Optimal. Leaf size=173 \[ -\frac {6 b^5 (d+e x)^{13} (b d-a e)}{13 e^7}+\frac {5 b^4 (d+e x)^{12} (b d-a e)^2}{4 e^7}-\frac {20 b^3 (d+e x)^{11} (b d-a e)^3}{11 e^7}+\frac {3 b^2 (d+e x)^{10} (b d-a e)^4}{2 e^7}-\frac {2 b (d+e x)^9 (b d-a e)^5}{3 e^7}+\frac {(d+e x)^8 (b d-a e)^6}{8 e^7}+\frac {b^6 (d+e x)^{14}}{14 e^7} \]
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Rubi [A] time = 0.43, antiderivative size = 173, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {27, 43} \begin {gather*} -\frac {6 b^5 (d+e x)^{13} (b d-a e)}{13 e^7}+\frac {5 b^4 (d+e x)^{12} (b d-a e)^2}{4 e^7}-\frac {20 b^3 (d+e x)^{11} (b d-a e)^3}{11 e^7}+\frac {3 b^2 (d+e x)^{10} (b d-a e)^4}{2 e^7}-\frac {2 b (d+e x)^9 (b d-a e)^5}{3 e^7}+\frac {(d+e x)^8 (b d-a e)^6}{8 e^7}+\frac {b^6 (d+e x)^{14}}{14 e^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int (d+e x)^7 \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx &=\int (a+b x)^6 (d+e x)^7 \, dx\\ &=\int \left (\frac {(-b d+a e)^6 (d+e x)^7}{e^6}-\frac {6 b (b d-a e)^5 (d+e x)^8}{e^6}+\frac {15 b^2 (b d-a e)^4 (d+e x)^9}{e^6}-\frac {20 b^3 (b d-a e)^3 (d+e x)^{10}}{e^6}+\frac {15 b^4 (b d-a e)^2 (d+e x)^{11}}{e^6}-\frac {6 b^5 (b d-a e) (d+e x)^{12}}{e^6}+\frac {b^6 (d+e x)^{13}}{e^6}\right ) \, dx\\ &=\frac {(b d-a e)^6 (d+e x)^8}{8 e^7}-\frac {2 b (b d-a e)^5 (d+e x)^9}{3 e^7}+\frac {3 b^2 (b d-a e)^4 (d+e x)^{10}}{2 e^7}-\frac {20 b^3 (b d-a e)^3 (d+e x)^{11}}{11 e^7}+\frac {5 b^4 (b d-a e)^2 (d+e x)^{12}}{4 e^7}-\frac {6 b^5 (b d-a e) (d+e x)^{13}}{13 e^7}+\frac {b^6 (d+e x)^{14}}{14 e^7}\\ \end {align*}
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Mathematica [B] time = 0.10, size = 684, normalized size = 3.95 \begin {gather*} a^6 d^7 x+\frac {1}{2} a^5 d^6 x^2 (7 a e+6 b d)+\frac {1}{4} b^4 e^5 x^{12} \left (5 a^2 e^2+14 a b d e+7 b^2 d^2\right )+a^4 d^5 x^3 \left (7 a^2 e^2+14 a b d e+5 b^2 d^2\right )+\frac {1}{11} b^3 e^4 x^{11} \left (20 a^3 e^3+105 a^2 b d e^2+126 a b^2 d^2 e+35 b^3 d^3\right )+\frac {1}{4} a^3 d^4 x^4 \left (35 a^3 e^3+126 a^2 b d e^2+105 a b^2 d^2 e+20 b^3 d^3\right )+\frac {1}{2} b^2 e^3 x^{10} \left (3 a^4 e^4+28 a^3 b d e^3+63 a^2 b^2 d^2 e^2+42 a b^3 d^3 e+7 b^4 d^4\right )+a^2 d^3 x^5 \left (7 a^4 e^4+42 a^3 b d e^3+63 a^2 b^2 d^2 e^2+28 a b^3 d^3 e+3 b^4 d^4\right )+\frac {1}{3} b e^2 x^9 \left (2 a^5 e^5+35 a^4 b d e^4+140 a^3 b^2 d^2 e^3+175 a^2 b^3 d^3 e^2+70 a b^4 d^4 e+7 b^5 d^5\right )+\frac {1}{2} a d^2 x^6 \left (7 a^5 e^5+70 a^4 b d e^4+175 a^3 b^2 d^2 e^3+140 a^2 b^3 d^3 e^2+35 a b^4 d^4 e+2 b^5 d^5\right )+\frac {1}{8} e x^8 \left (a^6 e^6+42 a^5 b d e^5+315 a^4 b^2 d^2 e^4+700 a^3 b^3 d^3 e^3+525 a^2 b^4 d^4 e^2+126 a b^5 d^5 e+7 b^6 d^6\right )+\frac {1}{7} d x^7 \left (7 a^6 e^6+126 a^5 b d e^5+525 a^4 b^2 d^2 e^4+700 a^3 b^3 d^3 e^3+315 a^2 b^4 d^4 e^2+42 a b^5 d^5 e+b^6 d^6\right )+\frac {1}{13} b^5 e^6 x^{13} (6 a e+7 b d)+\frac {1}{14} b^6 e^7 x^{14} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (d+e x)^7 \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.35, size = 798, normalized size = 4.61 \begin {gather*} \frac {1}{14} x^{14} e^{7} b^{6} + \frac {7}{13} x^{13} e^{6} d b^{6} + \frac {6}{13} x^{13} e^{7} b^{5} a + \frac {7}{4} x^{12} e^{5} d^{2} b^{6} + \frac {7}{2} x^{12} e^{6} d b^{5} a + \frac {5}{4} x^{12} e^{7} b^{4} a^{2} + \frac {35}{11} x^{11} e^{4} d^{3} b^{6} + \frac {126}{11} x^{11} e^{5} d^{2} b^{5} a + \frac {105}{11} x^{11} e^{6} d b^{4} a^{2} + \frac {20}{11} x^{11} e^{7} b^{3} a^{3} + \frac {7}{2} x^{10} e^{3} d^{4} b^{6} + 21 x^{10} e^{4} d^{3} b^{5} a + \frac {63}{2} x^{10} e^{5} d^{2} b^{4} a^{2} + 14 x^{10} e^{6} d b^{3} a^{3} + \frac {3}{2} x^{10} e^{7} b^{2} a^{4} + \frac {7}{3} x^{9} e^{2} d^{5} b^{6} + \frac {70}{3} x^{9} e^{3} d^{4} b^{5} a + \frac {175}{3} x^{9} e^{4} d^{3} b^{4} a^{2} + \frac {140}{3} x^{9} e^{5} d^{2} b^{3} a^{3} + \frac {35}{3} x^{9} e^{6} d b^{2} a^{4} + \frac {2}{3} x^{9} e^{7} b a^{5} + \frac {7}{8} x^{8} e d^{6} b^{6} + \frac {63}{4} x^{8} e^{2} d^{5} b^{5} a + \frac {525}{8} x^{8} e^{3} d^{4} b^{4} a^{2} + \frac {175}{2} x^{8} e^{4} d^{3} b^{3} a^{3} + \frac {315}{8} x^{8} e^{5} d^{2} b^{2} a^{4} + \frac {21}{4} x^{8} e^{6} d b a^{5} + \frac {1}{8} x^{8} e^{7} a^{6} + \frac {1}{7} x^{7} d^{7} b^{6} + 6 x^{7} e d^{6} b^{5} a + 45 x^{7} e^{2} d^{5} b^{4} a^{2} + 100 x^{7} e^{3} d^{4} b^{3} a^{3} + 75 x^{7} e^{4} d^{3} b^{2} a^{4} + 18 x^{7} e^{5} d^{2} b a^{5} + x^{7} e^{6} d a^{6} + x^{6} d^{7} b^{5} a + \frac {35}{2} x^{6} e d^{6} b^{4} a^{2} + 70 x^{6} e^{2} d^{5} b^{3} a^{3} + \frac {175}{2} x^{6} e^{3} d^{4} b^{2} a^{4} + 35 x^{6} e^{4} d^{3} b a^{5} + \frac {7}{2} x^{6} e^{5} d^{2} a^{6} + 3 x^{5} d^{7} b^{4} a^{2} + 28 x^{5} e d^{6} b^{3} a^{3} + 63 x^{5} e^{2} d^{5} b^{2} a^{4} + 42 x^{5} e^{3} d^{4} b a^{5} + 7 x^{5} e^{4} d^{3} a^{6} + 5 x^{4} d^{7} b^{3} a^{3} + \frac {105}{4} x^{4} e d^{6} b^{2} a^{4} + \frac {63}{2} x^{4} e^{2} d^{5} b a^{5} + \frac {35}{4} x^{4} e^{3} d^{4} a^{6} + 5 x^{3} d^{7} b^{2} a^{4} + 14 x^{3} e d^{6} b a^{5} + 7 x^{3} e^{2} d^{5} a^{6} + 3 x^{2} d^{7} b a^{5} + \frac {7}{2} x^{2} e d^{6} a^{6} + x d^{7} a^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 763, normalized size = 4.41 \begin {gather*} \frac {1}{14} \, b^{6} x^{14} e^{7} + \frac {7}{13} \, b^{6} d x^{13} e^{6} + \frac {7}{4} \, b^{6} d^{2} x^{12} e^{5} + \frac {35}{11} \, b^{6} d^{3} x^{11} e^{4} + \frac {7}{2} \, b^{6} d^{4} x^{10} e^{3} + \frac {7}{3} \, b^{6} d^{5} x^{9} e^{2} + \frac {7}{8} \, b^{6} d^{6} x^{8} e + \frac {1}{7} \, b^{6} d^{7} x^{7} + \frac {6}{13} \, a b^{5} x^{13} e^{7} + \frac {7}{2} \, a b^{5} d x^{12} e^{6} + \frac {126}{11} \, a b^{5} d^{2} x^{11} e^{5} + 21 \, a b^{5} d^{3} x^{10} e^{4} + \frac {70}{3} \, a b^{5} d^{4} x^{9} e^{3} + \frac {63}{4} \, a b^{5} d^{5} x^{8} e^{2} + 6 \, a b^{5} d^{6} x^{7} e + a b^{5} d^{7} x^{6} + \frac {5}{4} \, a^{2} b^{4} x^{12} e^{7} + \frac {105}{11} \, a^{2} b^{4} d x^{11} e^{6} + \frac {63}{2} \, a^{2} b^{4} d^{2} x^{10} e^{5} + \frac {175}{3} \, a^{2} b^{4} d^{3} x^{9} e^{4} + \frac {525}{8} \, a^{2} b^{4} d^{4} x^{8} e^{3} + 45 \, a^{2} b^{4} d^{5} x^{7} e^{2} + \frac {35}{2} \, a^{2} b^{4} d^{6} x^{6} e + 3 \, a^{2} b^{4} d^{7} x^{5} + \frac {20}{11} \, a^{3} b^{3} x^{11} e^{7} + 14 \, a^{3} b^{3} d x^{10} e^{6} + \frac {140}{3} \, a^{3} b^{3} d^{2} x^{9} e^{5} + \frac {175}{2} \, a^{3} b^{3} d^{3} x^{8} e^{4} + 100 \, a^{3} b^{3} d^{4} x^{7} e^{3} + 70 \, a^{3} b^{3} d^{5} x^{6} e^{2} + 28 \, a^{3} b^{3} d^{6} x^{5} e + 5 \, a^{3} b^{3} d^{7} x^{4} + \frac {3}{2} \, a^{4} b^{2} x^{10} e^{7} + \frac {35}{3} \, a^{4} b^{2} d x^{9} e^{6} + \frac {315}{8} \, a^{4} b^{2} d^{2} x^{8} e^{5} + 75 \, a^{4} b^{2} d^{3} x^{7} e^{4} + \frac {175}{2} \, a^{4} b^{2} d^{4} x^{6} e^{3} + 63 \, a^{4} b^{2} d^{5} x^{5} e^{2} + \frac {105}{4} \, a^{4} b^{2} d^{6} x^{4} e + 5 \, a^{4} b^{2} d^{7} x^{3} + \frac {2}{3} \, a^{5} b x^{9} e^{7} + \frac {21}{4} \, a^{5} b d x^{8} e^{6} + 18 \, a^{5} b d^{2} x^{7} e^{5} + 35 \, a^{5} b d^{3} x^{6} e^{4} + 42 \, a^{5} b d^{4} x^{5} e^{3} + \frac {63}{2} \, a^{5} b d^{5} x^{4} e^{2} + 14 \, a^{5} b d^{6} x^{3} e + 3 \, a^{5} b d^{7} x^{2} + \frac {1}{8} \, a^{6} x^{8} e^{7} + a^{6} d x^{7} e^{6} + \frac {7}{2} \, a^{6} d^{2} x^{6} e^{5} + 7 \, a^{6} d^{3} x^{5} e^{4} + \frac {35}{4} \, a^{6} d^{4} x^{4} e^{3} + 7 \, a^{6} d^{5} x^{3} e^{2} + \frac {7}{2} \, a^{6} d^{6} x^{2} e + a^{6} d^{7} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 709, normalized size = 4.10 \begin {gather*} \frac {b^{6} e^{7} x^{14}}{14}+a^{6} d^{7} x +\frac {\left (6 e^{7} a \,b^{5}+7 d \,e^{6} b^{6}\right ) x^{13}}{13}+\frac {\left (15 e^{7} a^{2} b^{4}+42 d \,e^{6} a \,b^{5}+21 d^{2} e^{5} b^{6}\right ) x^{12}}{12}+\frac {\left (20 e^{7} a^{3} b^{3}+105 d \,e^{6} a^{2} b^{4}+126 d^{2} e^{5} a \,b^{5}+35 d^{3} e^{4} b^{6}\right ) x^{11}}{11}+\frac {\left (15 e^{7} a^{4} b^{2}+140 d \,e^{6} a^{3} b^{3}+315 d^{2} e^{5} a^{2} b^{4}+210 d^{3} e^{4} a \,b^{5}+35 d^{4} e^{3} b^{6}\right ) x^{10}}{10}+\frac {\left (6 e^{7} a^{5} b +105 d \,e^{6} a^{4} b^{2}+420 d^{2} e^{5} a^{3} b^{3}+525 d^{3} e^{4} a^{2} b^{4}+210 d^{4} e^{3} a \,b^{5}+21 d^{5} e^{2} b^{6}\right ) x^{9}}{9}+\frac {\left (e^{7} a^{6}+42 d \,e^{6} a^{5} b +315 d^{2} e^{5} a^{4} b^{2}+700 d^{3} e^{4} a^{3} b^{3}+525 d^{4} e^{3} a^{2} b^{4}+126 d^{5} e^{2} a \,b^{5}+7 d^{6} e \,b^{6}\right ) x^{8}}{8}+\frac {\left (7 d \,e^{6} a^{6}+126 d^{2} e^{5} a^{5} b +525 d^{3} e^{4} a^{4} b^{2}+700 d^{4} e^{3} a^{3} b^{3}+315 d^{5} e^{2} a^{2} b^{4}+42 d^{6} e a \,b^{5}+d^{7} b^{6}\right ) x^{7}}{7}+\frac {\left (21 d^{2} e^{5} a^{6}+210 d^{3} e^{4} a^{5} b +525 d^{4} e^{3} a^{4} b^{2}+420 d^{5} e^{2} a^{3} b^{3}+105 d^{6} e \,a^{2} b^{4}+6 d^{7} a \,b^{5}\right ) x^{6}}{6}+\frac {\left (35 d^{3} e^{4} a^{6}+210 d^{4} e^{3} a^{5} b +315 d^{5} e^{2} a^{4} b^{2}+140 d^{6} e \,a^{3} b^{3}+15 d^{7} a^{2} b^{4}\right ) x^{5}}{5}+\frac {\left (35 d^{4} e^{3} a^{6}+126 d^{5} e^{2} a^{5} b +105 d^{6} e \,a^{4} b^{2}+20 d^{7} a^{3} b^{3}\right ) x^{4}}{4}+\frac {\left (21 d^{5} e^{2} a^{6}+42 d^{6} e \,a^{5} b +15 d^{7} a^{4} b^{2}\right ) x^{3}}{3}+\frac {\left (7 d^{6} e \,a^{6}+6 d^{7} a^{5} b \right ) x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.50, size = 706, normalized size = 4.08 \begin {gather*} \frac {1}{14} \, b^{6} e^{7} x^{14} + a^{6} d^{7} x + \frac {1}{13} \, {\left (7 \, b^{6} d e^{6} + 6 \, a b^{5} e^{7}\right )} x^{13} + \frac {1}{4} \, {\left (7 \, b^{6} d^{2} e^{5} + 14 \, a b^{5} d e^{6} + 5 \, a^{2} b^{4} e^{7}\right )} x^{12} + \frac {1}{11} \, {\left (35 \, b^{6} d^{3} e^{4} + 126 \, a b^{5} d^{2} e^{5} + 105 \, a^{2} b^{4} d e^{6} + 20 \, a^{3} b^{3} e^{7}\right )} x^{11} + \frac {1}{2} \, {\left (7 \, b^{6} d^{4} e^{3} + 42 \, a b^{5} d^{3} e^{4} + 63 \, a^{2} b^{4} d^{2} e^{5} + 28 \, a^{3} b^{3} d e^{6} + 3 \, a^{4} b^{2} e^{7}\right )} x^{10} + \frac {1}{3} \, {\left (7 \, b^{6} d^{5} e^{2} + 70 \, a b^{5} d^{4} e^{3} + 175 \, a^{2} b^{4} d^{3} e^{4} + 140 \, a^{3} b^{3} d^{2} e^{5} + 35 \, a^{4} b^{2} d e^{6} + 2 \, a^{5} b e^{7}\right )} x^{9} + \frac {1}{8} \, {\left (7 \, b^{6} d^{6} e + 126 \, a b^{5} d^{5} e^{2} + 525 \, a^{2} b^{4} d^{4} e^{3} + 700 \, a^{3} b^{3} d^{3} e^{4} + 315 \, a^{4} b^{2} d^{2} e^{5} + 42 \, a^{5} b d e^{6} + a^{6} e^{7}\right )} x^{8} + \frac {1}{7} \, {\left (b^{6} d^{7} + 42 \, a b^{5} d^{6} e + 315 \, a^{2} b^{4} d^{5} e^{2} + 700 \, a^{3} b^{3} d^{4} e^{3} + 525 \, a^{4} b^{2} d^{3} e^{4} + 126 \, a^{5} b d^{2} e^{5} + 7 \, a^{6} d e^{6}\right )} x^{7} + \frac {1}{2} \, {\left (2 \, a b^{5} d^{7} + 35 \, a^{2} b^{4} d^{6} e + 140 \, a^{3} b^{3} d^{5} e^{2} + 175 \, a^{4} b^{2} d^{4} e^{3} + 70 \, a^{5} b d^{3} e^{4} + 7 \, a^{6} d^{2} e^{5}\right )} x^{6} + {\left (3 \, a^{2} b^{4} d^{7} + 28 \, a^{3} b^{3} d^{6} e + 63 \, a^{4} b^{2} d^{5} e^{2} + 42 \, a^{5} b d^{4} e^{3} + 7 \, a^{6} d^{3} e^{4}\right )} x^{5} + \frac {1}{4} \, {\left (20 \, a^{3} b^{3} d^{7} + 105 \, a^{4} b^{2} d^{6} e + 126 \, a^{5} b d^{5} e^{2} + 35 \, a^{6} d^{4} e^{3}\right )} x^{4} + {\left (5 \, a^{4} b^{2} d^{7} + 14 \, a^{5} b d^{6} e + 7 \, a^{6} d^{5} e^{2}\right )} x^{3} + \frac {1}{2} \, {\left (6 \, a^{5} b d^{7} + 7 \, a^{6} d^{6} e\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.27, size = 683, normalized size = 3.95 \begin {gather*} x^5\,\left (7\,a^6\,d^3\,e^4+42\,a^5\,b\,d^4\,e^3+63\,a^4\,b^2\,d^5\,e^2+28\,a^3\,b^3\,d^6\,e+3\,a^2\,b^4\,d^7\right )+x^{10}\,\left (\frac {3\,a^4\,b^2\,e^7}{2}+14\,a^3\,b^3\,d\,e^6+\frac {63\,a^2\,b^4\,d^2\,e^5}{2}+21\,a\,b^5\,d^3\,e^4+\frac {7\,b^6\,d^4\,e^3}{2}\right )+x^6\,\left (\frac {7\,a^6\,d^2\,e^5}{2}+35\,a^5\,b\,d^3\,e^4+\frac {175\,a^4\,b^2\,d^4\,e^3}{2}+70\,a^3\,b^3\,d^5\,e^2+\frac {35\,a^2\,b^4\,d^6\,e}{2}+a\,b^5\,d^7\right )+x^9\,\left (\frac {2\,a^5\,b\,e^7}{3}+\frac {35\,a^4\,b^2\,d\,e^6}{3}+\frac {140\,a^3\,b^3\,d^2\,e^5}{3}+\frac {175\,a^2\,b^4\,d^3\,e^4}{3}+\frac {70\,a\,b^5\,d^4\,e^3}{3}+\frac {7\,b^6\,d^5\,e^2}{3}\right )+x^7\,\left (a^6\,d\,e^6+18\,a^5\,b\,d^2\,e^5+75\,a^4\,b^2\,d^3\,e^4+100\,a^3\,b^3\,d^4\,e^3+45\,a^2\,b^4\,d^5\,e^2+6\,a\,b^5\,d^6\,e+\frac {b^6\,d^7}{7}\right )+x^8\,\left (\frac {a^6\,e^7}{8}+\frac {21\,a^5\,b\,d\,e^6}{4}+\frac {315\,a^4\,b^2\,d^2\,e^5}{8}+\frac {175\,a^3\,b^3\,d^3\,e^4}{2}+\frac {525\,a^2\,b^4\,d^4\,e^3}{8}+\frac {63\,a\,b^5\,d^5\,e^2}{4}+\frac {7\,b^6\,d^6\,e}{8}\right )+x^4\,\left (\frac {35\,a^6\,d^4\,e^3}{4}+\frac {63\,a^5\,b\,d^5\,e^2}{2}+\frac {105\,a^4\,b^2\,d^6\,e}{4}+5\,a^3\,b^3\,d^7\right )+x^{11}\,\left (\frac {20\,a^3\,b^3\,e^7}{11}+\frac {105\,a^2\,b^4\,d\,e^6}{11}+\frac {126\,a\,b^5\,d^2\,e^5}{11}+\frac {35\,b^6\,d^3\,e^4}{11}\right )+a^6\,d^7\,x+\frac {b^6\,e^7\,x^{14}}{14}+\frac {a^5\,d^6\,x^2\,\left (7\,a\,e+6\,b\,d\right )}{2}+\frac {b^5\,e^6\,x^{13}\,\left (6\,a\,e+7\,b\,d\right )}{13}+a^4\,d^5\,x^3\,\left (7\,a^2\,e^2+14\,a\,b\,d\,e+5\,b^2\,d^2\right )+\frac {b^4\,e^5\,x^{12}\,\left (5\,a^2\,e^2+14\,a\,b\,d\,e+7\,b^2\,d^2\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.18, size = 796, normalized size = 4.60 \begin {gather*} a^{6} d^{7} x + \frac {b^{6} e^{7} x^{14}}{14} + x^{13} \left (\frac {6 a b^{5} e^{7}}{13} + \frac {7 b^{6} d e^{6}}{13}\right ) + x^{12} \left (\frac {5 a^{2} b^{4} e^{7}}{4} + \frac {7 a b^{5} d e^{6}}{2} + \frac {7 b^{6} d^{2} e^{5}}{4}\right ) + x^{11} \left (\frac {20 a^{3} b^{3} e^{7}}{11} + \frac {105 a^{2} b^{4} d e^{6}}{11} + \frac {126 a b^{5} d^{2} e^{5}}{11} + \frac {35 b^{6} d^{3} e^{4}}{11}\right ) + x^{10} \left (\frac {3 a^{4} b^{2} e^{7}}{2} + 14 a^{3} b^{3} d e^{6} + \frac {63 a^{2} b^{4} d^{2} e^{5}}{2} + 21 a b^{5} d^{3} e^{4} + \frac {7 b^{6} d^{4} e^{3}}{2}\right ) + x^{9} \left (\frac {2 a^{5} b e^{7}}{3} + \frac {35 a^{4} b^{2} d e^{6}}{3} + \frac {140 a^{3} b^{3} d^{2} e^{5}}{3} + \frac {175 a^{2} b^{4} d^{3} e^{4}}{3} + \frac {70 a b^{5} d^{4} e^{3}}{3} + \frac {7 b^{6} d^{5} e^{2}}{3}\right ) + x^{8} \left (\frac {a^{6} e^{7}}{8} + \frac {21 a^{5} b d e^{6}}{4} + \frac {315 a^{4} b^{2} d^{2} e^{5}}{8} + \frac {175 a^{3} b^{3} d^{3} e^{4}}{2} + \frac {525 a^{2} b^{4} d^{4} e^{3}}{8} + \frac {63 a b^{5} d^{5} e^{2}}{4} + \frac {7 b^{6} d^{6} e}{8}\right ) + x^{7} \left (a^{6} d e^{6} + 18 a^{5} b d^{2} e^{5} + 75 a^{4} b^{2} d^{3} e^{4} + 100 a^{3} b^{3} d^{4} e^{3} + 45 a^{2} b^{4} d^{5} e^{2} + 6 a b^{5} d^{6} e + \frac {b^{6} d^{7}}{7}\right ) + x^{6} \left (\frac {7 a^{6} d^{2} e^{5}}{2} + 35 a^{5} b d^{3} e^{4} + \frac {175 a^{4} b^{2} d^{4} e^{3}}{2} + 70 a^{3} b^{3} d^{5} e^{2} + \frac {35 a^{2} b^{4} d^{6} e}{2} + a b^{5} d^{7}\right ) + x^{5} \left (7 a^{6} d^{3} e^{4} + 42 a^{5} b d^{4} e^{3} + 63 a^{4} b^{2} d^{5} e^{2} + 28 a^{3} b^{3} d^{6} e + 3 a^{2} b^{4} d^{7}\right ) + x^{4} \left (\frac {35 a^{6} d^{4} e^{3}}{4} + \frac {63 a^{5} b d^{5} e^{2}}{2} + \frac {105 a^{4} b^{2} d^{6} e}{4} + 5 a^{3} b^{3} d^{7}\right ) + x^{3} \left (7 a^{6} d^{5} e^{2} + 14 a^{5} b d^{6} e + 5 a^{4} b^{2} d^{7}\right ) + x^{2} \left (\frac {7 a^{6} d^{6} e}{2} + 3 a^{5} b d^{7}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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