{3} \log \relax (h) - {\left (j^{4} m - 4 \, j^{4} \log \relax (h)\right )} d e^{4}\right )} \log \relax (c)\right )} x^{4} - 2 \, {\left (e^{5} i^{2} j^{2} m n + d^{2} e^{3} j^{4} m n + 24 \, d e^{4} i j^{3} \log \relax (c) \log \relax (h)\right )} x^{3} + 6 \, {\left (e^{5} i^{3} j m n + d^{3} e^{2} j^{4} m n\right )} x^{2} + 12 \, {\left (e^{5} i^{4} m n + d^{4} e j^{4} m n\right )} x + 12 \, {\left (d e^{4} i^{4} m n - d^{5} j^{4} m n + {\left (e^{5} i^{4} m n - d^{4} e j^{4} m n\right )} x\right )} \log \left (e x + d\right )}{48 \, {\left (e^{5} j^{4} x^{2} + d e^{4} i j^{3} + {\left (e^{5} i j^{3} + d e^{4} j^{4}\right )} x\right )}}\,{d x}\right )} \]
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 \[ \int x^3\,\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )\,\left (f+g\,\ln \left (h\,{\left (i+j\,x\right )}^m\right )\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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