Optimal. Leaf size=235 \[ -\frac {(B d-A e) (a+b x)^7}{11 e (b d-a e) (d+e x)^{11}}+\frac {(7 b B d+4 A b e-11 a B e) (a+b x)^7}{110 e (b d-a e)^2 (d+e x)^{10}}+\frac {b (7 b B d+4 A b e-11 a B e) (a+b x)^7}{330 e (b d-a e)^3 (d+e x)^9}+\frac {b^2 (7 b B d+4 A b e-11 a B e) (a+b x)^7}{1320 e (b d-a e)^4 (d+e x)^8}+\frac {b^3 (7 b B d+4 A b e-11 a B e) (a+b x)^7}{9240 e (b d-a e)^5 (d+e x)^7} \]
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Rubi [A]
time = 0.07, antiderivative size = 235, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {79, 47, 37}
\begin {gather*} \frac {b^3 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{9240 e (d+e x)^7 (b d-a e)^5}+\frac {b^2 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{1320 e (d+e x)^8 (b d-a e)^4}+\frac {b (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{330 e (d+e x)^9 (b d-a e)^3}+\frac {(a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{110 e (d+e x)^{10} (b d-a e)^2}-\frac {(a+b x)^7 (B d-A e)}{11 e (d+e x)^{11} (b d-a e)} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 47
Rule 79
Rubi steps
\begin {align*} \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^{12}} \, dx &=-\frac {(B d-A e) (a+b x)^7}{11 e (b d-a e) (d+e x)^{11}}+\frac {(7 b B d+4 A b e-11 a B e) \int \frac {(a+b x)^6}{(d+e x)^{11}} \, dx}{11 e (b d-a e)}\\ &=-\frac {(B d-A e) (a+b x)^7}{11 e (b d-a e) (d+e x)^{11}}+\frac {(7 b B d+4 A b e-11 a B e) (a+b x)^7}{110 e (b d-a e)^2 (d+e x)^{10}}+\frac {(3 b (7 b B d+4 A b e-11 a B e)) \int \frac {(a+b x)^6}{(d+e x)^{10}} \, dx}{110 e (b d-a e)^2}\\ &=-\frac {(B d-A e) (a+b x)^7}{11 e (b d-a e) (d+e x)^{11}}+\frac {(7 b B d+4 A b e-11 a B e) (a+b x)^7}{110 e (b d-a e)^2 (d+e x)^{10}}+\frac {b (7 b B d+4 A b e-11 a B e) (a+b x)^7}{330 e (b d-a e)^3 (d+e x)^9}+\frac {\left (b^2 (7 b B d+4 A b e-11 a B e)\right ) \int \frac {(a+b x)^6}{(d+e x)^9} \, dx}{165 e (b d-a e)^3}\\ &=-\frac {(B d-A e) (a+b x)^7}{11 e (b d-a e) (d+e x)^{11}}+\frac {(7 b B d+4 A b e-11 a B e) (a+b x)^7}{110 e (b d-a e)^2 (d+e x)^{10}}+\frac {b (7 b B d+4 A b e-11 a B e) (a+b x)^7}{330 e (b d-a e)^3 (d+e x)^9}+\frac {b^2 (7 b B d+4 A b e-11 a B e) (a+b x)^7}{1320 e (b d-a e)^4 (d+e x)^8}+\frac {\left (b^3 (7 b B d+4 A b e-11 a B e)\right ) \int \frac {(a+b x)^6}{(d+e x)^8} \, dx}{1320 e (b d-a e)^4}\\ &=-\frac {(B d-A e) (a+b x)^7}{11 e (b d-a e) (d+e x)^{11}}+\frac {(7 b B d+4 A b e-11 a B e) (a+b x)^7}{110 e (b d-a e)^2 (d+e x)^{10}}+\frac {b (7 b B d+4 A b e-11 a B e) (a+b x)^7}{330 e (b d-a e)^3 (d+e x)^9}+\frac {b^2 (7 b B d+4 A b e-11 a B e) (a+b x)^7}{1320 e (b d-a e)^4 (d+e x)^8}+\frac {b^3 (7 b B d+4 A b e-11 a B e) (a+b x)^7}{9240 e (b d-a e)^5 (d+e x)^7}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(605\) vs. \(2(235)=470\).
time = 0.19, size = 605, normalized size = 2.57 \begin {gather*} -\frac {84 a^6 e^6 (10 A e+B (d+11 e x))+56 a^5 b e^5 \left (9 A e (d+11 e x)+2 B \left (d^2+11 d e x+55 e^2 x^2\right )\right )+35 a^4 b^2 e^4 \left (8 A e \left (d^2+11 d e x+55 e^2 x^2\right )+3 B \left (d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right )\right )+20 a^3 b^3 e^3 \left (7 A e \left (d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right )+4 B \left (d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right )\right )+10 a^2 b^4 e^2 \left (6 A e \left (d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right )+5 B \left (d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right )\right )+4 a b^5 e \left (5 A e \left (d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right )+6 B \left (d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right )\right )+b^6 \left (4 A e \left (d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right )+7 B \left (d^7+11 d^6 e x+55 d^5 e^2 x^2+165 d^4 e^3 x^3+330 d^3 e^4 x^4+462 d^2 e^5 x^5+462 d e^6 x^6+330 e^7 x^7\right )\right )}{9240 e^8 (d+e x)^{11}} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(813\) vs.
\(2(225)=450\).
time = 0.10, size = 814, normalized size = 3.46 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 878 vs.
\(2 (239) = 478\).
time = 0.36, size = 878, normalized size = 3.74 \begin {gather*} -\frac {2310 \, B b^{6} x^{7} e^{7} + 7 \, B b^{6} d^{7} + 840 \, A a^{6} e^{7} + 4 \, {\left (6 \, B a b^{5} e + A b^{6} e\right )} d^{6} + 462 \, {\left (7 \, B b^{6} d e^{6} + 24 \, B a b^{5} e^{7} + 4 \, A b^{6} e^{7}\right )} x^{6} + 10 \, {\left (5 \, B a^{2} b^{4} e^{2} + 2 \, A a b^{5} e^{2}\right )} d^{5} + 462 \, {\left (7 \, B b^{6} d^{2} e^{5} + 50 \, B a^{2} b^{4} e^{7} + 20 \, A a b^{5} e^{7} + 4 \, {\left (6 \, B a b^{5} e^{6} + A b^{6} e^{6}\right )} d\right )} x^{5} + 20 \, {\left (4 \, B a^{3} b^{3} e^{3} + 3 \, A a^{2} b^{4} e^{3}\right )} d^{4} + 330 \, {\left (7 \, B b^{6} d^{3} e^{4} + 80 \, B a^{3} b^{3} e^{7} + 60 \, A a^{2} b^{4} e^{7} + 4 \, {\left (6 \, B a b^{5} e^{5} + A b^{6} e^{5}\right )} d^{2} + 10 \, {\left (5 \, B a^{2} b^{4} e^{6} + 2 \, A a b^{5} e^{6}\right )} d\right )} x^{4} + 35 \, {\left (3 \, B a^{4} b^{2} e^{4} + 4 \, A a^{3} b^{3} e^{4}\right )} d^{3} + 165 \, {\left (7 \, B b^{6} d^{4} e^{3} + 105 \, B a^{4} b^{2} e^{7} + 140 \, A a^{3} b^{3} e^{7} + 4 \, {\left (6 \, B a b^{5} e^{4} + A b^{6} e^{4}\right )} d^{3} + 10 \, {\left (5 \, B a^{2} b^{4} e^{5} + 2 \, A a b^{5} e^{5}\right )} d^{2} + 20 \, {\left (4 \, B a^{3} b^{3} e^{6} + 3 \, A a^{2} b^{4} e^{6}\right )} d\right )} x^{3} + 56 \, {\left (2 \, B a^{5} b e^{5} + 5 \, A a^{4} b^{2} e^{5}\right )} d^{2} + 55 \, {\left (7 \, B b^{6} d^{5} e^{2} + 112 \, B a^{5} b e^{7} + 280 \, A a^{4} b^{2} e^{7} + 4 \, {\left (6 \, B a b^{5} e^{3} + A b^{6} e^{3}\right )} d^{4} + 10 \, {\left (5 \, B a^{2} b^{4} e^{4} + 2 \, A a b^{5} e^{4}\right )} d^{3} + 20 \, {\left (4 \, B a^{3} b^{3} e^{5} + 3 \, A a^{2} b^{4} e^{5}\right )} d^{2} + 35 \, {\left (3 \, B a^{4} b^{2} e^{6} + 4 \, A a^{3} b^{3} e^{6}\right )} d\right )} x^{2} + 84 \, {\left (B a^{6} e^{6} + 6 \, A a^{5} b e^{6}\right )} d + 11 \, {\left (7 \, B b^{6} d^{6} e + 84 \, B a^{6} e^{7} + 504 \, A a^{5} b e^{7} + 4 \, {\left (6 \, B a b^{5} e^{2} + A b^{6} e^{2}\right )} d^{5} + 10 \, {\left (5 \, B a^{2} b^{4} e^{3} + 2 \, A a b^{5} e^{3}\right )} d^{4} + 20 \, {\left (4 \, B a^{3} b^{3} e^{4} + 3 \, A a^{2} b^{4} e^{4}\right )} d^{3} + 35 \, {\left (3 \, B a^{4} b^{2} e^{5} + 4 \, A a^{3} b^{3} e^{5}\right )} d^{2} + 56 \, {\left (2 \, B a^{5} b e^{6} + 5 \, A a^{4} b^{2} e^{6}\right )} d\right )} x}{9240 \, {\left (x^{11} e^{19} + 11 \, d x^{10} e^{18} + 55 \, d^{2} x^{9} e^{17} + 165 \, d^{3} x^{8} e^{16} + 330 \, d^{4} x^{7} e^{15} + 462 \, d^{5} x^{6} e^{14} + 462 \, d^{6} x^{5} e^{13} + 330 \, d^{7} x^{4} e^{12} + 165 \, d^{8} x^{3} e^{11} + 55 \, d^{9} x^{2} e^{10} + 11 \, d^{10} x e^{9} + d^{11} e^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 833 vs.
\(2 (239) = 478\).
time = 1.14, size = 833, normalized size = 3.54 \begin {gather*} -\frac {7 \, B b^{6} d^{7} + {\left (2310 \, B b^{6} x^{7} + 840 \, A a^{6} + 1848 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 4620 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + 6600 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 5775 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 3080 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 924 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x\right )} e^{7} + {\left (3234 \, B b^{6} d x^{6} + 1848 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d x^{5} + 3300 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d x^{4} + 3300 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d x^{3} + 1925 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d x^{2} + 616 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d x + 84 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d\right )} e^{6} + {\left (3234 \, B b^{6} d^{2} x^{5} + 1320 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} x^{4} + 1650 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} x^{3} + 1100 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} x^{2} + 385 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} x + 56 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2}\right )} e^{5} + 5 \, {\left (462 \, B b^{6} d^{3} x^{4} + 132 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} x^{3} + 110 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} x^{2} + 44 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} x + 7 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3}\right )} e^{4} + 5 \, {\left (231 \, B b^{6} d^{4} x^{3} + 44 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} x^{2} + 22 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} x + 4 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4}\right )} e^{3} + {\left (385 \, B b^{6} d^{5} x^{2} + 44 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} x + 10 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5}\right )} e^{2} + {\left (77 \, B b^{6} d^{6} x + 4 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6}\right )} e}{9240 \, {\left (x^{11} e^{19} + 11 \, d x^{10} e^{18} + 55 \, d^{2} x^{9} e^{17} + 165 \, d^{3} x^{8} e^{16} + 330 \, d^{4} x^{7} e^{15} + 462 \, d^{5} x^{6} e^{14} + 462 \, d^{6} x^{5} e^{13} + 330 \, d^{7} x^{4} e^{12} + 165 \, d^{8} x^{3} e^{11} + 55 \, d^{9} x^{2} e^{10} + 11 \, d^{10} x e^{9} + d^{11} e^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 856 vs.
\(2 (239) = 478\).
time = 2.07, size = 856, normalized size = 3.64 \begin {gather*} -\frac {{\left (2310 \, B b^{6} x^{7} e^{7} + 3234 \, B b^{6} d x^{6} e^{6} + 3234 \, B b^{6} d^{2} x^{5} e^{5} + 2310 \, B b^{6} d^{3} x^{4} e^{4} + 1155 \, B b^{6} d^{4} x^{3} e^{3} + 385 \, B b^{6} d^{5} x^{2} e^{2} + 77 \, B b^{6} d^{6} x e + 7 \, B b^{6} d^{7} + 11088 \, B a b^{5} x^{6} e^{7} + 1848 \, A b^{6} x^{6} e^{7} + 11088 \, B a b^{5} d x^{5} e^{6} + 1848 \, A b^{6} d x^{5} e^{6} + 7920 \, B a b^{5} d^{2} x^{4} e^{5} + 1320 \, A b^{6} d^{2} x^{4} e^{5} + 3960 \, B a b^{5} d^{3} x^{3} e^{4} + 660 \, A b^{6} d^{3} x^{3} e^{4} + 1320 \, B a b^{5} d^{4} x^{2} e^{3} + 220 \, A b^{6} d^{4} x^{2} e^{3} + 264 \, B a b^{5} d^{5} x e^{2} + 44 \, A b^{6} d^{5} x e^{2} + 24 \, B a b^{5} d^{6} e + 4 \, A b^{6} d^{6} e + 23100 \, B a^{2} b^{4} x^{5} e^{7} + 9240 \, A a b^{5} x^{5} e^{7} + 16500 \, B a^{2} b^{4} d x^{4} e^{6} + 6600 \, A a b^{5} d x^{4} e^{6} + 8250 \, B a^{2} b^{4} d^{2} x^{3} e^{5} + 3300 \, A a b^{5} d^{2} x^{3} e^{5} + 2750 \, B a^{2} b^{4} d^{3} x^{2} e^{4} + 1100 \, A a b^{5} d^{3} x^{2} e^{4} + 550 \, B a^{2} b^{4} d^{4} x e^{3} + 220 \, A a b^{5} d^{4} x e^{3} + 50 \, B a^{2} b^{4} d^{5} e^{2} + 20 \, A a b^{5} d^{5} e^{2} + 26400 \, B a^{3} b^{3} x^{4} e^{7} + 19800 \, A a^{2} b^{4} x^{4} e^{7} + 13200 \, B a^{3} b^{3} d x^{3} e^{6} + 9900 \, A a^{2} b^{4} d x^{3} e^{6} + 4400 \, B a^{3} b^{3} d^{2} x^{2} e^{5} + 3300 \, A a^{2} b^{4} d^{2} x^{2} e^{5} + 880 \, B a^{3} b^{3} d^{3} x e^{4} + 660 \, A a^{2} b^{4} d^{3} x e^{4} + 80 \, B a^{3} b^{3} d^{4} e^{3} + 60 \, A a^{2} b^{4} d^{4} e^{3} + 17325 \, B a^{4} b^{2} x^{3} e^{7} + 23100 \, A a^{3} b^{3} x^{3} e^{7} + 5775 \, B a^{4} b^{2} d x^{2} e^{6} + 7700 \, A a^{3} b^{3} d x^{2} e^{6} + 1155 \, B a^{4} b^{2} d^{2} x e^{5} + 1540 \, A a^{3} b^{3} d^{2} x e^{5} + 105 \, B a^{4} b^{2} d^{3} e^{4} + 140 \, A a^{3} b^{3} d^{3} e^{4} + 6160 \, B a^{5} b x^{2} e^{7} + 15400 \, A a^{4} b^{2} x^{2} e^{7} + 1232 \, B a^{5} b d x e^{6} + 3080 \, A a^{4} b^{2} d x e^{6} + 112 \, B a^{5} b d^{2} e^{5} + 280 \, A a^{4} b^{2} d^{2} e^{5} + 924 \, B a^{6} x e^{7} + 5544 \, A a^{5} b x e^{7} + 84 \, B a^{6} d e^{6} + 504 \, A a^{5} b d e^{6} + 840 \, A a^{6} e^{7}\right )} e^{\left (-8\right )}}{9240 \, {\left (x e + d\right )}^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.30, size = 899, normalized size = 3.83 \begin {gather*} -\frac {\frac {84\,B\,a^6\,d\,e^6+840\,A\,a^6\,e^7+112\,B\,a^5\,b\,d^2\,e^5+504\,A\,a^5\,b\,d\,e^6+105\,B\,a^4\,b^2\,d^3\,e^4+280\,A\,a^4\,b^2\,d^2\,e^5+80\,B\,a^3\,b^3\,d^4\,e^3+140\,A\,a^3\,b^3\,d^3\,e^4+50\,B\,a^2\,b^4\,d^5\,e^2+60\,A\,a^2\,b^4\,d^4\,e^3+24\,B\,a\,b^5\,d^6\,e+20\,A\,a\,b^5\,d^5\,e^2+7\,B\,b^6\,d^7+4\,A\,b^6\,d^6\,e}{9240\,e^8}+\frac {x\,\left (84\,B\,a^6\,e^6+112\,B\,a^5\,b\,d\,e^5+504\,A\,a^5\,b\,e^6+105\,B\,a^4\,b^2\,d^2\,e^4+280\,A\,a^4\,b^2\,d\,e^5+80\,B\,a^3\,b^3\,d^3\,e^3+140\,A\,a^3\,b^3\,d^2\,e^4+50\,B\,a^2\,b^4\,d^4\,e^2+60\,A\,a^2\,b^4\,d^3\,e^3+24\,B\,a\,b^5\,d^5\,e+20\,A\,a\,b^5\,d^4\,e^2+7\,B\,b^6\,d^6+4\,A\,b^6\,d^5\,e\right )}{840\,e^7}+\frac {b^3\,x^4\,\left (80\,B\,a^3\,e^3+50\,B\,a^2\,b\,d\,e^2+60\,A\,a^2\,b\,e^3+24\,B\,a\,b^2\,d^2\,e+20\,A\,a\,b^2\,d\,e^2+7\,B\,b^3\,d^3+4\,A\,b^3\,d^2\,e\right )}{28\,e^4}+\frac {b^5\,x^6\,\left (4\,A\,b\,e+24\,B\,a\,e+7\,B\,b\,d\right )}{20\,e^2}+\frac {b\,x^2\,\left (112\,B\,a^5\,e^5+105\,B\,a^4\,b\,d\,e^4+280\,A\,a^4\,b\,e^5+80\,B\,a^3\,b^2\,d^2\,e^3+140\,A\,a^3\,b^2\,d\,e^4+50\,B\,a^2\,b^3\,d^3\,e^2+60\,A\,a^2\,b^3\,d^2\,e^3+24\,B\,a\,b^4\,d^4\,e+20\,A\,a\,b^4\,d^3\,e^2+7\,B\,b^5\,d^5+4\,A\,b^5\,d^4\,e\right )}{168\,e^6}+\frac {b^2\,x^3\,\left (105\,B\,a^4\,e^4+80\,B\,a^3\,b\,d\,e^3+140\,A\,a^3\,b\,e^4+50\,B\,a^2\,b^2\,d^2\,e^2+60\,A\,a^2\,b^2\,d\,e^3+24\,B\,a\,b^3\,d^3\,e+20\,A\,a\,b^3\,d^2\,e^2+7\,B\,b^4\,d^4+4\,A\,b^4\,d^3\,e\right )}{56\,e^5}+\frac {b^4\,x^5\,\left (50\,B\,a^2\,e^2+24\,B\,a\,b\,d\,e+20\,A\,a\,b\,e^2+7\,B\,b^2\,d^2+4\,A\,b^2\,d\,e\right )}{20\,e^3}+\frac {B\,b^6\,x^7}{4\,e}}{d^{11}+11\,d^{10}\,e\,x+55\,d^9\,e^2\,x^2+165\,d^8\,e^3\,x^3+330\,d^7\,e^4\,x^4+462\,d^6\,e^5\,x^5+462\,d^5\,e^6\,x^6+330\,d^4\,e^7\,x^7+165\,d^3\,e^8\,x^8+55\,d^2\,e^9\,x^9+11\,d\,e^{10}\,x^{10}+e^{11}\,x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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