Optimal. Leaf size=531 \[ -\frac {x \left (A e \left (-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right )-3 B \left (c e^2 \left (a^2 e^2-6 a b d e+6 b^2 d^2\right )-b^2 e^3 (b d-a e)-2 c^2 d^2 e (5 b d-3 a e)+5 c^3 d^4\right )\right )}{e^7}-\frac {c x^3 \left (A c e (c d-b e)-B \left (-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right )\right )}{e^5}-\frac {3 \log (d+e x) \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8}-\frac {x^2 \left (B \left (-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right )-3 A c e \left (-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right )\right )}{2 e^6}+\frac {\left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{e^8 (d+e x)}+\frac {(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{2 e^8 (d+e x)^2}-\frac {c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}+\frac {B c^3 x^5}{5 e^3} \]
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Rubi [A] time = 1.08, antiderivative size = 530, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {771} \begin {gather*} -\frac {x \left (A e \left (-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right )-3 B \left (c e^2 \left (a^2 e^2-6 a b d e+6 b^2 d^2\right )-b^2 e^3 (b d-a e)-2 c^2 d^2 e (5 b d-3 a e)+5 c^3 d^4\right )\right )}{e^7}-\frac {c x^3 \left (A c e (c d-b e)-B \left (-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right )\right )}{e^5}-\frac {x^2 \left (B \left (-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right )-3 A c e \left (-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right )\right )}{2 e^6}-\frac {3 \log (d+e x) \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8}-\frac {\left (a e^2-b d e+c d^2\right )^2 \left (-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right )}{e^8 (d+e x)}+\frac {(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{2 e^8 (d+e x)^2}-\frac {c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}+\frac {B c^3 x^5}{5 e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a+b x+c x^2\right )^3}{(d+e x)^3} \, dx &=\int \left (\frac {-A e \left (10 c^3 d^3-b^3 e^3+3 b c e^2 (3 b d-2 a e)-9 c^2 d e (2 b d-a e)\right )+3 B \left (5 c^3 d^4-2 c^2 d^2 e (5 b d-3 a e)-b^2 e^3 (b d-a e)+c e^2 \left (6 b^2 d^2-6 a b d e+a^2 e^2\right )\right )}{e^7}+\frac {\left (-B \left (10 c^3 d^3-b^3 e^3+3 b c e^2 (3 b d-2 a e)-9 c^2 d e (2 b d-a e)\right )+3 A c e \left (2 c^2 d^2+b^2 e^2-c e (3 b d-a e)\right )\right ) x}{e^6}+\frac {3 c \left (-A c e (c d-b e)+B \left (2 c^2 d^2+b^2 e^2-c e (3 b d-a e)\right )\right ) x^2}{e^5}+\frac {c^2 (-3 B c d+3 b B e+A c e) x^3}{e^4}+\frac {B c^3 x^4}{e^3}+\frac {(-B d+A e) \left (c d^2-b d e+a e^2\right )^3}{e^7 (d+e x)^3}+\frac {\left (c d^2-b d e+a e^2\right )^2 \left (7 B c d^2-B e (4 b d-a e)-3 A e (2 c d-b e)\right )}{e^7 (d+e x)^2}+\frac {3 \left (c d^2-b d e+a e^2\right ) \left (-B \left (7 c^2 d^3-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)\right )+A e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right )}{e^7 (d+e x)}\right ) \, dx\\ &=-\frac {\left (A e \left (10 c^3 d^3-b^3 e^3+3 b c e^2 (3 b d-2 a e)-9 c^2 d e (2 b d-a e)\right )-3 B \left (5 c^3 d^4-2 c^2 d^2 e (5 b d-3 a e)-b^2 e^3 (b d-a e)+c e^2 \left (6 b^2 d^2-6 a b d e+a^2 e^2\right )\right )\right ) x}{e^7}-\frac {\left (B \left (10 c^3 d^3-b^3 e^3+3 b c e^2 (3 b d-2 a e)-9 c^2 d e (2 b d-a e)\right )-3 A c e \left (2 c^2 d^2+b^2 e^2-c e (3 b d-a e)\right )\right ) x^2}{2 e^6}-\frac {c \left (A c e (c d-b e)-B \left (2 c^2 d^2+b^2 e^2-c e (3 b d-a e)\right )\right ) x^3}{e^5}-\frac {c^2 (3 B c d-3 b B e-A c e) x^4}{4 e^4}+\frac {B c^3 x^5}{5 e^3}+\frac {(B d-A e) \left (c d^2-b d e+a e^2\right )^3}{2 e^8 (d+e x)^2}-\frac {\left (c d^2-b d e+a e^2\right )^2 \left (7 B c d^2-B e (4 b d-a e)-3 A e (2 c d-b e)\right )}{e^8 (d+e x)}-\frac {3 \left (c d^2-b d e+a e^2\right ) \left (B \left (7 c^2 d^3-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)\right )-A e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) \log (d+e x)}{e^8}\\ \end {align*}
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Mathematica [A] time = 0.28, size = 503, normalized size = 0.95 \begin {gather*} \frac {20 e x \left (3 B \left (c e^2 \left (a^2 e^2-6 a b d e+6 b^2 d^2\right )+b^2 e^3 (a e-b d)+2 c^2 d^2 e (3 a e-5 b d)+5 c^3 d^4\right )+A e \left (9 c^2 d e (2 b d-a e)+3 b c e^2 (2 a e-3 b d)+b^3 e^3-10 c^3 d^3\right )\right )+20 c e^3 x^3 \left (B \left (c e (a e-3 b d)+b^2 e^2+2 c^2 d^2\right )+A c e (b e-c d)\right )-60 \log (d+e x) \left (e (a e-b d)+c d^2\right ) \left (B \left (c d e (3 a e-8 b d)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right )\right )+10 e^2 x^2 \left (3 A c e \left (c e (a e-3 b d)+b^2 e^2+2 c^2 d^2\right )+B \left (9 c^2 d e (2 b d-a e)+3 b c e^2 (2 a e-3 b d)+b^3 e^3-10 c^3 d^3\right )\right )-\frac {20 \left (e (a e-b d)+c d^2\right )^2 \left (B e (a e-4 b d)+3 A e (b e-2 c d)+7 B c d^2\right )}{d+e x}+\frac {10 (B d-A e) \left (e (a e-b d)+c d^2\right )^3}{(d+e x)^2}+5 c^2 e^4 x^4 (A c e+3 b B e-3 B c d)+4 B c^3 e^5 x^5}{20 e^8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(A+B x) \left (a+b x+c x^2\right )^3}{(d+e x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.40, size = 1311, normalized size = 2.47
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 1048, normalized size = 1.97 \begin {gather*} -3 \, {\left (7 \, B c^{3} d^{5} - 15 \, B b c^{2} d^{4} e - 5 \, A c^{3} d^{4} e + 10 \, B b^{2} c d^{3} e^{2} + 10 \, B a c^{2} d^{3} e^{2} + 10 \, A b c^{2} d^{3} e^{2} - 2 \, B b^{3} d^{2} e^{3} - 12 \, B a b c d^{2} e^{3} - 6 \, A b^{2} c d^{2} e^{3} - 6 \, A a c^{2} d^{2} e^{3} + 3 \, B a b^{2} d e^{4} + A b^{3} d e^{4} + 3 \, B a^{2} c d e^{4} + 6 \, A a b c d e^{4} - B a^{2} b e^{5} - A a b^{2} e^{5} - A a^{2} c e^{5}\right )} e^{\left (-8\right )} \log \left ({\left | x e + d \right |}\right ) + \frac {1}{20} \, {\left (4 \, B c^{3} x^{5} e^{12} - 15 \, B c^{3} d x^{4} e^{11} + 40 \, B c^{3} d^{2} x^{3} e^{10} - 100 \, B c^{3} d^{3} x^{2} e^{9} + 300 \, B c^{3} d^{4} x e^{8} + 15 \, B b c^{2} x^{4} e^{12} + 5 \, A c^{3} x^{4} e^{12} - 60 \, B b c^{2} d x^{3} e^{11} - 20 \, A c^{3} d x^{3} e^{11} + 180 \, B b c^{2} d^{2} x^{2} e^{10} + 60 \, A c^{3} d^{2} x^{2} e^{10} - 600 \, B b c^{2} d^{3} x e^{9} - 200 \, A c^{3} d^{3} x e^{9} + 20 \, B b^{2} c x^{3} e^{12} + 20 \, B a c^{2} x^{3} e^{12} + 20 \, A b c^{2} x^{3} e^{12} - 90 \, B b^{2} c d x^{2} e^{11} - 90 \, B a c^{2} d x^{2} e^{11} - 90 \, A b c^{2} d x^{2} e^{11} + 360 \, B b^{2} c d^{2} x e^{10} + 360 \, B a c^{2} d^{2} x e^{10} + 360 \, A b c^{2} d^{2} x e^{10} + 10 \, B b^{3} x^{2} e^{12} + 60 \, B a b c x^{2} e^{12} + 30 \, A b^{2} c x^{2} e^{12} + 30 \, A a c^{2} x^{2} e^{12} - 60 \, B b^{3} d x e^{11} - 360 \, B a b c d x e^{11} - 180 \, A b^{2} c d x e^{11} - 180 \, A a c^{2} d x e^{11} + 60 \, B a b^{2} x e^{12} + 20 \, A b^{3} x e^{12} + 60 \, B a^{2} c x e^{12} + 120 \, A a b c x e^{12}\right )} e^{\left (-15\right )} - \frac {{\left (13 \, B c^{3} d^{7} - 33 \, B b c^{2} d^{6} e - 11 \, A c^{3} d^{6} e + 27 \, B b^{2} c d^{5} e^{2} + 27 \, B a c^{2} d^{5} e^{2} + 27 \, A b c^{2} d^{5} e^{2} - 7 \, B b^{3} d^{4} e^{3} - 42 \, B a b c d^{4} e^{3} - 21 \, A b^{2} c d^{4} e^{3} - 21 \, A a c^{2} d^{4} e^{3} + 15 \, B a b^{2} d^{3} e^{4} + 5 \, A b^{3} d^{3} e^{4} + 15 \, B a^{2} c d^{3} e^{4} + 30 \, A a b c d^{3} e^{4} - 9 \, B a^{2} b d^{2} e^{5} - 9 \, A a b^{2} d^{2} e^{5} - 9 \, A a^{2} c d^{2} e^{5} + B a^{3} d e^{6} + 3 \, A a^{2} b d e^{6} + A a^{3} e^{7} + 2 \, {\left (7 \, B c^{3} d^{6} e - 18 \, B b c^{2} d^{5} e^{2} - 6 \, A c^{3} d^{5} e^{2} + 15 \, B b^{2} c d^{4} e^{3} + 15 \, B a c^{2} d^{4} e^{3} + 15 \, A b c^{2} d^{4} e^{3} - 4 \, B b^{3} d^{3} e^{4} - 24 \, B a b c d^{3} e^{4} - 12 \, A b^{2} c d^{3} e^{4} - 12 \, A a c^{2} d^{3} e^{4} + 9 \, B a b^{2} d^{2} e^{5} + 3 \, A b^{3} d^{2} e^{5} + 9 \, B a^{2} c d^{2} e^{5} + 18 \, A a b c d^{2} e^{5} - 6 \, B a^{2} b d e^{6} - 6 \, A a b^{2} d e^{6} - 6 \, A a^{2} c d e^{6} + B a^{3} e^{7} + 3 \, A a^{2} b e^{7}\right )} x\right )} e^{\left (-8\right )}}{2 \, {\left (x e + d\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 1483, normalized size = 2.79
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 861, normalized size = 1.62 \begin {gather*} -\frac {13 \, B c^{3} d^{7} + A a^{3} e^{7} - 11 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{6} e + 27 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{5} e^{2} - 7 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d^{4} e^{3} + 5 \, {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} d^{3} e^{4} - 9 \, {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} d^{2} e^{5} + {\left (B a^{3} + 3 \, A a^{2} b\right )} d e^{6} + 2 \, {\left (7 \, B c^{3} d^{6} e - 6 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{5} e^{2} + 15 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{4} e^{3} - 4 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d^{3} e^{4} + 3 \, {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} d^{2} e^{5} - 6 \, {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} d e^{6} + {\left (B a^{3} + 3 \, A a^{2} b\right )} e^{7}\right )} x}{2 \, {\left (e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right )}} + \frac {4 \, B c^{3} e^{4} x^{5} - 5 \, {\left (3 \, B c^{3} d e^{3} - {\left (3 \, B b c^{2} + A c^{3}\right )} e^{4}\right )} x^{4} + 20 \, {\left (2 \, B c^{3} d^{2} e^{2} - {\left (3 \, B b c^{2} + A c^{3}\right )} d e^{3} + {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} e^{4}\right )} x^{3} - 10 \, {\left (10 \, B c^{3} d^{3} e - 6 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{2} e^{2} + 9 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d e^{3} - {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} e^{4}\right )} x^{2} + 20 \, {\left (15 \, B c^{3} d^{4} - 10 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{3} e + 18 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{2} e^{2} - 3 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d e^{3} + {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} e^{4}\right )} x}{20 \, e^{7}} - \frac {3 \, {\left (7 \, B c^{3} d^{5} - 5 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{4} e + 10 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{3} e^{2} - 2 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d^{2} e^{3} + {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} d e^{4} - {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} e^{5}\right )} \log \left (e x + d\right )}{e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.51, size = 1297, normalized size = 2.44 \begin {gather*} x\,\left (\frac {3\,B\,c\,a^2+3\,B\,a\,b^2+6\,A\,c\,a\,b+A\,b^3}{e^3}+\frac {3\,d^2\,\left (\frac {3\,d\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{e}-\frac {3\,B\,b^2\,c+3\,A\,b\,c^2+3\,B\,a\,c^2}{e^3}+\frac {3\,B\,c^3\,d^2}{e^5}\right )}{e^2}-\frac {3\,d\,\left (\frac {B\,b^3+3\,A\,b^2\,c+6\,B\,a\,b\,c+3\,A\,a\,c^2}{e^3}-\frac {3\,d^2\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{e^2}+\frac {3\,d\,\left (\frac {3\,d\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{e}-\frac {3\,B\,b^2\,c+3\,A\,b\,c^2+3\,B\,a\,c^2}{e^3}+\frac {3\,B\,c^3\,d^2}{e^5}\right )}{e}-\frac {B\,c^3\,d^3}{e^6}\right )}{e}-\frac {d^3\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{e^3}\right )-\frac {\frac {B\,a^3\,d\,e^6+A\,a^3\,e^7-9\,B\,a^2\,b\,d^2\,e^5+3\,A\,a^2\,b\,d\,e^6+15\,B\,a^2\,c\,d^3\,e^4-9\,A\,a^2\,c\,d^2\,e^5+15\,B\,a\,b^2\,d^3\,e^4-9\,A\,a\,b^2\,d^2\,e^5-42\,B\,a\,b\,c\,d^4\,e^3+30\,A\,a\,b\,c\,d^3\,e^4+27\,B\,a\,c^2\,d^5\,e^2-21\,A\,a\,c^2\,d^4\,e^3-7\,B\,b^3\,d^4\,e^3+5\,A\,b^3\,d^3\,e^4+27\,B\,b^2\,c\,d^5\,e^2-21\,A\,b^2\,c\,d^4\,e^3-33\,B\,b\,c^2\,d^6\,e+27\,A\,b\,c^2\,d^5\,e^2+13\,B\,c^3\,d^7-11\,A\,c^3\,d^6\,e}{2\,e}+x\,\left (B\,a^3\,e^6-6\,B\,a^2\,b\,d\,e^5+3\,A\,a^2\,b\,e^6+9\,B\,a^2\,c\,d^2\,e^4-6\,A\,a^2\,c\,d\,e^5+9\,B\,a\,b^2\,d^2\,e^4-6\,A\,a\,b^2\,d\,e^5-24\,B\,a\,b\,c\,d^3\,e^3+18\,A\,a\,b\,c\,d^2\,e^4+15\,B\,a\,c^2\,d^4\,e^2-12\,A\,a\,c^2\,d^3\,e^3-4\,B\,b^3\,d^3\,e^3+3\,A\,b^3\,d^2\,e^4+15\,B\,b^2\,c\,d^4\,e^2-12\,A\,b^2\,c\,d^3\,e^3-18\,B\,b\,c^2\,d^5\,e+15\,A\,b\,c^2\,d^4\,e^2+7\,B\,c^3\,d^6-6\,A\,c^3\,d^5\,e\right )}{d^2\,e^7+2\,d\,e^8\,x+e^9\,x^2}-x^3\,\left (\frac {d\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{e}-\frac {3\,B\,b^2\,c+3\,A\,b\,c^2+3\,B\,a\,c^2}{3\,e^3}+\frac {B\,c^3\,d^2}{e^5}\right )+x^4\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{4\,e^3}-\frac {3\,B\,c^3\,d}{4\,e^4}\right )+x^2\,\left (\frac {B\,b^3+3\,A\,b^2\,c+6\,B\,a\,b\,c+3\,A\,a\,c^2}{2\,e^3}-\frac {3\,d^2\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{2\,e^2}+\frac {3\,d\,\left (\frac {3\,d\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^3}-\frac {3\,B\,c^3\,d}{e^4}\right )}{e}-\frac {3\,B\,b^2\,c+3\,A\,b\,c^2+3\,B\,a\,c^2}{e^3}+\frac {3\,B\,c^3\,d^2}{e^5}\right )}{2\,e}-\frac {B\,c^3\,d^3}{2\,e^6}\right )+\frac {\ln \left (d+e\,x\right )\,\left (3\,B\,a^2\,b\,e^5-9\,B\,a^2\,c\,d\,e^4+3\,A\,a^2\,c\,e^5-9\,B\,a\,b^2\,d\,e^4+3\,A\,a\,b^2\,e^5+36\,B\,a\,b\,c\,d^2\,e^3-18\,A\,a\,b\,c\,d\,e^4-30\,B\,a\,c^2\,d^3\,e^2+18\,A\,a\,c^2\,d^2\,e^3+6\,B\,b^3\,d^2\,e^3-3\,A\,b^3\,d\,e^4-30\,B\,b^2\,c\,d^3\,e^2+18\,A\,b^2\,c\,d^2\,e^3+45\,B\,b\,c^2\,d^4\,e-30\,A\,b\,c^2\,d^3\,e^2-21\,B\,c^3\,d^5+15\,A\,c^3\,d^4\,e\right )}{e^8}+\frac {B\,c^3\,x^5}{5\,e^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 86.43, size = 1149, normalized size = 2.16 \begin {gather*} \frac {B c^{3} x^{5}}{5 e^{3}} + x^{4} \left (\frac {A c^{3}}{4 e^{3}} + \frac {3 B b c^{2}}{4 e^{3}} - \frac {3 B c^{3} d}{4 e^{4}}\right ) + x^{3} \left (\frac {A b c^{2}}{e^{3}} - \frac {A c^{3} d}{e^{4}} + \frac {B a c^{2}}{e^{3}} + \frac {B b^{2} c}{e^{3}} - \frac {3 B b c^{2} d}{e^{4}} + \frac {2 B c^{3} d^{2}}{e^{5}}\right ) + x^{2} \left (\frac {3 A a c^{2}}{2 e^{3}} + \frac {3 A b^{2} c}{2 e^{3}} - \frac {9 A b c^{2} d}{2 e^{4}} + \frac {3 A c^{3} d^{2}}{e^{5}} + \frac {3 B a b c}{e^{3}} - \frac {9 B a c^{2} d}{2 e^{4}} + \frac {B b^{3}}{2 e^{3}} - \frac {9 B b^{2} c d}{2 e^{4}} + \frac {9 B b c^{2} d^{2}}{e^{5}} - \frac {5 B c^{3} d^{3}}{e^{6}}\right ) + x \left (\frac {6 A a b c}{e^{3}} - \frac {9 A a c^{2} d}{e^{4}} + \frac {A b^{3}}{e^{3}} - \frac {9 A b^{2} c d}{e^{4}} + \frac {18 A b c^{2} d^{2}}{e^{5}} - \frac {10 A c^{3} d^{3}}{e^{6}} + \frac {3 B a^{2} c}{e^{3}} + \frac {3 B a b^{2}}{e^{3}} - \frac {18 B a b c d}{e^{4}} + \frac {18 B a c^{2} d^{2}}{e^{5}} - \frac {3 B b^{3} d}{e^{4}} + \frac {18 B b^{2} c d^{2}}{e^{5}} - \frac {30 B b c^{2} d^{3}}{e^{6}} + \frac {15 B c^{3} d^{4}}{e^{7}}\right ) + \frac {- A a^{3} e^{7} - 3 A a^{2} b d e^{6} + 9 A a^{2} c d^{2} e^{5} + 9 A a b^{2} d^{2} e^{5} - 30 A a b c d^{3} e^{4} + 21 A a c^{2} d^{4} e^{3} - 5 A b^{3} d^{3} e^{4} + 21 A b^{2} c d^{4} e^{3} - 27 A b c^{2} d^{5} e^{2} + 11 A c^{3} d^{6} e - B a^{3} d e^{6} + 9 B a^{2} b d^{2} e^{5} - 15 B a^{2} c d^{3} e^{4} - 15 B a b^{2} d^{3} e^{4} + 42 B a b c d^{4} e^{3} - 27 B a c^{2} d^{5} e^{2} + 7 B b^{3} d^{4} e^{3} - 27 B b^{2} c d^{5} e^{2} + 33 B b c^{2} d^{6} e - 13 B c^{3} d^{7} + x \left (- 6 A a^{2} b e^{7} + 12 A a^{2} c d e^{6} + 12 A a b^{2} d e^{6} - 36 A a b c d^{2} e^{5} + 24 A a c^{2} d^{3} e^{4} - 6 A b^{3} d^{2} e^{5} + 24 A b^{2} c d^{3} e^{4} - 30 A b c^{2} d^{4} e^{3} + 12 A c^{3} d^{5} e^{2} - 2 B a^{3} e^{7} + 12 B a^{2} b d e^{6} - 18 B a^{2} c d^{2} e^{5} - 18 B a b^{2} d^{2} e^{5} + 48 B a b c d^{3} e^{4} - 30 B a c^{2} d^{4} e^{3} + 8 B b^{3} d^{3} e^{4} - 30 B b^{2} c d^{4} e^{3} + 36 B b c^{2} d^{5} e^{2} - 14 B c^{3} d^{6} e\right )}{2 d^{2} e^{8} + 4 d e^{9} x + 2 e^{10} x^{2}} + \frac {3 \left (a e^{2} - b d e + c d^{2}\right ) \left (A a c e^{3} + A b^{2} e^{3} - 5 A b c d e^{2} + 5 A c^{2} d^{2} e + B a b e^{3} - 3 B a c d e^{2} - 2 B b^{2} d e^{2} + 8 B b c d^{2} e - 7 B c^{2} d^{3}\right ) \log {\left (d + e x \right )}}{e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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