Optimal. Leaf size=290 \[ \frac {(A b-a B) (b d-a e)^6 (a+b x)^7}{7 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^8}{8 b^8}+\frac {e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^9}{3 b^8}+\frac {e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{10}}{2 b^8}+\frac {5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{11}}{11 b^8}+\frac {e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{12}}{4 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {B e^6 (a+b x)^{14}}{14 b^8} \]
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Rubi [A]
time = 0.65, antiderivative size = 290, 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 = {78}
\begin {gather*} \frac {e^5 (a+b x)^{13} (-7 a B e+A b e+6 b B d)}{13 b^8}+\frac {e^4 (a+b x)^{12} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{4 b^8}+\frac {5 e^3 (a+b x)^{11} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{11 b^8}+\frac {e^2 (a+b x)^{10} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{2 b^8}+\frac {e (a+b x)^9 (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{3 b^8}+\frac {(a+b x)^8 (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{8 b^8}+\frac {(a+b x)^7 (A b-a B) (b d-a e)^6}{7 b^8}+\frac {B e^6 (a+b x)^{14}}{14 b^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (a+b x)^6 (A+B x) (d+e x)^6 \, dx &=\int \left (\frac {(A b-a B) (b d-a e)^6 (a+b x)^6}{b^7}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^7}{b^7}+\frac {3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^8}{b^7}+\frac {5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^9}{b^7}+\frac {5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{10}}{b^7}+\frac {3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{11}}{b^7}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{12}}{b^7}+\frac {B e^6 (a+b x)^{13}}{b^7}\right ) \, dx\\ &=\frac {(A b-a B) (b d-a e)^6 (a+b x)^7}{7 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^8}{8 b^8}+\frac {e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^9}{3 b^8}+\frac {e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{10}}{2 b^8}+\frac {5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{11}}{11 b^8}+\frac {e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{12}}{4 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {B e^6 (a+b x)^{14}}{14 b^8}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1069\) vs. \(2(290)=580\).
time = 0.27, size = 1069, normalized size = 3.69 \begin {gather*} a^6 A d^6 x+\frac {1}{2} a^5 d^5 (a B d+6 A (b d+a e)) x^2+a^4 d^4 \left (2 a B d (b d+a e)+A \left (5 b^2 d^2+12 a b d e+5 a^2 e^2\right )\right ) x^3+\frac {1}{4} a^3 d^3 \left (3 a B d \left (5 b^2 d^2+12 a b d e+5 a^2 e^2\right )+10 A \left (2 b^3 d^3+9 a b^2 d^2 e+9 a^2 b d e^2+2 a^3 e^3\right )\right ) x^4+a^2 d^2 \left (2 a B d \left (2 b^3 d^3+9 a b^2 d^2 e+9 a^2 b d e^2+2 a^3 e^3\right )+3 A \left (b^4 d^4+8 a b^3 d^3 e+15 a^2 b^2 d^2 e^2+8 a^3 b d e^3+a^4 e^4\right )\right ) x^5+\frac {1}{2} a d \left (5 a B d \left (b^4 d^4+8 a b^3 d^3 e+15 a^2 b^2 d^2 e^2+8 a^3 b d e^3+a^4 e^4\right )+2 A \left (b^5 d^5+15 a b^4 d^4 e+50 a^2 b^3 d^3 e^2+50 a^3 b^2 d^2 e^3+15 a^4 b d e^4+a^5 e^5\right )\right ) x^6+\frac {1}{7} \left (6 a B d \left (b^5 d^5+15 a b^4 d^4 e+50 a^2 b^3 d^3 e^2+50 a^3 b^2 d^2 e^3+15 a^4 b d e^4+a^5 e^5\right )+A \left (b^6 d^6+36 a b^5 d^5 e+225 a^2 b^4 d^4 e^2+400 a^3 b^3 d^3 e^3+225 a^4 b^2 d^2 e^4+36 a^5 b d e^5+a^6 e^6\right )\right ) x^7+\frac {1}{8} \left (a^6 B e^6+6 a^5 b e^5 (6 B d+A e)+45 a^4 b^2 d e^4 (5 B d+2 A e)+100 a^3 b^3 d^2 e^3 (4 B d+3 A e)+75 a^2 b^4 d^3 e^2 (3 B d+4 A e)+18 a b^5 d^4 e (2 B d+5 A e)+b^6 d^5 (B d+6 A e)\right ) x^8+\frac {1}{3} b e \left (2 a^5 B e^5+5 a^4 b e^4 (6 B d+A e)+20 a^3 b^2 d e^3 (5 B d+2 A e)+25 a^2 b^3 d^2 e^2 (4 B d+3 A e)+10 a b^4 d^3 e (3 B d+4 A e)+b^5 d^4 (2 B d+5 A e)\right ) x^9+\frac {1}{2} b^2 e^2 \left (3 a^4 B e^4+4 a^3 b e^3 (6 B d+A e)+9 a^2 b^2 d e^2 (5 B d+2 A e)+6 a b^3 d^2 e (4 B d+3 A e)+b^4 d^3 (3 B d+4 A e)\right ) x^{10}+\frac {1}{11} b^3 e^3 \left (20 a^3 B e^3+15 a^2 b e^2 (6 B d+A e)+18 a b^2 d e (5 B d+2 A e)+5 b^3 d^2 (4 B d+3 A e)\right ) x^{11}+\frac {1}{4} b^4 e^4 \left (5 a^2 B e^2+2 a b e (6 B d+A e)+b^2 d (5 B d+2 A e)\right ) x^{12}+\frac {1}{13} b^5 e^5 (6 b B d+A b e+6 a B e) x^{13}+\frac {1}{14} b^6 B e^6 x^{14} \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. \(1172\) vs.
\(2(274)=548\).
time = 0.07, size = 1173, normalized size = 4.04 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. 1199 vs.
\(2 (288) = 576\).
time = 0.32, size = 1199, normalized size = 4.13 \begin {gather*} \frac {1}{14} \, B b^{6} x^{14} e^{6} + A a^{6} d^{6} x + \frac {1}{13} \, {\left (6 \, B b^{6} d e^{5} + 6 \, B a b^{5} e^{6} + A b^{6} e^{6}\right )} x^{13} + \frac {1}{4} \, {\left (5 \, B b^{6} d^{2} e^{4} + 5 \, B a^{2} b^{4} e^{6} + 2 \, A a b^{5} e^{6} + 2 \, {\left (6 \, B a b^{5} e^{5} + A b^{6} e^{5}\right )} d\right )} x^{12} + \frac {1}{11} \, {\left (20 \, B b^{6} d^{3} e^{3} + 20 \, B a^{3} b^{3} e^{6} + 15 \, A a^{2} b^{4} e^{6} + 15 \, {\left (6 \, B a b^{5} e^{4} + A b^{6} e^{4}\right )} d^{2} + 18 \, {\left (5 \, B a^{2} b^{4} e^{5} + 2 \, A a b^{5} e^{5}\right )} d\right )} x^{11} + \frac {1}{2} \, {\left (3 \, B b^{6} d^{4} e^{2} + 3 \, B a^{4} b^{2} e^{6} + 4 \, A a^{3} b^{3} e^{6} + 4 \, {\left (6 \, B a b^{5} e^{3} + A b^{6} e^{3}\right )} d^{3} + 9 \, {\left (5 \, B a^{2} b^{4} e^{4} + 2 \, A a b^{5} e^{4}\right )} d^{2} + 6 \, {\left (4 \, B a^{3} b^{3} e^{5} + 3 \, A a^{2} b^{4} e^{5}\right )} d\right )} x^{10} + \frac {1}{3} \, {\left (2 \, B b^{6} d^{5} e + 2 \, B a^{5} b e^{6} + 5 \, A a^{4} b^{2} e^{6} + 5 \, {\left (6 \, B a b^{5} e^{2} + A b^{6} e^{2}\right )} d^{4} + 20 \, {\left (5 \, B a^{2} b^{4} e^{3} + 2 \, A a b^{5} e^{3}\right )} d^{3} + 25 \, {\left (4 \, B a^{3} b^{3} e^{4} + 3 \, A a^{2} b^{4} e^{4}\right )} d^{2} + 10 \, {\left (3 \, B a^{4} b^{2} e^{5} + 4 \, A a^{3} b^{3} e^{5}\right )} d\right )} x^{9} + \frac {1}{8} \, {\left (B b^{6} d^{6} + B a^{6} e^{6} + 6 \, A a^{5} b e^{6} + 6 \, {\left (6 \, B a b^{5} e + A b^{6} e\right )} d^{5} + 45 \, {\left (5 \, B a^{2} b^{4} e^{2} + 2 \, A a b^{5} e^{2}\right )} d^{4} + 100 \, {\left (4 \, B a^{3} b^{3} e^{3} + 3 \, A a^{2} b^{4} e^{3}\right )} d^{3} + 75 \, {\left (3 \, B a^{4} b^{2} e^{4} + 4 \, A a^{3} b^{3} e^{4}\right )} d^{2} + 18 \, {\left (2 \, B a^{5} b e^{5} + 5 \, A a^{4} b^{2} e^{5}\right )} d\right )} x^{8} + \frac {1}{7} \, {\left (A a^{6} e^{6} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} + 18 \, {\left (5 \, B a^{2} b^{4} e + 2 \, A a b^{5} e\right )} d^{5} + 75 \, {\left (4 \, B a^{3} b^{3} e^{2} + 3 \, A a^{2} b^{4} e^{2}\right )} d^{4} + 100 \, {\left (3 \, B a^{4} b^{2} e^{3} + 4 \, A a^{3} b^{3} e^{3}\right )} d^{3} + 45 \, {\left (2 \, B a^{5} b e^{4} + 5 \, A a^{4} b^{2} e^{4}\right )} d^{2} + 6 \, {\left (B a^{6} e^{5} + 6 \, A a^{5} b e^{5}\right )} d\right )} x^{7} + \frac {1}{2} \, {\left (2 \, A a^{6} d e^{5} + {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{6} + 10 \, {\left (4 \, B a^{3} b^{3} e + 3 \, A a^{2} b^{4} e\right )} d^{5} + 25 \, {\left (3 \, B a^{4} b^{2} e^{2} + 4 \, A a^{3} b^{3} e^{2}\right )} d^{4} + 20 \, {\left (2 \, B a^{5} b e^{3} + 5 \, A a^{4} b^{2} e^{3}\right )} d^{3} + 5 \, {\left (B a^{6} e^{4} + 6 \, A a^{5} b e^{4}\right )} d^{2}\right )} x^{6} + {\left (3 \, A a^{6} d^{2} e^{4} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{6} + 6 \, {\left (3 \, B a^{4} b^{2} e + 4 \, A a^{3} b^{3} e\right )} d^{5} + 9 \, {\left (2 \, B a^{5} b e^{2} + 5 \, A a^{4} b^{2} e^{2}\right )} d^{4} + 4 \, {\left (B a^{6} e^{3} + 6 \, A a^{5} b e^{3}\right )} d^{3}\right )} x^{5} + \frac {1}{4} \, {\left (20 \, A a^{6} d^{3} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{6} + 18 \, {\left (2 \, B a^{5} b e + 5 \, A a^{4} b^{2} e\right )} d^{5} + 15 \, {\left (B a^{6} e^{2} + 6 \, A a^{5} b e^{2}\right )} d^{4}\right )} x^{4} + {\left (5 \, A a^{6} d^{4} e^{2} + {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{6} + 2 \, {\left (B a^{6} e + 6 \, A a^{5} b e\right )} d^{5}\right )} x^{3} + \frac {1}{2} \, {\left (6 \, A a^{6} d^{5} e + {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{6}\right )} x^{2} \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. 1176 vs.
\(2 (288) = 576\).
time = 1.12, size = 1176, normalized size = 4.06 \begin {gather*} \frac {1}{8} \, B b^{6} d^{6} x^{8} + A a^{6} d^{6} x + \frac {1}{7} \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} x^{7} + \frac {1}{2} \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{6} x^{6} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{6} x^{5} + \frac {5}{4} \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{6} x^{4} + {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{6} x^{3} + \frac {1}{2} \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{6} x^{2} + \frac {1}{24024} \, {\left (1716 \, B b^{6} x^{14} + 3432 \, A a^{6} x^{7} + 1848 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{13} + 6006 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{12} + 10920 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{11} + 12012 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{10} + 8008 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{9} + 3003 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x^{8}\right )} e^{6} + \frac {1}{12012} \, {\left (5544 \, B b^{6} d x^{13} + 12012 \, A a^{6} d x^{6} + 6006 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d x^{12} + 19656 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d x^{11} + 36036 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d x^{10} + 40040 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d x^{9} + 27027 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d x^{8} + 10296 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d x^{7}\right )} e^{5} + \frac {1}{1848} \, {\left (2310 \, B b^{6} d^{2} x^{12} + 5544 \, A a^{6} d^{2} x^{5} + 2520 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} x^{11} + 8316 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} x^{10} + 15400 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} x^{9} + 17325 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} x^{8} + 11880 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} x^{7} + 4620 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{2} x^{6}\right )} e^{4} + \frac {1}{462} \, {\left (840 \, B b^{6} d^{3} x^{11} + 2310 \, A a^{6} d^{3} x^{4} + 924 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} x^{10} + 3080 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} x^{9} + 5775 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} x^{8} + 6600 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} x^{7} + 4620 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{3} x^{6} + 1848 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{3} x^{5}\right )} e^{3} + \frac {1}{168} \, {\left (252 \, B b^{6} d^{4} x^{10} + 840 \, A a^{6} d^{4} x^{3} + 280 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} x^{9} + 945 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} x^{8} + 1800 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} x^{7} + 2100 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{4} x^{6} + 1512 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{4} x^{5} + 630 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{4} x^{4}\right )} e^{2} + \frac {1}{84} \, {\left (56 \, B b^{6} d^{5} x^{9} + 252 \, A a^{6} d^{5} x^{2} + 63 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} x^{8} + 216 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} x^{7} + 420 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{5} x^{6} + 504 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{5} x^{5} + 378 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{5} x^{4} + 168 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{5} x^{3}\right )} e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1504 vs.
\(2 (292) = 584\).
time = 0.12, size = 1504, normalized size = 5.19 \begin {gather*} A a^{6} d^{6} x + \frac {B b^{6} e^{6} x^{14}}{14} + x^{13} \left (\frac {A b^{6} e^{6}}{13} + \frac {6 B a b^{5} e^{6}}{13} + \frac {6 B b^{6} d e^{5}}{13}\right ) + x^{12} \left (\frac {A a b^{5} e^{6}}{2} + \frac {A b^{6} d e^{5}}{2} + \frac {5 B a^{2} b^{4} e^{6}}{4} + 3 B a b^{5} d e^{5} + \frac {5 B b^{6} d^{2} e^{4}}{4}\right ) + x^{11} \cdot \left (\frac {15 A a^{2} b^{4} e^{6}}{11} + \frac {36 A a b^{5} d e^{5}}{11} + \frac {15 A b^{6} d^{2} e^{4}}{11} + \frac {20 B a^{3} b^{3} e^{6}}{11} + \frac {90 B a^{2} b^{4} d e^{5}}{11} + \frac {90 B a b^{5} d^{2} e^{4}}{11} + \frac {20 B b^{6} d^{3} e^{3}}{11}\right ) + x^{10} \cdot \left (2 A a^{3} b^{3} e^{6} + 9 A a^{2} b^{4} d e^{5} + 9 A a b^{5} d^{2} e^{4} + 2 A b^{6} d^{3} e^{3} + \frac {3 B a^{4} b^{2} e^{6}}{2} + 12 B a^{3} b^{3} d e^{5} + \frac {45 B a^{2} b^{4} d^{2} e^{4}}{2} + 12 B a b^{5} d^{3} e^{3} + \frac {3 B b^{6} d^{4} e^{2}}{2}\right ) + x^{9} \cdot \left (\frac {5 A a^{4} b^{2} e^{6}}{3} + \frac {40 A a^{3} b^{3} d e^{5}}{3} + 25 A a^{2} b^{4} d^{2} e^{4} + \frac {40 A a b^{5} d^{3} e^{3}}{3} + \frac {5 A b^{6} d^{4} e^{2}}{3} + \frac {2 B a^{5} b e^{6}}{3} + 10 B a^{4} b^{2} d e^{5} + \frac {100 B a^{3} b^{3} d^{2} e^{4}}{3} + \frac {100 B a^{2} b^{4} d^{3} e^{3}}{3} + 10 B a b^{5} d^{4} e^{2} + \frac {2 B b^{6} d^{5} e}{3}\right ) + x^{8} \cdot \left (\frac {3 A a^{5} b e^{6}}{4} + \frac {45 A a^{4} b^{2} d e^{5}}{4} + \frac {75 A a^{3} b^{3} d^{2} e^{4}}{2} + \frac {75 A a^{2} b^{4} d^{3} e^{3}}{2} + \frac {45 A a b^{5} d^{4} e^{2}}{4} + \frac {3 A b^{6} d^{5} e}{4} + \frac {B a^{6} e^{6}}{8} + \frac {9 B a^{5} b d e^{5}}{2} + \frac {225 B a^{4} b^{2} d^{2} e^{4}}{8} + 50 B a^{3} b^{3} d^{3} e^{3} + \frac {225 B a^{2} b^{4} d^{4} e^{2}}{8} + \frac {9 B a b^{5} d^{5} e}{2} + \frac {B b^{6} d^{6}}{8}\right ) + x^{7} \left (\frac {A a^{6} e^{6}}{7} + \frac {36 A a^{5} b d e^{5}}{7} + \frac {225 A a^{4} b^{2} d^{2} e^{4}}{7} + \frac {400 A a^{3} b^{3} d^{3} e^{3}}{7} + \frac {225 A a^{2} b^{4} d^{4} e^{2}}{7} + \frac {36 A a b^{5} d^{5} e}{7} + \frac {A b^{6} d^{6}}{7} + \frac {6 B a^{6} d e^{5}}{7} + \frac {90 B a^{5} b d^{2} e^{4}}{7} + \frac {300 B a^{4} b^{2} d^{3} e^{3}}{7} + \frac {300 B a^{3} b^{3} d^{4} e^{2}}{7} + \frac {90 B a^{2} b^{4} d^{5} e}{7} + \frac {6 B a b^{5} d^{6}}{7}\right ) + x^{6} \left (A a^{6} d e^{5} + 15 A a^{5} b d^{2} e^{4} + 50 A a^{4} b^{2} d^{3} e^{3} + 50 A a^{3} b^{3} d^{4} e^{2} + 15 A a^{2} b^{4} d^{5} e + A a b^{5} d^{6} + \frac {5 B a^{6} d^{2} e^{4}}{2} + 20 B a^{5} b d^{3} e^{3} + \frac {75 B a^{4} b^{2} d^{4} e^{2}}{2} + 20 B a^{3} b^{3} d^{5} e + \frac {5 B a^{2} b^{4} d^{6}}{2}\right ) + x^{5} \cdot \left (3 A a^{6} d^{2} e^{4} + 24 A a^{5} b d^{3} e^{3} + 45 A a^{4} b^{2} d^{4} e^{2} + 24 A a^{3} b^{3} d^{5} e + 3 A a^{2} b^{4} d^{6} + 4 B a^{6} d^{3} e^{3} + 18 B a^{5} b d^{4} e^{2} + 18 B a^{4} b^{2} d^{5} e + 4 B a^{3} b^{3} d^{6}\right ) + x^{4} \cdot \left (5 A a^{6} d^{3} e^{3} + \frac {45 A a^{5} b d^{4} e^{2}}{2} + \frac {45 A a^{4} b^{2} d^{5} e}{2} + 5 A a^{3} b^{3} d^{6} + \frac {15 B a^{6} d^{4} e^{2}}{4} + 9 B a^{5} b d^{5} e + \frac {15 B a^{4} b^{2} d^{6}}{4}\right ) + x^{3} \cdot \left (5 A a^{6} d^{4} e^{2} + 12 A a^{5} b d^{5} e + 5 A a^{4} b^{2} d^{6} + 2 B a^{6} d^{5} e + 2 B a^{5} b d^{6}\right ) + x^{2} \cdot \left (3 A a^{6} d^{5} e + 3 A a^{5} b d^{6} + \frac {B a^{6} d^{6}}{2}\right ) \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. 1424 vs.
\(2 (288) = 576\).
time = 2.49, size = 1424, normalized size = 4.91 \begin {gather*} \frac {1}{14} \, B b^{6} x^{14} e^{6} + \frac {6}{13} \, B b^{6} d x^{13} e^{5} + \frac {5}{4} \, B b^{6} d^{2} x^{12} e^{4} + \frac {20}{11} \, B b^{6} d^{3} x^{11} e^{3} + \frac {3}{2} \, B b^{6} d^{4} x^{10} e^{2} + \frac {2}{3} \, B b^{6} d^{5} x^{9} e + \frac {1}{8} \, B b^{6} d^{6} x^{8} + \frac {6}{13} \, B a b^{5} x^{13} e^{6} + \frac {1}{13} \, A b^{6} x^{13} e^{6} + 3 \, B a b^{5} d x^{12} e^{5} + \frac {1}{2} \, A b^{6} d x^{12} e^{5} + \frac {90}{11} \, B a b^{5} d^{2} x^{11} e^{4} + \frac {15}{11} \, A b^{6} d^{2} x^{11} e^{4} + 12 \, B a b^{5} d^{3} x^{10} e^{3} + 2 \, A b^{6} d^{3} x^{10} e^{3} + 10 \, B a b^{5} d^{4} x^{9} e^{2} + \frac {5}{3} \, A b^{6} d^{4} x^{9} e^{2} + \frac {9}{2} \, B a b^{5} d^{5} x^{8} e + \frac {3}{4} \, A b^{6} d^{5} x^{8} e + \frac {6}{7} \, B a b^{5} d^{6} x^{7} + \frac {1}{7} \, A b^{6} d^{6} x^{7} + \frac {5}{4} \, B a^{2} b^{4} x^{12} e^{6} + \frac {1}{2} \, A a b^{5} x^{12} e^{6} + \frac {90}{11} \, B a^{2} b^{4} d x^{11} e^{5} + \frac {36}{11} \, A a b^{5} d x^{11} e^{5} + \frac {45}{2} \, B a^{2} b^{4} d^{2} x^{10} e^{4} + 9 \, A a b^{5} d^{2} x^{10} e^{4} + \frac {100}{3} \, B a^{2} b^{4} d^{3} x^{9} e^{3} + \frac {40}{3} \, A a b^{5} d^{3} x^{9} e^{3} + \frac {225}{8} \, B a^{2} b^{4} d^{4} x^{8} e^{2} + \frac {45}{4} \, A a b^{5} d^{4} x^{8} e^{2} + \frac {90}{7} \, B a^{2} b^{4} d^{5} x^{7} e + \frac {36}{7} \, A a b^{5} d^{5} x^{7} e + \frac {5}{2} \, B a^{2} b^{4} d^{6} x^{6} + A a b^{5} d^{6} x^{6} + \frac {20}{11} \, B a^{3} b^{3} x^{11} e^{6} + \frac {15}{11} \, A a^{2} b^{4} x^{11} e^{6} + 12 \, B a^{3} b^{3} d x^{10} e^{5} + 9 \, A a^{2} b^{4} d x^{10} e^{5} + \frac {100}{3} \, B a^{3} b^{3} d^{2} x^{9} e^{4} + 25 \, A a^{2} b^{4} d^{2} x^{9} e^{4} + 50 \, B a^{3} b^{3} d^{3} x^{8} e^{3} + \frac {75}{2} \, A a^{2} b^{4} d^{3} x^{8} e^{3} + \frac {300}{7} \, B a^{3} b^{3} d^{4} x^{7} e^{2} + \frac {225}{7} \, A a^{2} b^{4} d^{4} x^{7} e^{2} + 20 \, B a^{3} b^{3} d^{5} x^{6} e + 15 \, A a^{2} b^{4} d^{5} x^{6} e + 4 \, B a^{3} b^{3} d^{6} x^{5} + 3 \, A a^{2} b^{4} d^{6} x^{5} + \frac {3}{2} \, B a^{4} b^{2} x^{10} e^{6} + 2 \, A a^{3} b^{3} x^{10} e^{6} + 10 \, B a^{4} b^{2} d x^{9} e^{5} + \frac {40}{3} \, A a^{3} b^{3} d x^{9} e^{5} + \frac {225}{8} \, B a^{4} b^{2} d^{2} x^{8} e^{4} + \frac {75}{2} \, A a^{3} b^{3} d^{2} x^{8} e^{4} + \frac {300}{7} \, B a^{4} b^{2} d^{3} x^{7} e^{3} + \frac {400}{7} \, A a^{3} b^{3} d^{3} x^{7} e^{3} + \frac {75}{2} \, B a^{4} b^{2} d^{4} x^{6} e^{2} + 50 \, A a^{3} b^{3} d^{4} x^{6} e^{2} + 18 \, B a^{4} b^{2} d^{5} x^{5} e + 24 \, A a^{3} b^{3} d^{5} x^{5} e + \frac {15}{4} \, B a^{4} b^{2} d^{6} x^{4} + 5 \, A a^{3} b^{3} d^{6} x^{4} + \frac {2}{3} \, B a^{5} b x^{9} e^{6} + \frac {5}{3} \, A a^{4} b^{2} x^{9} e^{6} + \frac {9}{2} \, B a^{5} b d x^{8} e^{5} + \frac {45}{4} \, A a^{4} b^{2} d x^{8} e^{5} + \frac {90}{7} \, B a^{5} b d^{2} x^{7} e^{4} + \frac {225}{7} \, A a^{4} b^{2} d^{2} x^{7} e^{4} + 20 \, B a^{5} b d^{3} x^{6} e^{3} + 50 \, A a^{4} b^{2} d^{3} x^{6} e^{3} + 18 \, B a^{5} b d^{4} x^{5} e^{2} + 45 \, A a^{4} b^{2} d^{4} x^{5} e^{2} + 9 \, B a^{5} b d^{5} x^{4} e + \frac {45}{2} \, A a^{4} b^{2} d^{5} x^{4} e + 2 \, B a^{5} b d^{6} x^{3} + 5 \, A a^{4} b^{2} d^{6} x^{3} + \frac {1}{8} \, B a^{6} x^{8} e^{6} + \frac {3}{4} \, A a^{5} b x^{8} e^{6} + \frac {6}{7} \, B a^{6} d x^{7} e^{5} + \frac {36}{7} \, A a^{5} b d x^{7} e^{5} + \frac {5}{2} \, B a^{6} d^{2} x^{6} e^{4} + 15 \, A a^{5} b d^{2} x^{6} e^{4} + 4 \, B a^{6} d^{3} x^{5} e^{3} + 24 \, A a^{5} b d^{3} x^{5} e^{3} + \frac {15}{4} \, B a^{6} d^{4} x^{4} e^{2} + \frac {45}{2} \, A a^{5} b d^{4} x^{4} e^{2} + 2 \, B a^{6} d^{5} x^{3} e + 12 \, A a^{5} b d^{5} x^{3} e + \frac {1}{2} \, B a^{6} d^{6} x^{2} + 3 \, A a^{5} b d^{6} x^{2} + \frac {1}{7} \, A a^{6} x^{7} e^{6} + A a^{6} d x^{6} e^{5} + 3 \, A a^{6} d^{2} x^{5} e^{4} + 5 \, A a^{6} d^{3} x^{4} e^{3} + 5 \, A a^{6} d^{4} x^{3} e^{2} + 3 \, A a^{6} d^{5} x^{2} e + A a^{6} d^{6} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.39, size = 1221, normalized size = 4.21 \begin {gather*} x^5\,\left (4\,B\,a^6\,d^3\,e^3+3\,A\,a^6\,d^2\,e^4+18\,B\,a^5\,b\,d^4\,e^2+24\,A\,a^5\,b\,d^3\,e^3+18\,B\,a^4\,b^2\,d^5\,e+45\,A\,a^4\,b^2\,d^4\,e^2+4\,B\,a^3\,b^3\,d^6+24\,A\,a^3\,b^3\,d^5\,e+3\,A\,a^2\,b^4\,d^6\right )+x^{10}\,\left (\frac {3\,B\,a^4\,b^2\,e^6}{2}+12\,B\,a^3\,b^3\,d\,e^5+2\,A\,a^3\,b^3\,e^6+\frac {45\,B\,a^2\,b^4\,d^2\,e^4}{2}+9\,A\,a^2\,b^4\,d\,e^5+12\,B\,a\,b^5\,d^3\,e^3+9\,A\,a\,b^5\,d^2\,e^4+\frac {3\,B\,b^6\,d^4\,e^2}{2}+2\,A\,b^6\,d^3\,e^3\right )+x^6\,\left (\frac {5\,B\,a^6\,d^2\,e^4}{2}+A\,a^6\,d\,e^5+20\,B\,a^5\,b\,d^3\,e^3+15\,A\,a^5\,b\,d^2\,e^4+\frac {75\,B\,a^4\,b^2\,d^4\,e^2}{2}+50\,A\,a^4\,b^2\,d^3\,e^3+20\,B\,a^3\,b^3\,d^5\,e+50\,A\,a^3\,b^3\,d^4\,e^2+\frac {5\,B\,a^2\,b^4\,d^6}{2}+15\,A\,a^2\,b^4\,d^5\,e+A\,a\,b^5\,d^6\right )+x^9\,\left (\frac {2\,B\,a^5\,b\,e^6}{3}+10\,B\,a^4\,b^2\,d\,e^5+\frac {5\,A\,a^4\,b^2\,e^6}{3}+\frac {100\,B\,a^3\,b^3\,d^2\,e^4}{3}+\frac {40\,A\,a^3\,b^3\,d\,e^5}{3}+\frac {100\,B\,a^2\,b^4\,d^3\,e^3}{3}+25\,A\,a^2\,b^4\,d^2\,e^4+10\,B\,a\,b^5\,d^4\,e^2+\frac {40\,A\,a\,b^5\,d^3\,e^3}{3}+\frac {2\,B\,b^6\,d^5\,e}{3}+\frac {5\,A\,b^6\,d^4\,e^2}{3}\right )+x^7\,\left (\frac {6\,B\,a^6\,d\,e^5}{7}+\frac {A\,a^6\,e^6}{7}+\frac {90\,B\,a^5\,b\,d^2\,e^4}{7}+\frac {36\,A\,a^5\,b\,d\,e^5}{7}+\frac {300\,B\,a^4\,b^2\,d^3\,e^3}{7}+\frac {225\,A\,a^4\,b^2\,d^2\,e^4}{7}+\frac {300\,B\,a^3\,b^3\,d^4\,e^2}{7}+\frac {400\,A\,a^3\,b^3\,d^3\,e^3}{7}+\frac {90\,B\,a^2\,b^4\,d^5\,e}{7}+\frac {225\,A\,a^2\,b^4\,d^4\,e^2}{7}+\frac {6\,B\,a\,b^5\,d^6}{7}+\frac {36\,A\,a\,b^5\,d^5\,e}{7}+\frac {A\,b^6\,d^6}{7}\right )+x^4\,\left (\frac {15\,B\,a^6\,d^4\,e^2}{4}+5\,A\,a^6\,d^3\,e^3+9\,B\,a^5\,b\,d^5\,e+\frac {45\,A\,a^5\,b\,d^4\,e^2}{2}+\frac {15\,B\,a^4\,b^2\,d^6}{4}+\frac {45\,A\,a^4\,b^2\,d^5\,e}{2}+5\,A\,a^3\,b^3\,d^6\right )+x^8\,\left (\frac {B\,a^6\,e^6}{8}+\frac {9\,B\,a^5\,b\,d\,e^5}{2}+\frac {3\,A\,a^5\,b\,e^6}{4}+\frac {225\,B\,a^4\,b^2\,d^2\,e^4}{8}+\frac {45\,A\,a^4\,b^2\,d\,e^5}{4}+50\,B\,a^3\,b^3\,d^3\,e^3+\frac {75\,A\,a^3\,b^3\,d^2\,e^4}{2}+\frac {225\,B\,a^2\,b^4\,d^4\,e^2}{8}+\frac {75\,A\,a^2\,b^4\,d^3\,e^3}{2}+\frac {9\,B\,a\,b^5\,d^5\,e}{2}+\frac {45\,A\,a\,b^5\,d^4\,e^2}{4}+\frac {B\,b^6\,d^6}{8}+\frac {3\,A\,b^6\,d^5\,e}{4}\right )+x^{11}\,\left (\frac {20\,B\,a^3\,b^3\,e^6}{11}+\frac {90\,B\,a^2\,b^4\,d\,e^5}{11}+\frac {15\,A\,a^2\,b^4\,e^6}{11}+\frac {90\,B\,a\,b^5\,d^2\,e^4}{11}+\frac {36\,A\,a\,b^5\,d\,e^5}{11}+\frac {20\,B\,b^6\,d^3\,e^3}{11}+\frac {15\,A\,b^6\,d^2\,e^4}{11}\right )+\frac {a^5\,d^5\,x^2\,\left (6\,A\,a\,e+6\,A\,b\,d+B\,a\,d\right )}{2}+\frac {b^5\,e^5\,x^{13}\,\left (A\,b\,e+6\,B\,a\,e+6\,B\,b\,d\right )}{13}+A\,a^6\,d^6\,x+a^4\,d^4\,x^3\,\left (2\,B\,a^2\,d\,e+5\,A\,a^2\,e^2+2\,B\,a\,b\,d^2+12\,A\,a\,b\,d\,e+5\,A\,b^2\,d^2\right )+\frac {b^4\,e^4\,x^{12}\,\left (5\,B\,a^2\,e^2+12\,B\,a\,b\,d\,e+2\,A\,a\,b\,e^2+5\,B\,b^2\,d^2+2\,A\,b^2\,d\,e\right )}{4}+\frac {B\,b^6\,e^6\,x^{14}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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