Optimal. Leaf size=206 \[ -\frac {b^3 (d+e x)^{11} (-4 a B e-A b e+5 b B d)}{11 e^6}+\frac {b^2 (d+e x)^{10} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{5 e^6}-\frac {2 b (d+e x)^9 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6}+\frac {(d+e x)^8 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{8 e^6}-\frac {(d+e x)^7 (b d-a e)^4 (B d-A e)}{7 e^6}+\frac {b^4 B (d+e x)^{12}}{12 e^6} \]
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Rubi [A] time = 0.66, antiderivative size = 206, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {27, 77} \begin {gather*} -\frac {b^3 (d+e x)^{11} (-4 a B e-A b e+5 b B d)}{11 e^6}+\frac {b^2 (d+e x)^{10} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{5 e^6}-\frac {2 b (d+e x)^9 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6}+\frac {(d+e x)^8 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{8 e^6}-\frac {(d+e x)^7 (b d-a e)^4 (B d-A e)}{7 e^6}+\frac {b^4 B (d+e x)^{12}}{12 e^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 77
Rubi steps
\begin {align*} \int (A+B x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^2 \, dx &=\int (a+b x)^4 (A+B x) (d+e x)^6 \, dx\\ &=\int \left (\frac {(-b d+a e)^4 (-B d+A e) (d+e x)^6}{e^5}+\frac {(-b d+a e)^3 (-5 b B d+4 A b e+a B e) (d+e x)^7}{e^5}+\frac {2 b (b d-a e)^2 (-5 b B d+3 A b e+2 a B e) (d+e x)^8}{e^5}-\frac {2 b^2 (b d-a e) (-5 b B d+2 A b e+3 a B e) (d+e x)^9}{e^5}+\frac {b^3 (-5 b B d+A b e+4 a B e) (d+e x)^{10}}{e^5}+\frac {b^4 B (d+e x)^{11}}{e^5}\right ) \, dx\\ &=-\frac {(b d-a e)^4 (B d-A e) (d+e x)^7}{7 e^6}+\frac {(b d-a e)^3 (5 b B d-4 A b e-a B e) (d+e x)^8}{8 e^6}-\frac {2 b (b d-a e)^2 (5 b B d-3 A b e-2 a B e) (d+e x)^9}{9 e^6}+\frac {b^2 (b d-a e) (5 b B d-2 A b e-3 a B e) (d+e x)^{10}}{5 e^6}-\frac {b^3 (5 b B d-A b e-4 a B e) (d+e x)^{11}}{11 e^6}+\frac {b^4 B (d+e x)^{12}}{12 e^6}\\ \end {align*}
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Mathematica [B] time = 0.25, size = 737, normalized size = 3.58 \begin {gather*} a^4 A d^6 x+\frac {1}{2} a^3 d^5 x^2 (6 a A e+a B d+4 A b d)+\frac {1}{3} a^2 d^4 x^3 \left (3 A \left (5 a^2 e^2+8 a b d e+2 b^2 d^2\right )+2 a B d (3 a e+2 b d)\right )+\frac {1}{10} b^2 e^4 x^{10} \left (6 a^2 B e^2+4 a b e (A e+6 B d)+3 b^2 d (2 A e+5 B d)\right )+\frac {1}{9} b e^3 x^9 \left (4 a^3 B e^3+6 a^2 b e^2 (A e+6 B d)+12 a b^2 d e (2 A e+5 B d)+5 b^3 d^2 (3 A e+4 B d)\right )+\frac {1}{4} a d^3 x^4 \left (3 a B d \left (5 a^2 e^2+8 a b d e+2 b^2 d^2\right )+4 A \left (5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right )\right )+\frac {1}{8} e^2 x^8 \left (a^4 B e^4+4 a^3 b e^3 (A e+6 B d)+18 a^2 b^2 d e^2 (2 A e+5 B d)+20 a b^3 d^2 e (3 A e+4 B d)+5 b^4 d^3 (4 A e+3 B d)\right )+\frac {1}{7} e x^7 \left (a^4 e^4 (A e+6 B d)+12 a^3 b d e^3 (2 A e+5 B d)+30 a^2 b^2 d^2 e^2 (3 A e+4 B d)+20 a b^3 d^3 e (4 A e+3 B d)+3 b^4 d^4 (5 A e+2 B d)\right )+\frac {1}{6} d x^6 \left (3 a^4 e^4 (2 A e+5 B d)+20 a^3 b d e^3 (3 A e+4 B d)+30 a^2 b^2 d^2 e^2 (4 A e+3 B d)+12 a b^3 d^3 e (5 A e+2 B d)+b^4 d^4 (6 A e+B d)\right )+\frac {1}{5} d^2 x^5 \left (4 a B d \left (5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right )+A \left (15 a^4 e^4+80 a^3 b d e^3+90 a^2 b^2 d^2 e^2+24 a b^3 d^3 e+b^4 d^4\right )\right )+\frac {1}{11} b^3 e^5 x^{11} (4 a B e+A b e+6 b B d)+\frac {1}{12} b^4 B e^6 x^{12} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (A+B x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.38, size = 1015, normalized size = 4.93 \begin {gather*} \frac {1}{12} x^{12} e^{6} b^{4} B + \frac {6}{11} x^{11} e^{5} d b^{4} B + \frac {4}{11} x^{11} e^{6} b^{3} a B + \frac {1}{11} x^{11} e^{6} b^{4} A + \frac {3}{2} x^{10} e^{4} d^{2} b^{4} B + \frac {12}{5} x^{10} e^{5} d b^{3} a B + \frac {3}{5} x^{10} e^{6} b^{2} a^{2} B + \frac {3}{5} x^{10} e^{5} d b^{4} A + \frac {2}{5} x^{10} e^{6} b^{3} a A + \frac {20}{9} x^{9} e^{3} d^{3} b^{4} B + \frac {20}{3} x^{9} e^{4} d^{2} b^{3} a B + 4 x^{9} e^{5} d b^{2} a^{2} B + \frac {4}{9} x^{9} e^{6} b a^{3} B + \frac {5}{3} x^{9} e^{4} d^{2} b^{4} A + \frac {8}{3} x^{9} e^{5} d b^{3} a A + \frac {2}{3} x^{9} e^{6} b^{2} a^{2} A + \frac {15}{8} x^{8} e^{2} d^{4} b^{4} B + 10 x^{8} e^{3} d^{3} b^{3} a B + \frac {45}{4} x^{8} e^{4} d^{2} b^{2} a^{2} B + 3 x^{8} e^{5} d b a^{3} B + \frac {1}{8} x^{8} e^{6} a^{4} B + \frac {5}{2} x^{8} e^{3} d^{3} b^{4} A + \frac {15}{2} x^{8} e^{4} d^{2} b^{3} a A + \frac {9}{2} x^{8} e^{5} d b^{2} a^{2} A + \frac {1}{2} x^{8} e^{6} b a^{3} A + \frac {6}{7} x^{7} e d^{5} b^{4} B + \frac {60}{7} x^{7} e^{2} d^{4} b^{3} a B + \frac {120}{7} x^{7} e^{3} d^{3} b^{2} a^{2} B + \frac {60}{7} x^{7} e^{4} d^{2} b a^{3} B + \frac {6}{7} x^{7} e^{5} d a^{4} B + \frac {15}{7} x^{7} e^{2} d^{4} b^{4} A + \frac {80}{7} x^{7} e^{3} d^{3} b^{3} a A + \frac {90}{7} x^{7} e^{4} d^{2} b^{2} a^{2} A + \frac {24}{7} x^{7} e^{5} d b a^{3} A + \frac {1}{7} x^{7} e^{6} a^{4} A + \frac {1}{6} x^{6} d^{6} b^{4} B + 4 x^{6} e d^{5} b^{3} a B + 15 x^{6} e^{2} d^{4} b^{2} a^{2} B + \frac {40}{3} x^{6} e^{3} d^{3} b a^{3} B + \frac {5}{2} x^{6} e^{4} d^{2} a^{4} B + x^{6} e d^{5} b^{4} A + 10 x^{6} e^{2} d^{4} b^{3} a A + 20 x^{6} e^{3} d^{3} b^{2} a^{2} A + 10 x^{6} e^{4} d^{2} b a^{3} A + x^{6} e^{5} d a^{4} A + \frac {4}{5} x^{5} d^{6} b^{3} a B + \frac {36}{5} x^{5} e d^{5} b^{2} a^{2} B + 12 x^{5} e^{2} d^{4} b a^{3} B + 4 x^{5} e^{3} d^{3} a^{4} B + \frac {1}{5} x^{5} d^{6} b^{4} A + \frac {24}{5} x^{5} e d^{5} b^{3} a A + 18 x^{5} e^{2} d^{4} b^{2} a^{2} A + 16 x^{5} e^{3} d^{3} b a^{3} A + 3 x^{5} e^{4} d^{2} a^{4} A + \frac {3}{2} x^{4} d^{6} b^{2} a^{2} B + 6 x^{4} e d^{5} b a^{3} B + \frac {15}{4} x^{4} e^{2} d^{4} a^{4} B + x^{4} d^{6} b^{3} a A + 9 x^{4} e d^{5} b^{2} a^{2} A + 15 x^{4} e^{2} d^{4} b a^{3} A + 5 x^{4} e^{3} d^{3} a^{4} A + \frac {4}{3} x^{3} d^{6} b a^{3} B + 2 x^{3} e d^{5} a^{4} B + 2 x^{3} d^{6} b^{2} a^{2} A + 8 x^{3} e d^{5} b a^{3} A + 5 x^{3} e^{2} d^{4} a^{4} A + \frac {1}{2} x^{2} d^{6} a^{4} B + 2 x^{2} d^{6} b a^{3} A + 3 x^{2} e d^{5} a^{4} A + x d^{6} a^{4} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 975, normalized size = 4.73 \begin {gather*} \frac {1}{12} \, B b^{4} x^{12} e^{6} + \frac {6}{11} \, B b^{4} d x^{11} e^{5} + \frac {3}{2} \, B b^{4} d^{2} x^{10} e^{4} + \frac {20}{9} \, B b^{4} d^{3} x^{9} e^{3} + \frac {15}{8} \, B b^{4} d^{4} x^{8} e^{2} + \frac {6}{7} \, B b^{4} d^{5} x^{7} e + \frac {1}{6} \, B b^{4} d^{6} x^{6} + \frac {4}{11} \, B a b^{3} x^{11} e^{6} + \frac {1}{11} \, A b^{4} x^{11} e^{6} + \frac {12}{5} \, B a b^{3} d x^{10} e^{5} + \frac {3}{5} \, A b^{4} d x^{10} e^{5} + \frac {20}{3} \, B a b^{3} d^{2} x^{9} e^{4} + \frac {5}{3} \, A b^{4} d^{2} x^{9} e^{4} + 10 \, B a b^{3} d^{3} x^{8} e^{3} + \frac {5}{2} \, A b^{4} d^{3} x^{8} e^{3} + \frac {60}{7} \, B a b^{3} d^{4} x^{7} e^{2} + \frac {15}{7} \, A b^{4} d^{4} x^{7} e^{2} + 4 \, B a b^{3} d^{5} x^{6} e + A b^{4} d^{5} x^{6} e + \frac {4}{5} \, B a b^{3} d^{6} x^{5} + \frac {1}{5} \, A b^{4} d^{6} x^{5} + \frac {3}{5} \, B a^{2} b^{2} x^{10} e^{6} + \frac {2}{5} \, A a b^{3} x^{10} e^{6} + 4 \, B a^{2} b^{2} d x^{9} e^{5} + \frac {8}{3} \, A a b^{3} d x^{9} e^{5} + \frac {45}{4} \, B a^{2} b^{2} d^{2} x^{8} e^{4} + \frac {15}{2} \, A a b^{3} d^{2} x^{8} e^{4} + \frac {120}{7} \, B a^{2} b^{2} d^{3} x^{7} e^{3} + \frac {80}{7} \, A a b^{3} d^{3} x^{7} e^{3} + 15 \, B a^{2} b^{2} d^{4} x^{6} e^{2} + 10 \, A a b^{3} d^{4} x^{6} e^{2} + \frac {36}{5} \, B a^{2} b^{2} d^{5} x^{5} e + \frac {24}{5} \, A a b^{3} d^{5} x^{5} e + \frac {3}{2} \, B a^{2} b^{2} d^{6} x^{4} + A a b^{3} d^{6} x^{4} + \frac {4}{9} \, B a^{3} b x^{9} e^{6} + \frac {2}{3} \, A a^{2} b^{2} x^{9} e^{6} + 3 \, B a^{3} b d x^{8} e^{5} + \frac {9}{2} \, A a^{2} b^{2} d x^{8} e^{5} + \frac {60}{7} \, B a^{3} b d^{2} x^{7} e^{4} + \frac {90}{7} \, A a^{2} b^{2} d^{2} x^{7} e^{4} + \frac {40}{3} \, B a^{3} b d^{3} x^{6} e^{3} + 20 \, A a^{2} b^{2} d^{3} x^{6} e^{3} + 12 \, B a^{3} b d^{4} x^{5} e^{2} + 18 \, A a^{2} b^{2} d^{4} x^{5} e^{2} + 6 \, B a^{3} b d^{5} x^{4} e + 9 \, A a^{2} b^{2} d^{5} x^{4} e + \frac {4}{3} \, B a^{3} b d^{6} x^{3} + 2 \, A a^{2} b^{2} d^{6} x^{3} + \frac {1}{8} \, B a^{4} x^{8} e^{6} + \frac {1}{2} \, A a^{3} b x^{8} e^{6} + \frac {6}{7} \, B a^{4} d x^{7} e^{5} + \frac {24}{7} \, A a^{3} b d x^{7} e^{5} + \frac {5}{2} \, B a^{4} d^{2} x^{6} e^{4} + 10 \, A a^{3} b d^{2} x^{6} e^{4} + 4 \, B a^{4} d^{3} x^{5} e^{3} + 16 \, A a^{3} b d^{3} x^{5} e^{3} + \frac {15}{4} \, B a^{4} d^{4} x^{4} e^{2} + 15 \, A a^{3} b d^{4} x^{4} e^{2} + 2 \, B a^{4} d^{5} x^{3} e + 8 \, A a^{3} b d^{5} x^{3} e + \frac {1}{2} \, B a^{4} d^{6} x^{2} + 2 \, A a^{3} b d^{6} x^{2} + \frac {1}{7} \, A a^{4} x^{7} e^{6} + A a^{4} d x^{6} e^{5} + 3 \, A a^{4} d^{2} x^{5} e^{4} + 5 \, A a^{4} d^{3} x^{4} e^{3} + 5 \, A a^{4} d^{4} x^{3} e^{2} + 3 \, A a^{4} d^{5} x^{2} e + A a^{4} d^{6} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 821, normalized size = 3.99 \begin {gather*} \frac {B \,b^{4} e^{6} x^{12}}{12}+A \,a^{4} d^{6} x +\frac {\left (4 B a \,b^{3} e^{6}+\left (A \,e^{6}+6 B d \,e^{5}\right ) b^{4}\right ) x^{11}}{11}+\frac {\left (6 B \,a^{2} b^{2} e^{6}+4 \left (A \,e^{6}+6 B d \,e^{5}\right ) a \,b^{3}+\left (6 A d \,e^{5}+15 B \,d^{2} e^{4}\right ) b^{4}\right ) x^{10}}{10}+\frac {\left (4 B \,a^{3} b \,e^{6}+6 \left (A \,e^{6}+6 B d \,e^{5}\right ) a^{2} b^{2}+4 \left (6 A d \,e^{5}+15 B \,d^{2} e^{4}\right ) a \,b^{3}+\left (15 A \,d^{2} e^{4}+20 B \,d^{3} e^{3}\right ) b^{4}\right ) x^{9}}{9}+\frac {\left (B \,a^{4} e^{6}+4 \left (A \,e^{6}+6 B d \,e^{5}\right ) a^{3} b +6 \left (6 A d \,e^{5}+15 B \,d^{2} e^{4}\right ) a^{2} b^{2}+4 \left (15 A \,d^{2} e^{4}+20 B \,d^{3} e^{3}\right ) a \,b^{3}+\left (20 A \,d^{3} e^{3}+15 B \,d^{4} e^{2}\right ) b^{4}\right ) x^{8}}{8}+\frac {\left (\left (A \,e^{6}+6 B d \,e^{5}\right ) a^{4}+4 \left (6 A d \,e^{5}+15 B \,d^{2} e^{4}\right ) a^{3} b +6 \left (15 A \,d^{2} e^{4}+20 B \,d^{3} e^{3}\right ) a^{2} b^{2}+4 \left (20 A \,d^{3} e^{3}+15 B \,d^{4} e^{2}\right ) a \,b^{3}+\left (15 A \,d^{4} e^{2}+6 B \,d^{5} e \right ) b^{4}\right ) x^{7}}{7}+\frac {\left (\left (6 A d \,e^{5}+15 B \,d^{2} e^{4}\right ) a^{4}+4 \left (15 A \,d^{2} e^{4}+20 B \,d^{3} e^{3}\right ) a^{3} b +6 \left (20 A \,d^{3} e^{3}+15 B \,d^{4} e^{2}\right ) a^{2} b^{2}+4 \left (15 A \,d^{4} e^{2}+6 B \,d^{5} e \right ) a \,b^{3}+\left (6 A \,d^{5} e +B \,d^{6}\right ) b^{4}\right ) x^{6}}{6}+\frac {\left (A \,b^{4} d^{6}+\left (15 A \,d^{2} e^{4}+20 B \,d^{3} e^{3}\right ) a^{4}+4 \left (20 A \,d^{3} e^{3}+15 B \,d^{4} e^{2}\right ) a^{3} b +6 \left (15 A \,d^{4} e^{2}+6 B \,d^{5} e \right ) a^{2} b^{2}+4 \left (6 A \,d^{5} e +B \,d^{6}\right ) a \,b^{3}\right ) x^{5}}{5}+\frac {\left (4 A a \,b^{3} d^{6}+\left (20 A \,d^{3} e^{3}+15 B \,d^{4} e^{2}\right ) a^{4}+4 \left (15 A \,d^{4} e^{2}+6 B \,d^{5} e \right ) a^{3} b +6 \left (6 A \,d^{5} e +B \,d^{6}\right ) a^{2} b^{2}\right ) x^{4}}{4}+\frac {\left (6 A \,a^{2} b^{2} d^{6}+\left (15 A \,d^{4} e^{2}+6 B \,d^{5} e \right ) a^{4}+4 \left (6 A \,d^{5} e +B \,d^{6}\right ) a^{3} b \right ) x^{3}}{3}+\frac {\left (4 A \,a^{3} b \,d^{6}+\left (6 A \,d^{5} e +B \,d^{6}\right ) a^{4}\right ) x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.78, size = 810, normalized size = 3.93 \begin {gather*} \frac {1}{12} \, B b^{4} e^{6} x^{12} + A a^{4} d^{6} x + \frac {1}{11} \, {\left (6 \, B b^{4} d e^{5} + {\left (4 \, B a b^{3} + A b^{4}\right )} e^{6}\right )} x^{11} + \frac {1}{10} \, {\left (15 \, B b^{4} d^{2} e^{4} + 6 \, {\left (4 \, B a b^{3} + A b^{4}\right )} d e^{5} + 2 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} e^{6}\right )} x^{10} + \frac {1}{9} \, {\left (20 \, B b^{4} d^{3} e^{3} + 15 \, {\left (4 \, B a b^{3} + A b^{4}\right )} d^{2} e^{4} + 12 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} d e^{5} + 2 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} e^{6}\right )} x^{9} + \frac {1}{8} \, {\left (15 \, B b^{4} d^{4} e^{2} + 20 \, {\left (4 \, B a b^{3} + A b^{4}\right )} d^{3} e^{3} + 30 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} d^{2} e^{4} + 12 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} d e^{5} + {\left (B a^{4} + 4 \, A a^{3} b\right )} e^{6}\right )} x^{8} + \frac {1}{7} \, {\left (6 \, B b^{4} d^{5} e + A a^{4} e^{6} + 15 \, {\left (4 \, B a b^{3} + A b^{4}\right )} d^{4} e^{2} + 40 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} d^{3} e^{3} + 30 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} d^{2} e^{4} + 6 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} d e^{5}\right )} x^{7} + \frac {1}{6} \, {\left (B b^{4} d^{6} + 6 \, A a^{4} d e^{5} + 6 \, {\left (4 \, B a b^{3} + A b^{4}\right )} d^{5} e + 30 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} d^{4} e^{2} + 40 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} d^{3} e^{3} + 15 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} d^{2} e^{4}\right )} x^{6} + \frac {1}{5} \, {\left (15 \, A a^{4} d^{2} e^{4} + {\left (4 \, B a b^{3} + A b^{4}\right )} d^{6} + 12 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} d^{5} e + 30 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} d^{4} e^{2} + 20 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} d^{3} e^{3}\right )} x^{5} + \frac {1}{4} \, {\left (20 \, A a^{4} d^{3} e^{3} + 2 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} d^{6} + 12 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} d^{5} e + 15 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} d^{4} e^{2}\right )} x^{4} + \frac {1}{3} \, {\left (15 \, A a^{4} d^{4} e^{2} + 2 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} d^{6} + 6 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} d^{5} e\right )} x^{3} + \frac {1}{2} \, {\left (6 \, A a^{4} d^{5} e + {\left (B a^{4} + 4 \, A a^{3} b\right )} d^{6}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.22, size = 845, normalized size = 4.10 \begin {gather*} x^4\,\left (\frac {15\,B\,a^4\,d^4\,e^2}{4}+5\,A\,a^4\,d^3\,e^3+6\,B\,a^3\,b\,d^5\,e+15\,A\,a^3\,b\,d^4\,e^2+\frac {3\,B\,a^2\,b^2\,d^6}{2}+9\,A\,a^2\,b^2\,d^5\,e+A\,a\,b^3\,d^6\right )+x^9\,\left (\frac {4\,B\,a^3\,b\,e^6}{9}+4\,B\,a^2\,b^2\,d\,e^5+\frac {2\,A\,a^2\,b^2\,e^6}{3}+\frac {20\,B\,a\,b^3\,d^2\,e^4}{3}+\frac {8\,A\,a\,b^3\,d\,e^5}{3}+\frac {20\,B\,b^4\,d^3\,e^3}{9}+\frac {5\,A\,b^4\,d^2\,e^4}{3}\right )+x^3\,\left (2\,B\,a^4\,d^5\,e+5\,A\,a^4\,d^4\,e^2+\frac {4\,B\,a^3\,b\,d^6}{3}+8\,A\,a^3\,b\,d^5\,e+2\,A\,a^2\,b^2\,d^6\right )+x^{10}\,\left (\frac {3\,B\,a^2\,b^2\,e^6}{5}+\frac {12\,B\,a\,b^3\,d\,e^5}{5}+\frac {2\,A\,a\,b^3\,e^6}{5}+\frac {3\,B\,b^4\,d^2\,e^4}{2}+\frac {3\,A\,b^4\,d\,e^5}{5}\right )+x^5\,\left (4\,B\,a^4\,d^3\,e^3+3\,A\,a^4\,d^2\,e^4+12\,B\,a^3\,b\,d^4\,e^2+16\,A\,a^3\,b\,d^3\,e^3+\frac {36\,B\,a^2\,b^2\,d^5\,e}{5}+18\,A\,a^2\,b^2\,d^4\,e^2+\frac {4\,B\,a\,b^3\,d^6}{5}+\frac {24\,A\,a\,b^3\,d^5\,e}{5}+\frac {A\,b^4\,d^6}{5}\right )+x^8\,\left (\frac {B\,a^4\,e^6}{8}+3\,B\,a^3\,b\,d\,e^5+\frac {A\,a^3\,b\,e^6}{2}+\frac {45\,B\,a^2\,b^2\,d^2\,e^4}{4}+\frac {9\,A\,a^2\,b^2\,d\,e^5}{2}+10\,B\,a\,b^3\,d^3\,e^3+\frac {15\,A\,a\,b^3\,d^2\,e^4}{2}+\frac {15\,B\,b^4\,d^4\,e^2}{8}+\frac {5\,A\,b^4\,d^3\,e^3}{2}\right )+x^6\,\left (\frac {5\,B\,a^4\,d^2\,e^4}{2}+A\,a^4\,d\,e^5+\frac {40\,B\,a^3\,b\,d^3\,e^3}{3}+10\,A\,a^3\,b\,d^2\,e^4+15\,B\,a^2\,b^2\,d^4\,e^2+20\,A\,a^2\,b^2\,d^3\,e^3+4\,B\,a\,b^3\,d^5\,e+10\,A\,a\,b^3\,d^4\,e^2+\frac {B\,b^4\,d^6}{6}+A\,b^4\,d^5\,e\right )+x^7\,\left (\frac {6\,B\,a^4\,d\,e^5}{7}+\frac {A\,a^4\,e^6}{7}+\frac {60\,B\,a^3\,b\,d^2\,e^4}{7}+\frac {24\,A\,a^3\,b\,d\,e^5}{7}+\frac {120\,B\,a^2\,b^2\,d^3\,e^3}{7}+\frac {90\,A\,a^2\,b^2\,d^2\,e^4}{7}+\frac {60\,B\,a\,b^3\,d^4\,e^2}{7}+\frac {80\,A\,a\,b^3\,d^3\,e^3}{7}+\frac {6\,B\,b^4\,d^5\,e}{7}+\frac {15\,A\,b^4\,d^4\,e^2}{7}\right )+\frac {a^3\,d^5\,x^2\,\left (6\,A\,a\,e+4\,A\,b\,d+B\,a\,d\right )}{2}+\frac {b^3\,e^5\,x^{11}\,\left (A\,b\,e+4\,B\,a\,e+6\,B\,b\,d\right )}{11}+A\,a^4\,d^6\,x+\frac {B\,b^4\,e^6\,x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.20, size = 1035, normalized size = 5.02 \begin {gather*} A a^{4} d^{6} x + \frac {B b^{4} e^{6} x^{12}}{12} + x^{11} \left (\frac {A b^{4} e^{6}}{11} + \frac {4 B a b^{3} e^{6}}{11} + \frac {6 B b^{4} d e^{5}}{11}\right ) + x^{10} \left (\frac {2 A a b^{3} e^{6}}{5} + \frac {3 A b^{4} d e^{5}}{5} + \frac {3 B a^{2} b^{2} e^{6}}{5} + \frac {12 B a b^{3} d e^{5}}{5} + \frac {3 B b^{4} d^{2} e^{4}}{2}\right ) + x^{9} \left (\frac {2 A a^{2} b^{2} e^{6}}{3} + \frac {8 A a b^{3} d e^{5}}{3} + \frac {5 A b^{4} d^{2} e^{4}}{3} + \frac {4 B a^{3} b e^{6}}{9} + 4 B a^{2} b^{2} d e^{5} + \frac {20 B a b^{3} d^{2} e^{4}}{3} + \frac {20 B b^{4} d^{3} e^{3}}{9}\right ) + x^{8} \left (\frac {A a^{3} b e^{6}}{2} + \frac {9 A a^{2} b^{2} d e^{5}}{2} + \frac {15 A a b^{3} d^{2} e^{4}}{2} + \frac {5 A b^{4} d^{3} e^{3}}{2} + \frac {B a^{4} e^{6}}{8} + 3 B a^{3} b d e^{5} + \frac {45 B a^{2} b^{2} d^{2} e^{4}}{4} + 10 B a b^{3} d^{3} e^{3} + \frac {15 B b^{4} d^{4} e^{2}}{8}\right ) + x^{7} \left (\frac {A a^{4} e^{6}}{7} + \frac {24 A a^{3} b d e^{5}}{7} + \frac {90 A a^{2} b^{2} d^{2} e^{4}}{7} + \frac {80 A a b^{3} d^{3} e^{3}}{7} + \frac {15 A b^{4} d^{4} e^{2}}{7} + \frac {6 B a^{4} d e^{5}}{7} + \frac {60 B a^{3} b d^{2} e^{4}}{7} + \frac {120 B a^{2} b^{2} d^{3} e^{3}}{7} + \frac {60 B a b^{3} d^{4} e^{2}}{7} + \frac {6 B b^{4} d^{5} e}{7}\right ) + x^{6} \left (A a^{4} d e^{5} + 10 A a^{3} b d^{2} e^{4} + 20 A a^{2} b^{2} d^{3} e^{3} + 10 A a b^{3} d^{4} e^{2} + A b^{4} d^{5} e + \frac {5 B a^{4} d^{2} e^{4}}{2} + \frac {40 B a^{3} b d^{3} e^{3}}{3} + 15 B a^{2} b^{2} d^{4} e^{2} + 4 B a b^{3} d^{5} e + \frac {B b^{4} d^{6}}{6}\right ) + x^{5} \left (3 A a^{4} d^{2} e^{4} + 16 A a^{3} b d^{3} e^{3} + 18 A a^{2} b^{2} d^{4} e^{2} + \frac {24 A a b^{3} d^{5} e}{5} + \frac {A b^{4} d^{6}}{5} + 4 B a^{4} d^{3} e^{3} + 12 B a^{3} b d^{4} e^{2} + \frac {36 B a^{2} b^{2} d^{5} e}{5} + \frac {4 B a b^{3} d^{6}}{5}\right ) + x^{4} \left (5 A a^{4} d^{3} e^{3} + 15 A a^{3} b d^{4} e^{2} + 9 A a^{2} b^{2} d^{5} e + A a b^{3} d^{6} + \frac {15 B a^{4} d^{4} e^{2}}{4} + 6 B a^{3} b d^{5} e + \frac {3 B a^{2} b^{2} d^{6}}{2}\right ) + x^{3} \left (5 A a^{4} d^{4} e^{2} + 8 A a^{3} b d^{5} e + 2 A a^{2} b^{2} d^{6} + 2 B a^{4} d^{5} e + \frac {4 B a^{3} b d^{6}}{3}\right ) + x^{2} \left (3 A a^{4} d^{5} e + 2 A a^{3} b d^{6} + \frac {B a^{4} d^{6}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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