Optimal. Leaf size=435 \[ -\frac {6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{4 e^9 (d+e x)^4}-\frac {c^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (d+e x)^2}+\frac {4 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{3 e^9 (d+e x)^3}+\frac {4 (2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{5 e^9 (d+e x)^5}-\frac {\left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{3 e^9 (d+e x)^6}+\frac {4 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{7 e^9 (d+e x)^7}-\frac {\left (a e^2-b d e+c d^2\right )^4}{8 e^9 (d+e x)^8}+\frac {4 c^3 (2 c d-b e)}{e^9 (d+e x)}+\frac {c^4 \log (d+e x)}{e^9} \]
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Rubi [A] time = 0.46, antiderivative size = 435, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {698} \[ -\frac {6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{4 e^9 (d+e x)^4}-\frac {c^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (d+e x)^2}+\frac {4 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{3 e^9 (d+e x)^3}+\frac {4 (2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{5 e^9 (d+e x)^5}-\frac {\left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{3 e^9 (d+e x)^6}+\frac {4 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{7 e^9 (d+e x)^7}-\frac {\left (a e^2-b d e+c d^2\right )^4}{8 e^9 (d+e x)^8}+\frac {4 c^3 (2 c d-b e)}{e^9 (d+e x)}+\frac {c^4 \log (d+e x)}{e^9} \]
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin {align*} \int \frac {\left (a+b x+c x^2\right )^4}{(d+e x)^9} \, dx &=\int \left (\frac {\left (c d^2-b d e+a e^2\right )^4}{e^8 (d+e x)^9}+\frac {4 (-2 c d+b e) \left (c d^2-b d e+a e^2\right )^3}{e^8 (d+e x)^8}+\frac {2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^8 (d+e x)^7}+\frac {4 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (-7 c^2 d^2+7 b c d e-b^2 e^2-3 a c e^2\right )}{e^8 (d+e x)^6}+\frac {70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )}{e^8 (d+e x)^5}+\frac {4 c (2 c d-b e) \left (-7 c^2 d^2-b^2 e^2+c e (7 b d-3 a e)\right )}{e^8 (d+e x)^4}+\frac {2 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^8 (d+e x)^3}-\frac {4 c^3 (2 c d-b e)}{e^8 (d+e x)^2}+\frac {c^4}{e^8 (d+e x)}\right ) \, dx\\ &=-\frac {\left (c d^2-b d e+a e^2\right )^4}{8 e^9 (d+e x)^8}+\frac {4 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^3}{7 e^9 (d+e x)^7}-\frac {\left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{3 e^9 (d+e x)^6}+\frac {4 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right )}{5 e^9 (d+e x)^5}-\frac {70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )}{4 e^9 (d+e x)^4}+\frac {4 c (2 c d-b e) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right )}{3 e^9 (d+e x)^3}-\frac {c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^9 (d+e x)^2}+\frac {4 c^3 (2 c d-b e)}{e^9 (d+e x)}+\frac {c^4 \log (d+e x)}{e^9}\\ \end {align*}
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Mathematica [A] time = 0.35, size = 740, normalized size = 1.70 \[ \frac {-6 c^2 e^2 \left (3 a^2 e^2 \left (d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right )+10 a b e \left (d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right )+15 b^2 \left (d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right )\right )-4 c e^3 \left (5 a^3 e^3 \left (d^2+8 d e x+28 e^2 x^2\right )+9 a^2 b e^2 \left (d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right )+9 a b^2 e \left (d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right )+5 b^3 \left (d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right )\right )-3 e^4 \left (35 a^4 e^4+20 a^3 b e^3 (d+8 e x)+10 a^2 b^2 e^2 \left (d^2+8 d e x+28 e^2 x^2\right )+4 a b^3 e \left (d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right )+b^4 \left (d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right )\right )-60 c^3 e \left (a e \left (d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right )+7 b \left (d^7+8 d^6 e x+28 d^5 e^2 x^2+56 d^4 e^3 x^3+70 d^3 e^4 x^4+56 d^2 e^5 x^5+28 d e^6 x^6+8 e^7 x^7\right )\right )+c^4 d \left (2283 d^7+17424 d^6 e x+57624 d^5 e^2 x^2+107408 d^4 e^3 x^3+122500 d^3 e^4 x^4+86240 d^2 e^5 x^5+35280 d e^6 x^6+6720 e^7 x^7\right )+840 c^4 (d+e x)^8 \log (d+e x)}{840 e^9 (d+e x)^8} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.82, size = 998, normalized size = 2.29 \[ \frac {2283 \, c^{4} d^{8} - 420 \, b c^{3} d^{7} e - 60 \, a^{3} b d e^{7} - 105 \, a^{4} e^{8} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{6} e^{2} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{5} e^{3} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{4} e^{4} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{3} e^{5} - 10 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d^{2} e^{6} + 3360 \, {\left (2 \, c^{4} d e^{7} - b c^{3} e^{8}\right )} x^{7} + 840 \, {\left (42 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} - {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} e^{8}\right )} x^{6} + 560 \, {\left (154 \, c^{4} d^{3} e^{5} - 42 \, b c^{3} d^{2} e^{6} - 3 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d e^{7} - 2 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} e^{8}\right )} x^{5} + 70 \, {\left (1750 \, c^{4} d^{4} e^{4} - 420 \, b c^{3} d^{3} e^{5} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{2} e^{6} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d e^{7} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} e^{8}\right )} x^{4} + 56 \, {\left (1918 \, c^{4} d^{5} e^{3} - 420 \, b c^{3} d^{4} e^{4} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{3} e^{5} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{2} e^{6} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d e^{7} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} e^{8}\right )} x^{3} + 28 \, {\left (2058 \, c^{4} d^{6} e^{2} - 420 \, b c^{3} d^{5} e^{3} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{4} e^{4} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{3} e^{5} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{2} e^{6} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d e^{7} - 10 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} e^{8}\right )} x^{2} + 8 \, {\left (2178 \, c^{4} d^{7} e - 420 \, b c^{3} d^{6} e^{2} - 60 \, a^{3} b e^{8} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{5} e^{3} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{4} e^{4} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{3} e^{5} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{2} e^{6} - 10 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d e^{7}\right )} x + 840 \, {\left (c^{4} e^{8} x^{8} + 8 \, c^{4} d e^{7} x^{7} + 28 \, c^{4} d^{2} e^{6} x^{6} + 56 \, c^{4} d^{3} e^{5} x^{5} + 70 \, c^{4} d^{4} e^{4} x^{4} + 56 \, c^{4} d^{5} e^{3} x^{3} + 28 \, c^{4} d^{6} e^{2} x^{2} + 8 \, c^{4} d^{7} e x + c^{4} d^{8}\right )} \log \left (e x + d\right )}{840 \, {\left (e^{17} x^{8} + 8 \, d e^{16} x^{7} + 28 \, d^{2} e^{15} x^{6} + 56 \, d^{3} e^{14} x^{5} + 70 \, d^{4} e^{13} x^{4} + 56 \, d^{5} e^{12} x^{3} + 28 \, d^{6} e^{11} x^{2} + 8 \, d^{7} e^{10} x + d^{8} e^{9}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 843, normalized size = 1.94 \[ c^{4} e^{\left (-9\right )} \log \left ({\left | x e + d \right |}\right ) + \frac {{\left (3360 \, {\left (2 \, c^{4} d e^{6} - b c^{3} e^{7}\right )} x^{7} + 840 \, {\left (42 \, c^{4} d^{2} e^{5} - 14 \, b c^{3} d e^{6} - 3 \, b^{2} c^{2} e^{7} - 2 \, a c^{3} e^{7}\right )} x^{6} + 560 \, {\left (154 \, c^{4} d^{3} e^{4} - 42 \, b c^{3} d^{2} e^{5} - 9 \, b^{2} c^{2} d e^{6} - 6 \, a c^{3} d e^{6} - 2 \, b^{3} c e^{7} - 6 \, a b c^{2} e^{7}\right )} x^{5} + 70 \, {\left (1750 \, c^{4} d^{4} e^{3} - 420 \, b c^{3} d^{3} e^{4} - 90 \, b^{2} c^{2} d^{2} e^{5} - 60 \, a c^{3} d^{2} e^{5} - 20 \, b^{3} c d e^{6} - 60 \, a b c^{2} d e^{6} - 3 \, b^{4} e^{7} - 36 \, a b^{2} c e^{7} - 18 \, a^{2} c^{2} e^{7}\right )} x^{4} + 56 \, {\left (1918 \, c^{4} d^{5} e^{2} - 420 \, b c^{3} d^{4} e^{3} - 90 \, b^{2} c^{2} d^{3} e^{4} - 60 \, a c^{3} d^{3} e^{4} - 20 \, b^{3} c d^{2} e^{5} - 60 \, a b c^{2} d^{2} e^{5} - 3 \, b^{4} d e^{6} - 36 \, a b^{2} c d e^{6} - 18 \, a^{2} c^{2} d e^{6} - 12 \, a b^{3} e^{7} - 36 \, a^{2} b c e^{7}\right )} x^{3} + 28 \, {\left (2058 \, c^{4} d^{6} e - 420 \, b c^{3} d^{5} e^{2} - 90 \, b^{2} c^{2} d^{4} e^{3} - 60 \, a c^{3} d^{4} e^{3} - 20 \, b^{3} c d^{3} e^{4} - 60 \, a b c^{2} d^{3} e^{4} - 3 \, b^{4} d^{2} e^{5} - 36 \, a b^{2} c d^{2} e^{5} - 18 \, a^{2} c^{2} d^{2} e^{5} - 12 \, a b^{3} d e^{6} - 36 \, a^{2} b c d e^{6} - 30 \, a^{2} b^{2} e^{7} - 20 \, a^{3} c e^{7}\right )} x^{2} + 8 \, {\left (2178 \, c^{4} d^{7} - 420 \, b c^{3} d^{6} e - 90 \, b^{2} c^{2} d^{5} e^{2} - 60 \, a c^{3} d^{5} e^{2} - 20 \, b^{3} c d^{4} e^{3} - 60 \, a b c^{2} d^{4} e^{3} - 3 \, b^{4} d^{3} e^{4} - 36 \, a b^{2} c d^{3} e^{4} - 18 \, a^{2} c^{2} d^{3} e^{4} - 12 \, a b^{3} d^{2} e^{5} - 36 \, a^{2} b c d^{2} e^{5} - 30 \, a^{2} b^{2} d e^{6} - 20 \, a^{3} c d e^{6} - 60 \, a^{3} b e^{7}\right )} x + {\left (2283 \, c^{4} d^{8} - 420 \, b c^{3} d^{7} e - 90 \, b^{2} c^{2} d^{6} e^{2} - 60 \, a c^{3} d^{6} e^{2} - 20 \, b^{3} c d^{5} e^{3} - 60 \, a b c^{2} d^{5} e^{3} - 3 \, b^{4} d^{4} e^{4} - 36 \, a b^{2} c d^{4} e^{4} - 18 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a b^{3} d^{3} e^{5} - 36 \, a^{2} b c d^{3} e^{5} - 30 \, a^{2} b^{2} d^{2} e^{6} - 20 \, a^{3} c d^{2} e^{6} - 60 \, a^{3} b d e^{7} - 105 \, a^{4} e^{8}\right )} e^{\left (-1\right )}\right )} e^{\left (-8\right )}}{840 \, {\left (x e + d\right )}^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 1382, normalized size = 3.18 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.51, size = 894, normalized size = 2.06 \[ \frac {2283 \, c^{4} d^{8} - 420 \, b c^{3} d^{7} e - 60 \, a^{3} b d e^{7} - 105 \, a^{4} e^{8} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{6} e^{2} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{5} e^{3} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{4} e^{4} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{3} e^{5} - 10 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d^{2} e^{6} + 3360 \, {\left (2 \, c^{4} d e^{7} - b c^{3} e^{8}\right )} x^{7} + 840 \, {\left (42 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} - {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} e^{8}\right )} x^{6} + 560 \, {\left (154 \, c^{4} d^{3} e^{5} - 42 \, b c^{3} d^{2} e^{6} - 3 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d e^{7} - 2 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} e^{8}\right )} x^{5} + 70 \, {\left (1750 \, c^{4} d^{4} e^{4} - 420 \, b c^{3} d^{3} e^{5} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{2} e^{6} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d e^{7} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} e^{8}\right )} x^{4} + 56 \, {\left (1918 \, c^{4} d^{5} e^{3} - 420 \, b c^{3} d^{4} e^{4} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{3} e^{5} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{2} e^{6} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d e^{7} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} e^{8}\right )} x^{3} + 28 \, {\left (2058 \, c^{4} d^{6} e^{2} - 420 \, b c^{3} d^{5} e^{3} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{4} e^{4} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{3} e^{5} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{2} e^{6} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d e^{7} - 10 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} e^{8}\right )} x^{2} + 8 \, {\left (2178 \, c^{4} d^{7} e - 420 \, b c^{3} d^{6} e^{2} - 60 \, a^{3} b e^{8} - 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{5} e^{3} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{4} e^{4} - 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{3} e^{5} - 12 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{2} e^{6} - 10 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d e^{7}\right )} x}{840 \, {\left (e^{17} x^{8} + 8 \, d e^{16} x^{7} + 28 \, d^{2} e^{15} x^{6} + 56 \, d^{3} e^{14} x^{5} + 70 \, d^{4} e^{13} x^{4} + 56 \, d^{5} e^{12} x^{3} + 28 \, d^{6} e^{11} x^{2} + 8 \, d^{7} e^{10} x + d^{8} e^{9}\right )}} + \frac {c^{4} \log \left (e x + d\right )}{e^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.94, size = 1168, normalized size = 2.69 \[ -\frac {\frac {a^4\,e^8}{8}-\frac {761\,c^4\,d^8}{280}-c^4\,d^8\,\ln \left (d+e\,x\right )+\frac {b^4\,d^4\,e^4}{280}+\frac {b^4\,e^8\,x^4}{4}+\frac {a\,b^3\,d^3\,e^5}{70}+\frac {a\,c^3\,d^6\,e^2}{14}+\frac {a^3\,c\,d^2\,e^6}{42}+\frac {b^3\,c\,d^5\,e^3}{42}+\frac {4\,a\,b^3\,e^8\,x^3}{5}+\frac {2\,a^3\,c\,e^8\,x^2}{3}+2\,a\,c^3\,e^8\,x^6+\frac {4\,b^3\,c\,e^8\,x^5}{3}+4\,b\,c^3\,e^8\,x^7+\frac {b^4\,d^3\,e^5\,x}{35}+\frac {b^4\,d\,e^7\,x^3}{5}-8\,c^4\,d\,e^7\,x^7-c^4\,e^8\,x^8\,\ln \left (d+e\,x\right )+\frac {a^2\,b^2\,d^2\,e^6}{28}+\frac {3\,a^2\,c^2\,d^4\,e^4}{140}+\frac {3\,b^2\,c^2\,d^6\,e^2}{28}+a^2\,b^2\,e^8\,x^2+\frac {3\,a^2\,c^2\,e^8\,x^4}{2}+3\,b^2\,c^2\,e^8\,x^6+\frac {b^4\,d^2\,e^6\,x^2}{10}-\frac {343\,c^4\,d^6\,e^2\,x^2}{5}-\frac {1918\,c^4\,d^5\,e^3\,x^3}{15}-\frac {875\,c^4\,d^4\,e^4\,x^4}{6}-\frac {308\,c^4\,d^3\,e^5\,x^5}{3}-42\,c^4\,d^2\,e^6\,x^6+\frac {a^3\,b\,d\,e^7}{14}+\frac {b\,c^3\,d^7\,e}{2}+\frac {4\,a^3\,b\,e^8\,x}{7}-\frac {726\,c^4\,d^7\,e\,x}{35}+\frac {4\,a^3\,c\,d\,e^7\,x}{21}-8\,c^4\,d^7\,e\,x\,\ln \left (d+e\,x\right )+\frac {3\,a^2\,c^2\,d^2\,e^6\,x^2}{5}+3\,b^2\,c^2\,d^4\,e^4\,x^2+6\,b^2\,c^2\,d^3\,e^5\,x^3+\frac {15\,b^2\,c^2\,d^2\,e^6\,x^4}{2}+\frac {a\,b\,c^2\,d^5\,e^3}{14}+\frac {3\,a\,b^2\,c\,d^4\,e^4}{70}+\frac {3\,a^2\,b\,c\,d^3\,e^5}{70}+\frac {12\,a^2\,b\,c\,e^8\,x^3}{5}+3\,a\,b^2\,c\,e^8\,x^4+4\,a\,b\,c^2\,e^8\,x^5+\frac {4\,a\,b^3\,d^2\,e^6\,x}{35}+\frac {2\,a^2\,b^2\,d\,e^7\,x}{7}+\frac {2\,a\,b^3\,d\,e^7\,x^2}{5}+\frac {4\,a\,c^3\,d^5\,e^3\,x}{7}+4\,a\,c^3\,d\,e^7\,x^5+4\,b\,c^3\,d^6\,e^2\,x+\frac {4\,b^3\,c\,d^4\,e^4\,x}{21}+\frac {5\,b^3\,c\,d\,e^7\,x^4}{3}+14\,b\,c^3\,d\,e^7\,x^6-8\,c^4\,d\,e^7\,x^7\,\ln \left (d+e\,x\right )+\frac {6\,a^2\,c^2\,d^3\,e^5\,x}{35}+2\,a\,c^3\,d^4\,e^4\,x^2+4\,a\,c^3\,d^3\,e^5\,x^3+\frac {6\,a^2\,c^2\,d\,e^7\,x^3}{5}+5\,a\,c^3\,d^2\,e^6\,x^4+\frac {6\,b^2\,c^2\,d^5\,e^3\,x}{7}+14\,b\,c^3\,d^5\,e^3\,x^2+\frac {2\,b^3\,c\,d^3\,e^5\,x^2}{3}+28\,b\,c^3\,d^4\,e^4\,x^3+\frac {4\,b^3\,c\,d^2\,e^6\,x^3}{3}+35\,b\,c^3\,d^3\,e^5\,x^4+28\,b\,c^3\,d^2\,e^6\,x^5+6\,b^2\,c^2\,d\,e^7\,x^5-28\,c^4\,d^6\,e^2\,x^2\,\ln \left (d+e\,x\right )-56\,c^4\,d^5\,e^3\,x^3\,\ln \left (d+e\,x\right )-70\,c^4\,d^4\,e^4\,x^4\,\ln \left (d+e\,x\right )-56\,c^4\,d^3\,e^5\,x^5\,\ln \left (d+e\,x\right )-28\,c^4\,d^2\,e^6\,x^6\,\ln \left (d+e\,x\right )+2\,a\,b\,c^2\,d^3\,e^5\,x^2+\frac {6\,a\,b^2\,c\,d^2\,e^6\,x^2}{5}+4\,a\,b\,c^2\,d^2\,e^6\,x^3+\frac {4\,a\,b\,c^2\,d^4\,e^4\,x}{7}+\frac {12\,a\,b^2\,c\,d^3\,e^5\,x}{35}+\frac {12\,a^2\,b\,c\,d^2\,e^6\,x}{35}+\frac {6\,a^2\,b\,c\,d\,e^7\,x^2}{5}+\frac {12\,a\,b^2\,c\,d\,e^7\,x^3}{5}+5\,a\,b\,c^2\,d\,e^7\,x^4}{e^9\,{\left (d+e\,x\right )}^8} \]
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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