Optimal. Leaf size=404 \[ \frac {1}{4} a^3 e x^4 \left (e (A e+3 B d)+3 C d^2\right )+a^3 A d^3 x+\frac {1}{6} a^2 e x^6 \left (a C e^2+3 c \left (e (A e+3 B d)+3 C d^2\right )\right )+\frac {1}{3} a^2 d x^3 \left (3 A \left (a e^2+c d^2\right )+a d (3 B e+C d)\right )+\frac {1}{10} c^2 e x^{10} \left (3 a C e^2+c \left (e (A e+3 B d)+3 C d^2\right )\right )+\frac {1}{9} c^2 x^9 \left (3 a e^2 (B e+3 C d)+c d \left (3 e (A e+B d)+C d^2\right )\right )+\frac {3}{8} a c e x^8 \left (a C e^2+c \left (e (A e+3 B d)+3 C d^2\right )\right )+\frac {1}{7} c x^7 \left (A c d \left (9 a e^2+c d^2\right )+3 a \left (a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right )\right )+\frac {1}{5} a x^5 \left (3 A c d \left (3 a e^2+c d^2\right )+a \left (a e^2 (B e+3 C d)+3 c d^2 (3 B e+C d)\right )\right )+\frac {d^2 \left (a+c x^2\right )^4 (3 A e+B d)}{8 c}+\frac {1}{11} c^3 e^2 x^{11} (B e+3 C d)+\frac {1}{12} c^3 C e^3 x^{12} \]
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Rubi [A] time = 0.69, antiderivative size = 400, normalized size of antiderivative = 0.99, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {1582, 1810} \[ \frac {1}{6} a^2 e x^6 \left (a C e^2+3 c e (A e+3 B d)+9 c C d^2\right )+\frac {1}{3} a^2 d x^3 \left (3 A \left (a e^2+c d^2\right )+a d (3 B e+C d)\right )+\frac {1}{4} a^3 e x^4 \left (e (A e+3 B d)+3 C d^2\right )+a^3 A d^3 x+\frac {1}{10} c^2 e x^{10} \left (3 a C e^2+c e (A e+3 B d)+3 c C d^2\right )+\frac {1}{9} c^2 x^9 \left (3 a e^2 (B e+3 C d)+3 c d e (A e+B d)+c C d^3\right )+\frac {3}{8} a c e x^8 \left (a C e^2+c e (A e+3 B d)+3 c C d^2\right )+\frac {1}{7} c x^7 \left (A c d \left (9 a e^2+c d^2\right )+3 a \left (a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right )\right )+\frac {1}{5} a x^5 \left (3 A c d \left (3 a e^2+c d^2\right )+a \left (a e^2 (B e+3 C d)+3 c d^2 (3 B e+C d)\right )\right )+\frac {d^2 \left (a+c x^2\right )^4 (3 A e+B d)}{8 c}+\frac {1}{11} c^3 e^2 x^{11} (B e+3 C d)+\frac {1}{12} c^3 C e^3 x^{12} \]
Antiderivative was successfully verified.
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Rule 1582
Rule 1810
Rubi steps
\begin {align*} \int (d+e x)^3 \left (a+c x^2\right )^3 \left (A+B x+C x^2\right ) \, dx &=\frac {d^2 (B d+3 A e) \left (a+c x^2\right )^4}{8 c}+\int \left (a+c x^2\right )^3 \left (-\left (B d^3+3 A d^2 e\right ) x+(d+e x)^3 \left (A+B x+C x^2\right )\right ) \, dx\\ &=\frac {d^2 (B d+3 A e) \left (a+c x^2\right )^4}{8 c}+\int \left (a^3 A d^3+a^2 d \left (a d (C d+3 B e)+3 A \left (c d^2+a e^2\right )\right ) x^2+a^3 e \left (3 C d^2+e (3 B d+A e)\right ) x^3+a \left (3 A c d \left (c d^2+3 a e^2\right )+a \left (a e^2 (3 C d+B e)+3 c d^2 (C d+3 B e)\right )\right ) x^4+a^2 e \left (9 c C d^2+a C e^2+3 c e (3 B d+A e)\right ) x^5+c \left (A c d \left (c d^2+9 a e^2\right )+3 a \left (a e^2 (3 C d+B e)+c d^2 (C d+3 B e)\right )\right ) x^6+3 a c e \left (3 c C d^2+a C e^2+c e (3 B d+A e)\right ) x^7+c^2 \left (c C d^3+3 c d e (B d+A e)+3 a e^2 (3 C d+B e)\right ) x^8+c^2 e \left (3 c C d^2+3 a C e^2+c e (3 B d+A e)\right ) x^9+c^3 e^2 (3 C d+B e) x^{10}+c^3 C e^3 x^{11}\right ) \, dx\\ &=a^3 A d^3 x+\frac {1}{3} a^2 d \left (a d (C d+3 B e)+3 A \left (c d^2+a e^2\right )\right ) x^3+\frac {1}{4} a^3 e \left (3 C d^2+e (3 B d+A e)\right ) x^4+\frac {1}{5} a \left (3 A c d \left (c d^2+3 a e^2\right )+a \left (a e^2 (3 C d+B e)+3 c d^2 (C d+3 B e)\right )\right ) x^5+\frac {1}{6} a^2 e \left (9 c C d^2+a C e^2+3 c e (3 B d+A e)\right ) x^6+\frac {1}{7} c \left (A c d \left (c d^2+9 a e^2\right )+3 a \left (a e^2 (3 C d+B e)+c d^2 (C d+3 B e)\right )\right ) x^7+\frac {3}{8} a c e \left (3 c C d^2+a C e^2+c e (3 B d+A e)\right ) x^8+\frac {1}{9} c^2 \left (c C d^3+3 c d e (B d+A e)+3 a e^2 (3 C d+B e)\right ) x^9+\frac {1}{10} c^2 e \left (3 c C d^2+3 a C e^2+c e (3 B d+A e)\right ) x^{10}+\frac {1}{11} c^3 e^2 (3 C d+B e) x^{11}+\frac {1}{12} c^3 C e^3 x^{12}+\frac {d^2 (B d+3 A e) \left (a+c x^2\right )^4}{8 c}\\ \end {align*}
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Mathematica [A] time = 0.21, size = 459, normalized size = 1.14 \[ \frac {1}{2} a^3 d^2 x^2 (3 A e+B d)+a^3 A d^3 x+\frac {1}{3} a^2 d x^3 \left (3 A \left (a e^2+c d^2\right )+a d (3 B e+C d)\right )+\frac {1}{4} a^2 x^4 \left (a A e^3+3 a B d e^2+3 a C d^2 e+9 A c d^2 e+3 B c d^3\right )+\frac {1}{9} c^2 x^9 \left (3 a e^2 (B e+3 C d)+3 c d e (A e+B d)+c C d^3\right )+\frac {1}{10} c^2 e x^{10} \left (3 a C e^2+c e (A e+3 B d)+3 c C d^2\right )+\frac {1}{8} c x^8 \left (3 e \left (A c \left (a e^2+c d^2\right )+a C \left (a e^2+3 c d^2\right )\right )+B c d \left (9 a e^2+c d^2\right )\right )+\frac {1}{7} c x^7 \left (A c d \left (9 a e^2+c d^2\right )+3 a \left (a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right )\right )+\frac {1}{6} a x^6 \left (3 A c e \left (a e^2+3 c d^2\right )+3 B c d \left (3 a e^2+c d^2\right )+a C e \left (a e^2+9 c d^2\right )\right )+\frac {1}{5} a x^5 \left (3 A c d \left (3 a e^2+c d^2\right )+a \left (a e^2 (B e+3 C d)+3 c d^2 (3 B e+C d)\right )\right )+\frac {1}{11} c^3 e^2 x^{11} (B e+3 C d)+\frac {1}{12} c^3 C e^3 x^{12} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 618, normalized size = 1.53 \[ \frac {1}{12} x^{12} e^{3} c^{3} C + \frac {3}{11} x^{11} e^{2} d c^{3} C + \frac {1}{11} x^{11} e^{3} c^{3} B + \frac {3}{10} x^{10} e d^{2} c^{3} C + \frac {3}{10} x^{10} e^{3} c^{2} a C + \frac {3}{10} x^{10} e^{2} d c^{3} B + \frac {1}{10} x^{10} e^{3} c^{3} A + \frac {1}{9} x^{9} d^{3} c^{3} C + x^{9} e^{2} d c^{2} a C + \frac {1}{3} x^{9} e d^{2} c^{3} B + \frac {1}{3} x^{9} e^{3} c^{2} a B + \frac {1}{3} x^{9} e^{2} d c^{3} A + \frac {9}{8} x^{8} e d^{2} c^{2} a C + \frac {3}{8} x^{8} e^{3} c a^{2} C + \frac {1}{8} x^{8} d^{3} c^{3} B + \frac {9}{8} x^{8} e^{2} d c^{2} a B + \frac {3}{8} x^{8} e d^{2} c^{3} A + \frac {3}{8} x^{8} e^{3} c^{2} a A + \frac {3}{7} x^{7} d^{3} c^{2} a C + \frac {9}{7} x^{7} e^{2} d c a^{2} C + \frac {9}{7} x^{7} e d^{2} c^{2} a B + \frac {3}{7} x^{7} e^{3} c a^{2} B + \frac {1}{7} x^{7} d^{3} c^{3} A + \frac {9}{7} x^{7} e^{2} d c^{2} a A + \frac {3}{2} x^{6} e d^{2} c a^{2} C + \frac {1}{6} x^{6} e^{3} a^{3} C + \frac {1}{2} x^{6} d^{3} c^{2} a B + \frac {3}{2} x^{6} e^{2} d c a^{2} B + \frac {3}{2} x^{6} e d^{2} c^{2} a A + \frac {1}{2} x^{6} e^{3} c a^{2} A + \frac {3}{5} x^{5} d^{3} c a^{2} C + \frac {3}{5} x^{5} e^{2} d a^{3} C + \frac {9}{5} x^{5} e d^{2} c a^{2} B + \frac {1}{5} x^{5} e^{3} a^{3} B + \frac {3}{5} x^{5} d^{3} c^{2} a A + \frac {9}{5} x^{5} e^{2} d c a^{2} A + \frac {3}{4} x^{4} e d^{2} a^{3} C + \frac {3}{4} x^{4} d^{3} c a^{2} B + \frac {3}{4} x^{4} e^{2} d a^{3} B + \frac {9}{4} x^{4} e d^{2} c a^{2} A + \frac {1}{4} x^{4} e^{3} a^{3} A + \frac {1}{3} x^{3} d^{3} a^{3} C + x^{3} e d^{2} a^{3} B + x^{3} d^{3} c a^{2} A + x^{3} e^{2} d a^{3} A + \frac {1}{2} x^{2} d^{3} a^{3} B + \frac {3}{2} x^{2} e d^{2} a^{3} A + x d^{3} a^{3} A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 606, normalized size = 1.50 \[ \frac {1}{12} \, C c^{3} x^{12} e^{3} + \frac {3}{11} \, C c^{3} d x^{11} e^{2} + \frac {3}{10} \, C c^{3} d^{2} x^{10} e + \frac {1}{9} \, C c^{3} d^{3} x^{9} + \frac {1}{11} \, B c^{3} x^{11} e^{3} + \frac {3}{10} \, B c^{3} d x^{10} e^{2} + \frac {1}{3} \, B c^{3} d^{2} x^{9} e + \frac {1}{8} \, B c^{3} d^{3} x^{8} + \frac {3}{10} \, C a c^{2} x^{10} e^{3} + \frac {1}{10} \, A c^{3} x^{10} e^{3} + C a c^{2} d x^{9} e^{2} + \frac {1}{3} \, A c^{3} d x^{9} e^{2} + \frac {9}{8} \, C a c^{2} d^{2} x^{8} e + \frac {3}{8} \, A c^{3} d^{2} x^{8} e + \frac {3}{7} \, C a c^{2} d^{3} x^{7} + \frac {1}{7} \, A c^{3} d^{3} x^{7} + \frac {1}{3} \, B a c^{2} x^{9} e^{3} + \frac {9}{8} \, B a c^{2} d x^{8} e^{2} + \frac {9}{7} \, B a c^{2} d^{2} x^{7} e + \frac {1}{2} \, B a c^{2} d^{3} x^{6} + \frac {3}{8} \, C a^{2} c x^{8} e^{3} + \frac {3}{8} \, A a c^{2} x^{8} e^{3} + \frac {9}{7} \, C a^{2} c d x^{7} e^{2} + \frac {9}{7} \, A a c^{2} d x^{7} e^{2} + \frac {3}{2} \, C a^{2} c d^{2} x^{6} e + \frac {3}{2} \, A a c^{2} d^{2} x^{6} e + \frac {3}{5} \, C a^{2} c d^{3} x^{5} + \frac {3}{5} \, A a c^{2} d^{3} x^{5} + \frac {3}{7} \, B a^{2} c x^{7} e^{3} + \frac {3}{2} \, B a^{2} c d x^{6} e^{2} + \frac {9}{5} \, B a^{2} c d^{2} x^{5} e + \frac {3}{4} \, B a^{2} c d^{3} x^{4} + \frac {1}{6} \, C a^{3} x^{6} e^{3} + \frac {1}{2} \, A a^{2} c x^{6} e^{3} + \frac {3}{5} \, C a^{3} d x^{5} e^{2} + \frac {9}{5} \, A a^{2} c d x^{5} e^{2} + \frac {3}{4} \, C a^{3} d^{2} x^{4} e + \frac {9}{4} \, A a^{2} c d^{2} x^{4} e + \frac {1}{3} \, C a^{3} d^{3} x^{3} + A a^{2} c d^{3} x^{3} + \frac {1}{5} \, B a^{3} x^{5} e^{3} + \frac {3}{4} \, B a^{3} d x^{4} e^{2} + B a^{3} d^{2} x^{3} e + \frac {1}{2} \, B a^{3} d^{3} x^{2} + \frac {1}{4} \, A a^{3} x^{4} e^{3} + A a^{3} d x^{3} e^{2} + \frac {3}{2} \, A a^{3} d^{2} x^{2} e + A a^{3} d^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 553, normalized size = 1.37 \[ \frac {C \,c^{3} e^{3} x^{12}}{12}+\frac {\left (e^{3} c^{3} B +3 d \,e^{2} c^{3} C \right ) x^{11}}{11}+\frac {\left (A \,c^{3} e^{3}+3 B \,c^{3} d \,e^{2}+\left (3 e^{3} a \,c^{2}+3 d^{2} e \,c^{3}\right ) C \right ) x^{10}}{10}+\frac {\left (3 A \,c^{3} d \,e^{2}+\left (3 e^{3} a \,c^{2}+3 d^{2} e \,c^{3}\right ) B +\left (9 d \,e^{2} a \,c^{2}+d^{3} c^{3}\right ) C \right ) x^{9}}{9}+A \,a^{3} d^{3} x +\frac {\left (\left (3 e^{3} a \,c^{2}+3 d^{2} e \,c^{3}\right ) A +\left (9 d \,e^{2} a \,c^{2}+d^{3} c^{3}\right ) B +\left (3 e^{3} a^{2} c +9 d^{2} e a \,c^{2}\right ) C \right ) x^{8}}{8}+\frac {\left (\left (9 d \,e^{2} a \,c^{2}+d^{3} c^{3}\right ) A +\left (3 e^{3} a^{2} c +9 d^{2} e a \,c^{2}\right ) B +\left (9 d \,e^{2} a^{2} c +3 d^{3} a \,c^{2}\right ) C \right ) x^{7}}{7}+\frac {\left (\left (3 e^{3} a^{2} c +9 d^{2} e a \,c^{2}\right ) A +\left (9 d \,e^{2} a^{2} c +3 d^{3} a \,c^{2}\right ) B +\left (e^{3} a^{3}+9 d^{2} e \,a^{2} c \right ) C \right ) x^{6}}{6}+\frac {\left (\left (9 d \,e^{2} a^{2} c +3 d^{3} a \,c^{2}\right ) A +\left (e^{3} a^{3}+9 d^{2} e \,a^{2} c \right ) B +\left (3 d \,e^{2} a^{3}+3 d^{3} a^{2} c \right ) C \right ) x^{5}}{5}+\frac {\left (3 C \,a^{3} d^{2} e +\left (e^{3} a^{3}+9 d^{2} e \,a^{2} c \right ) A +\left (3 d \,e^{2} a^{3}+3 d^{3} a^{2} c \right ) B \right ) x^{4}}{4}+\frac {\left (3 B \,a^{3} d^{2} e +C \,a^{3} d^{3}+\left (3 d \,e^{2} a^{3}+3 d^{3} a^{2} c \right ) A \right ) x^{3}}{3}+\frac {\left (3 d^{2} e \,a^{3} A +d^{3} a^{3} B \right ) x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 512, normalized size = 1.27 \[ \frac {1}{12} \, C c^{3} e^{3} x^{12} + \frac {1}{11} \, {\left (3 \, C c^{3} d e^{2} + B c^{3} e^{3}\right )} x^{11} + \frac {1}{10} \, {\left (3 \, C c^{3} d^{2} e + 3 \, B c^{3} d e^{2} + {\left (3 \, C a c^{2} + A c^{3}\right )} e^{3}\right )} x^{10} + \frac {1}{9} \, {\left (C c^{3} d^{3} + 3 \, B c^{3} d^{2} e + 3 \, B a c^{2} e^{3} + 3 \, {\left (3 \, C a c^{2} + A c^{3}\right )} d e^{2}\right )} x^{9} + \frac {1}{8} \, {\left (B c^{3} d^{3} + 9 \, B a c^{2} d e^{2} + 3 \, {\left (3 \, C a c^{2} + A c^{3}\right )} d^{2} e + 3 \, {\left (C a^{2} c + A a c^{2}\right )} e^{3}\right )} x^{8} + A a^{3} d^{3} x + \frac {1}{7} \, {\left (9 \, B a c^{2} d^{2} e + 3 \, B a^{2} c e^{3} + {\left (3 \, C a c^{2} + A c^{3}\right )} d^{3} + 9 \, {\left (C a^{2} c + A a c^{2}\right )} d e^{2}\right )} x^{7} + \frac {1}{6} \, {\left (3 \, B a c^{2} d^{3} + 9 \, B a^{2} c d e^{2} + 9 \, {\left (C a^{2} c + A a c^{2}\right )} d^{2} e + {\left (C a^{3} + 3 \, A a^{2} c\right )} e^{3}\right )} x^{6} + \frac {1}{5} \, {\left (9 \, B a^{2} c d^{2} e + B a^{3} e^{3} + 3 \, {\left (C a^{2} c + A a c^{2}\right )} d^{3} + 3 \, {\left (C a^{3} + 3 \, A a^{2} c\right )} d e^{2}\right )} x^{5} + \frac {1}{4} \, {\left (3 \, B a^{2} c d^{3} + 3 \, B a^{3} d e^{2} + A a^{3} e^{3} + 3 \, {\left (C a^{3} + 3 \, A a^{2} c\right )} d^{2} e\right )} x^{4} + \frac {1}{3} \, {\left (3 \, B a^{3} d^{2} e + 3 \, A a^{3} d e^{2} + {\left (C a^{3} + 3 \, A a^{2} c\right )} d^{3}\right )} x^{3} + \frac {1}{2} \, {\left (B a^{3} d^{3} + 3 \, A a^{3} d^{2} e\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.05, size = 490, normalized size = 1.21 \[ x^5\,\left (\frac {3\,C\,a^3\,d\,e^2}{5}+\frac {B\,a^3\,e^3}{5}+\frac {3\,C\,a^2\,c\,d^3}{5}+\frac {9\,B\,a^2\,c\,d^2\,e}{5}+\frac {9\,A\,a^2\,c\,d\,e^2}{5}+\frac {3\,A\,a\,c^2\,d^3}{5}\right )+x^8\,\left (\frac {3\,C\,a^2\,c\,e^3}{8}+\frac {9\,C\,a\,c^2\,d^2\,e}{8}+\frac {9\,B\,a\,c^2\,d\,e^2}{8}+\frac {3\,A\,a\,c^2\,e^3}{8}+\frac {B\,c^3\,d^3}{8}+\frac {3\,A\,c^3\,d^2\,e}{8}\right )+x^6\,\left (\frac {C\,a^3\,e^3}{6}+\frac {3\,C\,a^2\,c\,d^2\,e}{2}+\frac {3\,B\,a^2\,c\,d\,e^2}{2}+\frac {A\,a^2\,c\,e^3}{2}+\frac {B\,a\,c^2\,d^3}{2}+\frac {3\,A\,a\,c^2\,d^2\,e}{2}\right )+x^7\,\left (\frac {9\,C\,a^2\,c\,d\,e^2}{7}+\frac {3\,B\,a^2\,c\,e^3}{7}+\frac {3\,C\,a\,c^2\,d^3}{7}+\frac {9\,B\,a\,c^2\,d^2\,e}{7}+\frac {9\,A\,a\,c^2\,d\,e^2}{7}+\frac {A\,c^3\,d^3}{7}\right )+\frac {a^2\,x^4\,\left (A\,a\,e^3+3\,B\,c\,d^3+3\,B\,a\,d\,e^2+9\,A\,c\,d^2\,e+3\,C\,a\,d^2\,e\right )}{4}+\frac {c^2\,x^9\,\left (3\,B\,a\,e^3+C\,c\,d^3+3\,A\,c\,d\,e^2+9\,C\,a\,d\,e^2+3\,B\,c\,d^2\,e\right )}{9}+\frac {C\,c^3\,e^3\,x^{12}}{12}+\frac {a^3\,d^2\,x^2\,\left (3\,A\,e+B\,d\right )}{2}+\frac {c^3\,e^2\,x^{11}\,\left (B\,e+3\,C\,d\right )}{11}+A\,a^3\,d^3\,x+\frac {a^2\,d\,x^3\,\left (3\,A\,a\,e^2+3\,A\,c\,d^2+C\,a\,d^2+3\,B\,a\,d\,e\right )}{3}+\frac {c^2\,e\,x^{10}\,\left (A\,c\,e^2+3\,C\,a\,e^2+3\,C\,c\,d^2+3\,B\,c\,d\,e\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 646, normalized size = 1.60 \[ A a^{3} d^{3} x + \frac {C c^{3} e^{3} x^{12}}{12} + x^{11} \left (\frac {B c^{3} e^{3}}{11} + \frac {3 C c^{3} d e^{2}}{11}\right ) + x^{10} \left (\frac {A c^{3} e^{3}}{10} + \frac {3 B c^{3} d e^{2}}{10} + \frac {3 C a c^{2} e^{3}}{10} + \frac {3 C c^{3} d^{2} e}{10}\right ) + x^{9} \left (\frac {A c^{3} d e^{2}}{3} + \frac {B a c^{2} e^{3}}{3} + \frac {B c^{3} d^{2} e}{3} + C a c^{2} d e^{2} + \frac {C c^{3} d^{3}}{9}\right ) + x^{8} \left (\frac {3 A a c^{2} e^{3}}{8} + \frac {3 A c^{3} d^{2} e}{8} + \frac {9 B a c^{2} d e^{2}}{8} + \frac {B c^{3} d^{3}}{8} + \frac {3 C a^{2} c e^{3}}{8} + \frac {9 C a c^{2} d^{2} e}{8}\right ) + x^{7} \left (\frac {9 A a c^{2} d e^{2}}{7} + \frac {A c^{3} d^{3}}{7} + \frac {3 B a^{2} c e^{3}}{7} + \frac {9 B a c^{2} d^{2} e}{7} + \frac {9 C a^{2} c d e^{2}}{7} + \frac {3 C a c^{2} d^{3}}{7}\right ) + x^{6} \left (\frac {A a^{2} c e^{3}}{2} + \frac {3 A a c^{2} d^{2} e}{2} + \frac {3 B a^{2} c d e^{2}}{2} + \frac {B a c^{2} d^{3}}{2} + \frac {C a^{3} e^{3}}{6} + \frac {3 C a^{2} c d^{2} e}{2}\right ) + x^{5} \left (\frac {9 A a^{2} c d e^{2}}{5} + \frac {3 A a c^{2} d^{3}}{5} + \frac {B a^{3} e^{3}}{5} + \frac {9 B a^{2} c d^{2} e}{5} + \frac {3 C a^{3} d e^{2}}{5} + \frac {3 C a^{2} c d^{3}}{5}\right ) + x^{4} \left (\frac {A a^{3} e^{3}}{4} + \frac {9 A a^{2} c d^{2} e}{4} + \frac {3 B a^{3} d e^{2}}{4} + \frac {3 B a^{2} c d^{3}}{4} + \frac {3 C a^{3} d^{2} e}{4}\right ) + x^{3} \left (A a^{3} d e^{2} + A a^{2} c d^{3} + B a^{3} d^{2} e + \frac {C a^{3} d^{3}}{3}\right ) + x^{2} \left (\frac {3 A a^{3} d^{2} e}{2} + \frac {B a^{3} d^{3}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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