Optimal. Leaf size=534 \[ \frac {A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )}{2 e^8 (d+e x)^2}-\frac {3 c \log (d+e x) \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{e^8}+\frac {\left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (d+e x)^3}+\frac {B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )}{e^8 (d+e x)}+\frac {\left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{4 e^8 (d+e x)^4}+\frac {(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{5 e^8 (d+e x)^5}-\frac {c^2 x (-A c e-3 b B e+6 B c d)}{e^7}+\frac {B c^3 x^2}{2 e^6} \]
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Rubi [A] time = 0.90, antiderivative size = 532, 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 {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 )}{2 e^8 (d+e x)^2}+\frac {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 )}{e^8 (d+e x)}+\frac {\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 (d+e x)^3}-\frac {3 c \log (d+e x) \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 )}{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 )}{4 e^8 (d+e x)^4}+\frac {(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{5 e^8 (d+e x)^5}-\frac {c^2 x (-A c e-3 b B e+6 B c d)}{e^7}+\frac {B c^3 x^2}{2 e^6} \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)^6} \, dx &=\int \left (\frac {c^2 (-6 B c d+3 b B e+A c e)}{e^7}+\frac {B c^3 x}{e^6}+\frac {(-B d+A e) \left (c d^2-b d e+a e^2\right )^3}{e^7 (d+e x)^6}+\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)^5}+\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)^4}+\frac {-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 )}{e^7 (d+e x)^3}+\frac {-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 )}{e^7 (d+e x)^2}+\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 )}{e^7 (d+e x)}\right ) \, dx\\ &=-\frac {c^2 (6 B c d-3 b B e-A c e) x}{e^7}+\frac {B c^3 x^2}{2 e^6}+\frac {(B d-A e) \left (c d^2-b d e+a e^2\right )^3}{5 e^8 (d+e x)^5}-\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 )}{4 e^8 (d+e x)^4}+\frac {\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^8 (d+e x)^3}+\frac {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 )}{2 e^8 (d+e x)^2}+\frac {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 )}{e^8 (d+e x)}-\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 ) \log (d+e x)}{e^8}\\ \end {align*}
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Mathematica [A] time = 0.56, size = 885, normalized size = 1.66 \begin {gather*} \frac {60 c \left (A c e (b e-2 c d)+B \left (7 c^2 d^2+b^2 e^2+c e (a e-6 b d)\right )\right ) \log (d+e x) (d+e x)^5+A e \left (-2 \left (87 d^6+375 e x d^5+600 e^2 x^2 d^4+400 e^3 x^3 d^3+50 e^4 x^4 d^2-50 e^5 x^5 d-10 e^6 x^6\right ) c^3+e \left (b d \left (137 d^4+625 e x d^3+1100 e^2 x^2 d^2+900 e^3 x^3 d+300 e^4 x^4\right )-12 a e \left (d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right )\right ) c^2-2 e^2 \left (6 \left (d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right ) b^2+3 a e \left (d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right ) b+a^2 e^2 \left (d^2+5 e x d+10 e^2 x^2\right )\right ) c-e^3 \left (\left (d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right ) b^3+2 a e \left (d^2+5 e x d+10 e^2 x^2\right ) b^2+3 a^2 e^2 (d+5 e x) b+4 a^3 e^3\right )\right )+B \left (\left (459 d^7+1875 e x d^6+2700 e^2 x^2 d^5+1300 e^3 x^3 d^4-400 e^4 x^4 d^3-500 e^5 x^5 d^2-70 e^6 x^6 d+10 e^7 x^7\right ) c^3+e \left (a d e \left (137 d^4+625 e x d^3+1100 e^2 x^2 d^2+900 e^3 x^3 d+300 e^4 x^4\right )-6 b \left (87 d^6+375 e x d^5+600 e^2 x^2 d^4+400 e^3 x^3 d^3+50 e^4 x^4 d^2-50 e^5 x^5 d-10 e^6 x^6\right )\right ) c^2+e^2 \left (d \left (137 d^4+625 e x d^3+1100 e^2 x^2 d^2+900 e^3 x^3 d+300 e^4 x^4\right ) b^2-24 a e \left (d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right ) b-3 a^2 e^2 \left (d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right )\right ) c-e^3 \left (4 \left (d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right ) b^3+3 a e \left (d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right ) b^2+2 a^2 e^2 \left (d^2+5 e x d+10 e^2 x^2\right ) b+a^3 e^3 (d+5 e x)\right )\right )}{20 e^8 (d+e x)^5} \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)^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.40, size = 1247, normalized size = 2.34
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 998, normalized size = 1.87 \begin {gather*} 3 \, {\left (7 \, B c^{3} d^{2} - 6 \, B b c^{2} d e - 2 \, A c^{3} d e + B b^{2} c e^{2} + B a c^{2} e^{2} + A b c^{2} e^{2}\right )} e^{\left (-8\right )} \log \left ({\left | x e + d \right |}\right ) + \frac {1}{2} \, {\left (B c^{3} x^{2} e^{6} - 12 \, B c^{3} d x e^{5} + 6 \, B b c^{2} x e^{6} + 2 \, A c^{3} x e^{6}\right )} e^{\left (-12\right )} + \frac {{\left (459 \, B c^{3} d^{7} - 522 \, B b c^{2} d^{6} e - 174 \, A c^{3} d^{6} e + 137 \, B b^{2} c d^{5} e^{2} + 137 \, B a c^{2} d^{5} e^{2} + 137 \, A b c^{2} d^{5} e^{2} - 4 \, B b^{3} d^{4} e^{3} - 24 \, B a b c d^{4} e^{3} - 12 \, A b^{2} c d^{4} e^{3} - 12 \, A a c^{2} d^{4} e^{3} - 3 \, B a b^{2} d^{3} e^{4} - A b^{3} d^{3} e^{4} - 3 \, B a^{2} c d^{3} e^{4} - 6 \, A a b c d^{3} e^{4} - 2 \, B a^{2} b d^{2} e^{5} - 2 \, A a b^{2} d^{2} e^{5} - 2 \, A a^{2} c d^{2} e^{5} - B a^{3} d e^{6} - 3 \, A a^{2} b d e^{6} + 20 \, {\left (35 \, B c^{3} d^{3} e^{4} - 45 \, B b c^{2} d^{2} e^{5} - 15 \, A c^{3} d^{2} e^{5} + 15 \, B b^{2} c d e^{6} + 15 \, B a c^{2} d e^{6} + 15 \, A b c^{2} d e^{6} - B b^{3} e^{7} - 6 \, B a b c e^{7} - 3 \, A b^{2} c e^{7} - 3 \, A a c^{2} e^{7}\right )} x^{4} - 4 \, A a^{3} e^{7} + 10 \, {\left (245 \, B c^{3} d^{4} e^{3} - 300 \, B b c^{2} d^{3} e^{4} - 100 \, A c^{3} d^{3} e^{4} + 90 \, B b^{2} c d^{2} e^{5} + 90 \, B a c^{2} d^{2} e^{5} + 90 \, A b c^{2} d^{2} e^{5} - 4 \, B b^{3} d e^{6} - 24 \, B a b c d e^{6} - 12 \, A b^{2} c d e^{6} - 12 \, A a c^{2} d e^{6} - 3 \, B a b^{2} e^{7} - A b^{3} e^{7} - 3 \, B a^{2} c e^{7} - 6 \, A a b c e^{7}\right )} x^{3} + 10 \, {\left (329 \, B c^{3} d^{5} e^{2} - 390 \, B b c^{2} d^{4} e^{3} - 130 \, A c^{3} d^{4} e^{3} + 110 \, B b^{2} c d^{3} e^{4} + 110 \, B a c^{2} d^{3} e^{4} + 110 \, A b c^{2} d^{3} e^{4} - 4 \, B b^{3} d^{2} e^{5} - 24 \, B a b c d^{2} e^{5} - 12 \, A b^{2} c d^{2} e^{5} - 12 \, A a c^{2} d^{2} e^{5} - 3 \, B a b^{2} d e^{6} - A b^{3} d e^{6} - 3 \, B a^{2} c d e^{6} - 6 \, A a b c d e^{6} - 2 \, B a^{2} b e^{7} - 2 \, A a b^{2} e^{7} - 2 \, A a^{2} c e^{7}\right )} x^{2} + 5 \, {\left (399 \, B c^{3} d^{6} e - 462 \, B b c^{2} d^{5} e^{2} - 154 \, A c^{3} d^{5} e^{2} + 125 \, B b^{2} c d^{4} e^{3} + 125 \, B a c^{2} d^{4} e^{3} + 125 \, 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} - 3 \, B a b^{2} d^{2} e^{5} - A b^{3} d^{2} e^{5} - 3 \, B a^{2} c d^{2} e^{5} - 6 \, A a b c d^{2} e^{5} - 2 \, B a^{2} b d e^{6} - 2 \, A a b^{2} d e^{6} - 2 \, 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 )}}{20 \, {\left (x e + d\right )}^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 1637, normalized size = 3.07
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 898, normalized size = 1.68 \begin {gather*} \frac {459 \, B c^{3} d^{7} - 4 \, A a^{3} e^{7} - 174 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{6} e + 137 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{5} e^{2} - 4 \, {\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} - {\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} - 2 \, {\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} + 20 \, {\left (35 \, B c^{3} d^{3} e^{4} - 15 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{2} e^{5} + 15 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d e^{6} - {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} e^{7}\right )} x^{4} + 10 \, {\left (245 \, B c^{3} d^{4} e^{3} - 100 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{3} e^{4} + 90 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{2} e^{5} - 4 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d e^{6} - {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} e^{7}\right )} x^{3} + 10 \, {\left (329 \, B c^{3} d^{5} e^{2} - 130 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{4} e^{3} + 110 \, {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} d^{3} e^{4} - 4 \, {\left (B b^{3} + 3 \, A a c^{2} + 3 \, {\left (2 \, B a b + A b^{2}\right )} c\right )} d^{2} e^{5} - {\left (3 \, B a b^{2} + A b^{3} + 3 \, {\left (B a^{2} + 2 \, A a b\right )} c\right )} d e^{6} - 2 \, {\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} e^{7}\right )} x^{2} + 5 \, {\left (399 \, B c^{3} d^{6} e - 154 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d^{5} e^{2} + 125 \, {\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} - {\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} - 2 \, {\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}{20 \, {\left (e^{13} x^{5} + 5 \, d e^{12} x^{4} + 10 \, d^{2} e^{11} x^{3} + 10 \, d^{3} e^{10} x^{2} + 5 \, d^{4} e^{9} x + d^{5} e^{8}\right )}} + \frac {B c^{3} e x^{2} - 2 \, {\left (6 \, B c^{3} d - {\left (3 \, B b c^{2} + A c^{3}\right )} e\right )} x}{2 \, e^{7}} + \frac {3 \, {\left (7 \, B c^{3} d^{2} - 2 \, {\left (3 \, B b c^{2} + A c^{3}\right )} d e + {\left (B b^{2} c + {\left (B a + A b\right )} c^{2}\right )} e^{2}\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 = 0.26, size = 1106, normalized size = 2.07 \begin {gather*} x\,\left (\frac {A\,c^3+3\,B\,b\,c^2}{e^6}-\frac {6\,B\,c^3\,d}{e^7}\right )-\frac {\frac {B\,a^3\,d\,e^6+4\,A\,a^3\,e^7+2\,B\,a^2\,b\,d^2\,e^5+3\,A\,a^2\,b\,d\,e^6+3\,B\,a^2\,c\,d^3\,e^4+2\,A\,a^2\,c\,d^2\,e^5+3\,B\,a\,b^2\,d^3\,e^4+2\,A\,a\,b^2\,d^2\,e^5+24\,B\,a\,b\,c\,d^4\,e^3+6\,A\,a\,b\,c\,d^3\,e^4-137\,B\,a\,c^2\,d^5\,e^2+12\,A\,a\,c^2\,d^4\,e^3+4\,B\,b^3\,d^4\,e^3+A\,b^3\,d^3\,e^4-137\,B\,b^2\,c\,d^5\,e^2+12\,A\,b^2\,c\,d^4\,e^3+522\,B\,b\,c^2\,d^6\,e-137\,A\,b\,c^2\,d^5\,e^2-459\,B\,c^3\,d^7+174\,A\,c^3\,d^6\,e}{20\,e}+x^4\,\left (B\,b^3\,e^6-15\,B\,b^2\,c\,d\,e^5+3\,A\,b^2\,c\,e^6+45\,B\,b\,c^2\,d^2\,e^4-15\,A\,b\,c^2\,d\,e^5+6\,B\,a\,b\,c\,e^6-35\,B\,c^3\,d^3\,e^3+15\,A\,c^3\,d^2\,e^4-15\,B\,a\,c^2\,d\,e^5+3\,A\,a\,c^2\,e^6\right )+x^3\,\left (\frac {3\,B\,a^2\,c\,e^6}{2}+\frac {3\,B\,a\,b^2\,e^6}{2}+12\,B\,a\,b\,c\,d\,e^5+3\,A\,a\,b\,c\,e^6-45\,B\,a\,c^2\,d^2\,e^4+6\,A\,a\,c^2\,d\,e^5+2\,B\,b^3\,d\,e^5+\frac {A\,b^3\,e^6}{2}-45\,B\,b^2\,c\,d^2\,e^4+6\,A\,b^2\,c\,d\,e^5+150\,B\,b\,c^2\,d^3\,e^3-45\,A\,b\,c^2\,d^2\,e^4-\frac {245\,B\,c^3\,d^4\,e^2}{2}+50\,A\,c^3\,d^3\,e^3\right )+x\,\left (\frac {B\,a^3\,e^6}{4}+\frac {B\,a^2\,b\,d\,e^5}{2}+\frac {3\,A\,a^2\,b\,e^6}{4}+\frac {3\,B\,a^2\,c\,d^2\,e^4}{4}+\frac {A\,a^2\,c\,d\,e^5}{2}+\frac {3\,B\,a\,b^2\,d^2\,e^4}{4}+\frac {A\,a\,b^2\,d\,e^5}{2}+6\,B\,a\,b\,c\,d^3\,e^3+\frac {3\,A\,a\,b\,c\,d^2\,e^4}{2}-\frac {125\,B\,a\,c^2\,d^4\,e^2}{4}+3\,A\,a\,c^2\,d^3\,e^3+B\,b^3\,d^3\,e^3+\frac {A\,b^3\,d^2\,e^4}{4}-\frac {125\,B\,b^2\,c\,d^4\,e^2}{4}+3\,A\,b^2\,c\,d^3\,e^3+\frac {231\,B\,b\,c^2\,d^5\,e}{2}-\frac {125\,A\,b\,c^2\,d^4\,e^2}{4}-\frac {399\,B\,c^3\,d^6}{4}+\frac {77\,A\,c^3\,d^5\,e}{2}\right )+x^2\,\left (B\,a^2\,b\,e^6+\frac {3\,B\,a^2\,c\,d\,e^5}{2}+A\,a^2\,c\,e^6+\frac {3\,B\,a\,b^2\,d\,e^5}{2}+A\,a\,b^2\,e^6+12\,B\,a\,b\,c\,d^2\,e^4+3\,A\,a\,b\,c\,d\,e^5-55\,B\,a\,c^2\,d^3\,e^3+6\,A\,a\,c^2\,d^2\,e^4+2\,B\,b^3\,d^2\,e^4+\frac {A\,b^3\,d\,e^5}{2}-55\,B\,b^2\,c\,d^3\,e^3+6\,A\,b^2\,c\,d^2\,e^4+195\,B\,b\,c^2\,d^4\,e^2-55\,A\,b\,c^2\,d^3\,e^3-\frac {329\,B\,c^3\,d^5\,e}{2}+65\,A\,c^3\,d^4\,e^2\right )}{d^5\,e^7+5\,d^4\,e^8\,x+10\,d^3\,e^9\,x^2+10\,d^2\,e^{10}\,x^3+5\,d\,e^{11}\,x^4+e^{12}\,x^5}+\frac {\ln \left (d+e\,x\right )\,\left (3\,B\,b^2\,c\,e^2-18\,B\,b\,c^2\,d\,e+3\,A\,b\,c^2\,e^2+21\,B\,c^3\,d^2-6\,A\,c^3\,d\,e+3\,B\,a\,c^2\,e^2\right )}{e^8}+\frac {B\,c^3\,x^2}{2\,e^6} \end {gather*}
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 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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