Optimal. Leaf size=555 \[ -\frac {(d+e x)^6 \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{6 e^8}-\frac {3 c (d+e x)^8 \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{8 e^8}-\frac {3 (d+e x)^5 \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{5 e^8}-\frac {(d+e x)^7 \left (B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{7 e^8}-\frac {(d+e x)^4 \left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{4 e^8}-\frac {(d+e x)^3 (B d-A e) \left (a e^2-b d e+c d^2\right )^3}{3 e^8}-\frac {c^2 (d+e x)^9 (-A c e-3 b B e+7 B c d)}{9 e^8}+\frac {B c^3 (d+e x)^{10}}{10 e^8} \]
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Rubi [A] time = 0.86, antiderivative size = 553, 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} \[ -\frac {(d+e x)^6 \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{6 e^8}-\frac {3 c (d+e x)^8 \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{8 e^8}-\frac {(d+e x)^7 \left (B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{7 e^8}-\frac {3 (d+e x)^5 \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{5 e^8}+\frac {(d+e x)^4 \left (a e^2-b d e+c d^2\right )^2 \left (-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right )}{4 e^8}-\frac {(d+e x)^3 (B d-A e) \left (a e^2-b d e+c d^2\right )^3}{3 e^8}-\frac {c^2 (d+e x)^9 (-A c e-3 b B e+7 B c d)}{9 e^8}+\frac {B c^3 (d+e x)^{10}}{10 e^8} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (A+B x) (d+e x)^2 \left (a+b x+c x^2\right )^3 \, dx &=\int \left (\frac {(-B d+A e) \left (c d^2-b d e+a e^2\right )^3 (d+e x)^2}{e^7}+\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 ) (d+e x)^3}{e^7}+\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 ) (d+e x)^4}{e^7}+\frac {\left (-A e (2 c d-b e) \left (10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right )+B \left (35 c^3 d^4-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+3 c e^2 \left (10 b^2 d^2-8 a b d e+a^2 e^2\right )\right )\right ) (d+e x)^5}{e^7}+\frac {\left (-B \left (35 c^3 d^3-b^3 e^3+3 b c e^2 (5 b d-2 a e)-15 c^2 d e (3 b d-a e)\right )+3 A c e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) (d+e x)^6}{e^7}+\frac {3 c \left (-A c e (2 c d-b e)+B \left (7 c^2 d^2+b^2 e^2-c e (6 b d-a e)\right )\right ) (d+e x)^7}{e^7}+\frac {c^2 (-7 B c d+3 b B e+A c e) (d+e x)^8}{e^7}+\frac {B c^3 (d+e x)^9}{e^7}\right ) \, dx\\ &=-\frac {(B d-A e) \left (c d^2-b d e+a e^2\right )^3 (d+e x)^3}{3 e^8}+\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 ) (d+e x)^4}{4 e^8}-\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 ) (d+e x)^5}{5 e^8}-\frac {\left (A e (2 c d-b e) \left (10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right )-B \left (35 c^3 d^4-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+3 c e^2 \left (10 b^2 d^2-8 a b d e+a^2 e^2\right )\right )\right ) (d+e x)^6}{6 e^8}-\frac {\left (B \left (35 c^3 d^3-b^3 e^3+3 b c e^2 (5 b d-2 a e)-15 c^2 d e (3 b d-a e)\right )-3 A c e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) (d+e x)^7}{7 e^8}-\frac {3 c \left (A c e (2 c d-b e)-B \left (7 c^2 d^2+b^2 e^2-c e (6 b d-a e)\right )\right ) (d+e x)^8}{8 e^8}-\frac {c^2 (7 B c d-3 b B e-A c e) (d+e x)^9}{9 e^8}+\frac {B c^3 (d+e x)^{10}}{10 e^8}\\ \end {align*}
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Mathematica [A] time = 0.27, size = 526, normalized size = 0.95 \[ a^3 A d^2 x+\frac {1}{4} x^4 \left (A \left (6 a^2 c d e+6 a b^2 d e+3 a b \left (a e^2+2 c d^2\right )+b^3 d^2\right )+a B \left (6 a b d e+a \left (a e^2+3 c d^2\right )+3 b^2 d^2\right )\right )+\frac {1}{2} a^2 d x^2 (2 a A e+a B d+3 A b d)+\frac {1}{8} c x^8 \left (B \left (3 c e (a e+2 b d)+3 b^2 e^2+c^2 d^2\right )+A c e (3 b e+2 c d)\right )+\frac {1}{3} a x^3 \left (A \left (6 a b d e+a \left (a e^2+3 c d^2\right )+3 b^2 d^2\right )+a B d (2 a e+3 b d)\right )+\frac {1}{7} x^7 \left (3 b c \left (2 a B e^2+2 A c d e+B c d^2\right )+c^2 \left (3 a A e^2+6 a B d e+A c d^2\right )+3 b^2 c e (A e+2 B d)+b^3 B e^2\right )+\frac {1}{6} x^6 \left (3 b^2 \left (a B e^2+2 A c d e+B c d^2\right )+3 b c \left (2 a A e^2+4 a B d e+A c d^2\right )+3 a c \left (a B e^2+2 A c d e+B c d^2\right )+b^3 e (A e+2 B d)\right )+\frac {1}{5} x^5 \left (3 b^2 \left (a A e^2+2 a B d e+A c d^2\right )+3 a b \left (a B e^2+4 A c d e+2 B c d^2\right )+3 a c \left (a A e^2+2 a B d e+A c d^2\right )+b^3 d (2 A e+B d)\right )+\frac {1}{9} c^2 e x^9 (A c e+3 b B e+2 B c d)+\frac {1}{10} B c^3 e^2 x^{10} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 727, normalized size = 1.31 \[ \frac {1}{10} x^{10} e^{2} c^{3} B + \frac {2}{9} x^{9} e d c^{3} B + \frac {1}{3} x^{9} e^{2} c^{2} b B + \frac {1}{9} x^{9} e^{2} c^{3} A + \frac {1}{8} x^{8} d^{2} c^{3} B + \frac {3}{4} x^{8} e d c^{2} b B + \frac {3}{8} x^{8} e^{2} c b^{2} B + \frac {3}{8} x^{8} e^{2} c^{2} a B + \frac {1}{4} x^{8} e d c^{3} A + \frac {3}{8} x^{8} e^{2} c^{2} b A + \frac {3}{7} x^{7} d^{2} c^{2} b B + \frac {6}{7} x^{7} e d c b^{2} B + \frac {1}{7} x^{7} e^{2} b^{3} B + \frac {6}{7} x^{7} e d c^{2} a B + \frac {6}{7} x^{7} e^{2} c b a B + \frac {1}{7} x^{7} d^{2} c^{3} A + \frac {6}{7} x^{7} e d c^{2} b A + \frac {3}{7} x^{7} e^{2} c b^{2} A + \frac {3}{7} x^{7} e^{2} c^{2} a A + \frac {1}{2} x^{6} d^{2} c b^{2} B + \frac {1}{3} x^{6} e d b^{3} B + \frac {1}{2} x^{6} d^{2} c^{2} a B + 2 x^{6} e d c b a B + \frac {1}{2} x^{6} e^{2} b^{2} a B + \frac {1}{2} x^{6} e^{2} c a^{2} B + \frac {1}{2} x^{6} d^{2} c^{2} b A + x^{6} e d c b^{2} A + \frac {1}{6} x^{6} e^{2} b^{3} A + x^{6} e d c^{2} a A + x^{6} e^{2} c b a A + \frac {1}{5} x^{5} d^{2} b^{3} B + \frac {6}{5} x^{5} d^{2} c b a B + \frac {6}{5} x^{5} e d b^{2} a B + \frac {6}{5} x^{5} e d c a^{2} B + \frac {3}{5} x^{5} e^{2} b a^{2} B + \frac {3}{5} x^{5} d^{2} c b^{2} A + \frac {2}{5} x^{5} e d b^{3} A + \frac {3}{5} x^{5} d^{2} c^{2} a A + \frac {12}{5} x^{5} e d c b a A + \frac {3}{5} x^{5} e^{2} b^{2} a A + \frac {3}{5} x^{5} e^{2} c a^{2} A + \frac {3}{4} x^{4} d^{2} b^{2} a B + \frac {3}{4} x^{4} d^{2} c a^{2} B + \frac {3}{2} x^{4} e d b a^{2} B + \frac {1}{4} x^{4} e^{2} a^{3} B + \frac {1}{4} x^{4} d^{2} b^{3} A + \frac {3}{2} x^{4} d^{2} c b a A + \frac {3}{2} x^{4} e d b^{2} a A + \frac {3}{2} x^{4} e d c a^{2} A + \frac {3}{4} x^{4} e^{2} b a^{2} A + x^{3} d^{2} b a^{2} B + \frac {2}{3} x^{3} e d a^{3} B + x^{3} d^{2} b^{2} a A + x^{3} d^{2} c a^{2} A + 2 x^{3} e d b a^{2} A + \frac {1}{3} x^{3} e^{2} a^{3} A + \frac {1}{2} x^{2} d^{2} a^{3} B + \frac {3}{2} x^{2} d^{2} b a^{2} A + x^{2} e d a^{3} A + x d^{2} a^{3} A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 727, normalized size = 1.31 \[ \frac {1}{10} \, B c^{3} x^{10} e^{2} + \frac {2}{9} \, B c^{3} d x^{9} e + \frac {1}{8} \, B c^{3} d^{2} x^{8} + \frac {1}{3} \, B b c^{2} x^{9} e^{2} + \frac {1}{9} \, A c^{3} x^{9} e^{2} + \frac {3}{4} \, B b c^{2} d x^{8} e + \frac {1}{4} \, A c^{3} d x^{8} e + \frac {3}{7} \, B b c^{2} d^{2} x^{7} + \frac {1}{7} \, A c^{3} d^{2} x^{7} + \frac {3}{8} \, B b^{2} c x^{8} e^{2} + \frac {3}{8} \, B a c^{2} x^{8} e^{2} + \frac {3}{8} \, A b c^{2} x^{8} e^{2} + \frac {6}{7} \, B b^{2} c d x^{7} e + \frac {6}{7} \, B a c^{2} d x^{7} e + \frac {6}{7} \, A b c^{2} d x^{7} e + \frac {1}{2} \, B b^{2} c d^{2} x^{6} + \frac {1}{2} \, B a c^{2} d^{2} x^{6} + \frac {1}{2} \, A b c^{2} d^{2} x^{6} + \frac {1}{7} \, B b^{3} x^{7} e^{2} + \frac {6}{7} \, B a b c x^{7} e^{2} + \frac {3}{7} \, A b^{2} c x^{7} e^{2} + \frac {3}{7} \, A a c^{2} x^{7} e^{2} + \frac {1}{3} \, B b^{3} d x^{6} e + 2 \, B a b c d x^{6} e + A b^{2} c d x^{6} e + A a c^{2} d x^{6} e + \frac {1}{5} \, B b^{3} d^{2} x^{5} + \frac {6}{5} \, B a b c d^{2} x^{5} + \frac {3}{5} \, A b^{2} c d^{2} x^{5} + \frac {3}{5} \, A a c^{2} d^{2} x^{5} + \frac {1}{2} \, B a b^{2} x^{6} e^{2} + \frac {1}{6} \, A b^{3} x^{6} e^{2} + \frac {1}{2} \, B a^{2} c x^{6} e^{2} + A a b c x^{6} e^{2} + \frac {6}{5} \, B a b^{2} d x^{5} e + \frac {2}{5} \, A b^{3} d x^{5} e + \frac {6}{5} \, B a^{2} c d x^{5} e + \frac {12}{5} \, A a b c d x^{5} e + \frac {3}{4} \, B a b^{2} d^{2} x^{4} + \frac {1}{4} \, A b^{3} d^{2} x^{4} + \frac {3}{4} \, B a^{2} c d^{2} x^{4} + \frac {3}{2} \, A a b c d^{2} x^{4} + \frac {3}{5} \, B a^{2} b x^{5} e^{2} + \frac {3}{5} \, A a b^{2} x^{5} e^{2} + \frac {3}{5} \, A a^{2} c x^{5} e^{2} + \frac {3}{2} \, B a^{2} b d x^{4} e + \frac {3}{2} \, A a b^{2} d x^{4} e + \frac {3}{2} \, A a^{2} c d x^{4} e + B a^{2} b d^{2} x^{3} + A a b^{2} d^{2} x^{3} + A a^{2} c d^{2} x^{3} + \frac {1}{4} \, B a^{3} x^{4} e^{2} + \frac {3}{4} \, A a^{2} b x^{4} e^{2} + \frac {2}{3} \, B a^{3} d x^{3} e + 2 \, A a^{2} b d x^{3} e + \frac {1}{2} \, B a^{3} d^{2} x^{2} + \frac {3}{2} \, A a^{2} b d^{2} x^{2} + \frac {1}{3} \, A a^{3} x^{3} e^{2} + A a^{3} d x^{2} e + A a^{3} d^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 597, normalized size = 1.08 \[ \frac {B \,c^{3} e^{2} x^{10}}{10}+\frac {\left (3 B b \,c^{2} e^{2}+\left (A \,e^{2}+2 B d e \right ) c^{3}\right ) x^{9}}{9}+\frac {\left (\left (a \,c^{2}+2 b^{2} c +\left (2 a c +b^{2}\right ) c \right ) B \,e^{2}+3 \left (A \,e^{2}+2 B d e \right ) b \,c^{2}+\left (2 A d e +B \,d^{2}\right ) c^{3}\right ) x^{8}}{8}+A \,a^{3} d^{2} x +\frac {\left (A \,c^{3} d^{2}+\left (4 a b c +\left (2 a c +b^{2}\right ) b \right ) B \,e^{2}+3 \left (2 A d e +B \,d^{2}\right ) b \,c^{2}+\left (A \,e^{2}+2 B d e \right ) \left (a \,c^{2}+2 b^{2} c +\left (2 a c +b^{2}\right ) c \right )\right ) x^{7}}{7}+\frac {\left (3 A b \,c^{2} d^{2}+\left (a^{2} c +2 a \,b^{2}+\left (2 a c +b^{2}\right ) a \right ) B \,e^{2}+\left (2 A d e +B \,d^{2}\right ) \left (a \,c^{2}+2 b^{2} c +\left (2 a c +b^{2}\right ) c \right )+\left (A \,e^{2}+2 B d e \right ) \left (4 a b c +\left (2 a c +b^{2}\right ) b \right )\right ) x^{6}}{6}+\frac {\left (3 B \,a^{2} b \,e^{2}+\left (a \,c^{2}+2 b^{2} c +\left (2 a c +b^{2}\right ) c \right ) A \,d^{2}+\left (2 A d e +B \,d^{2}\right ) \left (4 a b c +\left (2 a c +b^{2}\right ) b \right )+\left (A \,e^{2}+2 B d e \right ) \left (a^{2} c +2 a \,b^{2}+\left (2 a c +b^{2}\right ) a \right )\right ) x^{5}}{5}+\frac {\left (B \,a^{3} e^{2}+\left (4 a b c +\left (2 a c +b^{2}\right ) b \right ) A \,d^{2}+3 \left (A \,e^{2}+2 B d e \right ) a^{2} b +\left (2 A d e +B \,d^{2}\right ) \left (a^{2} c +2 a \,b^{2}+\left (2 a c +b^{2}\right ) a \right )\right ) x^{4}}{4}+\frac {\left (\left (a^{2} c +2 a \,b^{2}+\left (2 a c +b^{2}\right ) a \right ) A \,d^{2}+\left (A \,e^{2}+2 B d e \right ) a^{3}+3 \left (2 A d e +B \,d^{2}\right ) a^{2} b \right ) x^{3}}{3}+\frac {\left (3 A \,a^{2} b \,d^{2}+\left (2 A d e +B \,d^{2}\right ) a^{3}\right ) x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 529, normalized size = 0.95 \[ \frac {1}{10} \, B c^{3} e^{2} x^{10} + \frac {1}{9} \, {\left (2 \, B c^{3} d e + {\left (3 \, B b c^{2} + A c^{3}\right )} e^{2}\right )} x^{9} + \frac {1}{8} \, {\left (B c^{3} d^{2} + 2 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d e + 3 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} e^{2}\right )} x^{8} + \frac {1}{7} \, {\left ({\left (3 \, B b c^{2} + A c^{3}\right )} d^{2} + 6 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d e + {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} e^{2}\right )} x^{7} + A a^{3} d^{2} x + \frac {1}{6} \, {\left (3 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{2} + 2 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d e + {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} e^{2}\right )} x^{6} + \frac {1}{5} \, {\left ({\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d^{2} + 2 \, {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} d e + 3 \, {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} e^{2}\right )} x^{5} + \frac {1}{4} \, {\left ({\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} d^{2} + 6 \, {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} d e + {\left (B a^{3} + 3 \, A a^{2} b\right )} e^{2}\right )} x^{4} + \frac {1}{3} \, {\left (A a^{3} e^{2} + 3 \, {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} d^{2} + 2 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} d e\right )} x^{3} + \frac {1}{2} \, {\left (2 \, A a^{3} d e + {\left (B a^{3} + 3 \, A a^{2} b\right )} d^{2}\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.49, size = 578, normalized size = 1.04 \[ x^3\,\left (\frac {2\,B\,a^3\,d\,e}{3}+\frac {A\,a^3\,e^2}{3}+B\,a^2\,b\,d^2+2\,A\,a^2\,b\,d\,e+A\,c\,a^2\,d^2+A\,a\,b^2\,d^2\right )+x^8\,\left (\frac {3\,B\,b^2\,c\,e^2}{8}+\frac {3\,B\,b\,c^2\,d\,e}{4}+\frac {3\,A\,b\,c^2\,e^2}{8}+\frac {B\,c^3\,d^2}{8}+\frac {A\,c^3\,d\,e}{4}+\frac {3\,B\,a\,c^2\,e^2}{8}\right )+x^4\,\left (\frac {B\,a^3\,e^2}{4}+\frac {3\,B\,a^2\,b\,d\,e}{2}+\frac {3\,A\,a^2\,b\,e^2}{4}+\frac {3\,B\,c\,a^2\,d^2}{4}+\frac {3\,A\,c\,a^2\,d\,e}{2}+\frac {3\,B\,a\,b^2\,d^2}{4}+\frac {3\,A\,a\,b^2\,d\,e}{2}+\frac {3\,A\,c\,a\,b\,d^2}{2}+\frac {A\,b^3\,d^2}{4}\right )+x^7\,\left (\frac {B\,b^3\,e^2}{7}+\frac {6\,B\,b^2\,c\,d\,e}{7}+\frac {3\,A\,b^2\,c\,e^2}{7}+\frac {3\,B\,b\,c^2\,d^2}{7}+\frac {6\,A\,b\,c^2\,d\,e}{7}+\frac {6\,B\,a\,b\,c\,e^2}{7}+\frac {A\,c^3\,d^2}{7}+\frac {6\,B\,a\,c^2\,d\,e}{7}+\frac {3\,A\,a\,c^2\,e^2}{7}\right )+x^5\,\left (\frac {3\,B\,a^2\,b\,e^2}{5}+\frac {6\,B\,a^2\,c\,d\,e}{5}+\frac {3\,A\,a^2\,c\,e^2}{5}+\frac {6\,B\,a\,b^2\,d\,e}{5}+\frac {3\,A\,a\,b^2\,e^2}{5}+\frac {6\,B\,a\,b\,c\,d^2}{5}+\frac {12\,A\,a\,b\,c\,d\,e}{5}+\frac {3\,A\,a\,c^2\,d^2}{5}+\frac {B\,b^3\,d^2}{5}+\frac {2\,A\,b^3\,d\,e}{5}+\frac {3\,A\,b^2\,c\,d^2}{5}\right )+x^6\,\left (\frac {B\,a^2\,c\,e^2}{2}+\frac {B\,a\,b^2\,e^2}{2}+2\,B\,a\,b\,c\,d\,e+A\,a\,b\,c\,e^2+\frac {B\,a\,c^2\,d^2}{2}+A\,a\,c^2\,d\,e+\frac {B\,b^3\,d\,e}{3}+\frac {A\,b^3\,e^2}{6}+\frac {B\,b^2\,c\,d^2}{2}+A\,b^2\,c\,d\,e+\frac {A\,b\,c^2\,d^2}{2}\right )+A\,a^3\,d^2\,x+\frac {a^2\,d\,x^2\,\left (2\,A\,a\,e+3\,A\,b\,d+B\,a\,d\right )}{2}+\frac {c^2\,e\,x^9\,\left (A\,c\,e+3\,B\,b\,e+2\,B\,c\,d\right )}{9}+\frac {B\,c^3\,e^2\,x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 753, normalized size = 1.36 \[ A a^{3} d^{2} x + \frac {B c^{3} e^{2} x^{10}}{10} + x^{9} \left (\frac {A c^{3} e^{2}}{9} + \frac {B b c^{2} e^{2}}{3} + \frac {2 B c^{3} d e}{9}\right ) + x^{8} \left (\frac {3 A b c^{2} e^{2}}{8} + \frac {A c^{3} d e}{4} + \frac {3 B a c^{2} e^{2}}{8} + \frac {3 B b^{2} c e^{2}}{8} + \frac {3 B b c^{2} d e}{4} + \frac {B c^{3} d^{2}}{8}\right ) + x^{7} \left (\frac {3 A a c^{2} e^{2}}{7} + \frac {3 A b^{2} c e^{2}}{7} + \frac {6 A b c^{2} d e}{7} + \frac {A c^{3} d^{2}}{7} + \frac {6 B a b c e^{2}}{7} + \frac {6 B a c^{2} d e}{7} + \frac {B b^{3} e^{2}}{7} + \frac {6 B b^{2} c d e}{7} + \frac {3 B b c^{2} d^{2}}{7}\right ) + x^{6} \left (A a b c e^{2} + A a c^{2} d e + \frac {A b^{3} e^{2}}{6} + A b^{2} c d e + \frac {A b c^{2} d^{2}}{2} + \frac {B a^{2} c e^{2}}{2} + \frac {B a b^{2} e^{2}}{2} + 2 B a b c d e + \frac {B a c^{2} d^{2}}{2} + \frac {B b^{3} d e}{3} + \frac {B b^{2} c d^{2}}{2}\right ) + x^{5} \left (\frac {3 A a^{2} c e^{2}}{5} + \frac {3 A a b^{2} e^{2}}{5} + \frac {12 A a b c d e}{5} + \frac {3 A a c^{2} d^{2}}{5} + \frac {2 A b^{3} d e}{5} + \frac {3 A b^{2} c d^{2}}{5} + \frac {3 B a^{2} b e^{2}}{5} + \frac {6 B a^{2} c d e}{5} + \frac {6 B a b^{2} d e}{5} + \frac {6 B a b c d^{2}}{5} + \frac {B b^{3} d^{2}}{5}\right ) + x^{4} \left (\frac {3 A a^{2} b e^{2}}{4} + \frac {3 A a^{2} c d e}{2} + \frac {3 A a b^{2} d e}{2} + \frac {3 A a b c d^{2}}{2} + \frac {A b^{3} d^{2}}{4} + \frac {B a^{3} e^{2}}{4} + \frac {3 B a^{2} b d e}{2} + \frac {3 B a^{2} c d^{2}}{4} + \frac {3 B a b^{2} d^{2}}{4}\right ) + x^{3} \left (\frac {A a^{3} e^{2}}{3} + 2 A a^{2} b d e + A a^{2} c d^{2} + A a b^{2} d^{2} + \frac {2 B a^{3} d e}{3} + B a^{2} b d^{2}\right ) + x^{2} \left (A a^{3} d e + \frac {3 A a^{2} b d^{2}}{2} + \frac {B a^{3} d^{2}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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