Optimal. Leaf size=243 \[ \frac {(A b-a B) (b d-a e)^5 (a+b x)^{11}}{11 b^7}+\frac {(b d-a e)^4 (b B d+5 A b e-6 a B e) (a+b x)^{12}}{12 b^7}+\frac {5 e (b d-a e)^3 (b B d+2 A b e-3 a B e) (a+b x)^{13}}{13 b^7}+\frac {5 e^2 (b d-a e)^2 (b B d+A b e-2 a B e) (a+b x)^{14}}{7 b^7}+\frac {e^3 (b d-a e) (2 b B d+A b e-3 a B e) (a+b x)^{15}}{3 b^7}+\frac {e^4 (5 b B d+A b e-6 a B e) (a+b x)^{16}}{16 b^7}+\frac {B e^5 (a+b x)^{17}}{17 b^7} \]
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Rubi [A]
time = 0.99, antiderivative size = 243, 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^4 (a+b x)^{16} (-6 a B e+A b e+5 b B d)}{16 b^7}+\frac {e^3 (a+b x)^{15} (b d-a e) (-3 a B e+A b e+2 b B d)}{3 b^7}+\frac {5 e^2 (a+b x)^{14} (b d-a e)^2 (-2 a B e+A b e+b B d)}{7 b^7}+\frac {5 e (a+b x)^{13} (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{13 b^7}+\frac {(a+b x)^{12} (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{12 b^7}+\frac {(a+b x)^{11} (A b-a B) (b d-a e)^5}{11 b^7}+\frac {B e^5 (a+b x)^{17}}{17 b^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (a+b x)^{10} (A+B x) (d+e x)^5 \, dx &=\int \left (\frac {(A b-a B) (b d-a e)^5 (a+b x)^{10}}{b^6}+\frac {(b d-a e)^4 (b B d+5 A b e-6 a B e) (a+b x)^{11}}{b^6}+\frac {5 e (b d-a e)^3 (b B d+2 A b e-3 a B e) (a+b x)^{12}}{b^6}+\frac {10 e^2 (b d-a e)^2 (b B d+A b e-2 a B e) (a+b x)^{13}}{b^6}+\frac {5 e^3 (b d-a e) (2 b B d+A b e-3 a B e) (a+b x)^{14}}{b^6}+\frac {e^4 (5 b B d+A b e-6 a B e) (a+b x)^{15}}{b^6}+\frac {B e^5 (a+b x)^{16}}{b^6}\right ) \, dx\\ &=\frac {(A b-a B) (b d-a e)^5 (a+b x)^{11}}{11 b^7}+\frac {(b d-a e)^4 (b B d+5 A b e-6 a B e) (a+b x)^{12}}{12 b^7}+\frac {5 e (b d-a e)^3 (b B d+2 A b e-3 a B e) (a+b x)^{13}}{13 b^7}+\frac {5 e^2 (b d-a e)^2 (b B d+A b e-2 a B e) (a+b x)^{14}}{7 b^7}+\frac {e^3 (b d-a e) (2 b B d+A b e-3 a B e) (a+b x)^{15}}{3 b^7}+\frac {e^4 (5 b B d+A b e-6 a B e) (a+b x)^{16}}{16 b^7}+\frac {B e^5 (a+b x)^{17}}{17 b^7}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1509\) vs. \(2(243)=486\).
time = 0.35, size = 1509, normalized size = 6.21 \begin {gather*} a^{10} A d^5 x+\frac {1}{2} a^9 d^4 (a B d+5 A (2 b d+a e)) x^2+\frac {5}{3} a^8 d^3 \left (a B d (2 b d+a e)+A \left (9 b^2 d^2+10 a b d e+2 a^2 e^2\right )\right ) x^3+\frac {5}{4} a^7 d^2 \left (a B d \left (9 b^2 d^2+10 a b d e+2 a^2 e^2\right )+A \left (24 b^3 d^3+45 a b^2 d^2 e+20 a^2 b d e^2+2 a^3 e^3\right )\right ) x^4+a^6 d \left (a B d \left (24 b^3 d^3+45 a b^2 d^2 e+20 a^2 b d e^2+2 a^3 e^3\right )+A \left (42 b^4 d^4+120 a b^3 d^3 e+90 a^2 b^2 d^2 e^2+20 a^3 b d e^3+a^4 e^4\right )\right ) x^5+\frac {1}{6} a^5 \left (5 a B d \left (42 b^4 d^4+120 a b^3 d^3 e+90 a^2 b^2 d^2 e^2+20 a^3 b d e^3+a^4 e^4\right )+A \left (252 b^5 d^5+1050 a b^4 d^4 e+1200 a^2 b^3 d^3 e^2+450 a^3 b^2 d^2 e^3+50 a^4 b d e^4+a^5 e^5\right )\right ) x^6+\frac {1}{7} a^4 \left (a B \left (252 b^5 d^5+1050 a b^4 d^4 e+1200 a^2 b^3 d^3 e^2+450 a^3 b^2 d^2 e^3+50 a^4 b d e^4+a^5 e^5\right )+5 A b \left (42 b^5 d^5+252 a b^4 d^4 e+420 a^2 b^3 d^3 e^2+240 a^3 b^2 d^2 e^3+45 a^4 b d e^4+2 a^5 e^5\right )\right ) x^7+\frac {5}{8} a^3 b \left (a B \left (42 b^5 d^5+252 a b^4 d^4 e+420 a^2 b^3 d^3 e^2+240 a^3 b^2 d^2 e^3+45 a^4 b d e^4+2 a^5 e^5\right )+3 A b \left (8 b^5 d^5+70 a b^4 d^4 e+168 a^2 b^3 d^3 e^2+140 a^3 b^2 d^2 e^3+40 a^4 b d e^4+3 a^5 e^5\right )\right ) x^8+\frac {5}{3} a^2 b^2 \left (a B \left (8 b^5 d^5+70 a b^4 d^4 e+168 a^2 b^3 d^3 e^2+140 a^3 b^2 d^2 e^3+40 a^4 b d e^4+3 a^5 e^5\right )+A b \left (3 b^5 d^5+40 a b^4 d^4 e+140 a^2 b^3 d^3 e^2+168 a^3 b^2 d^2 e^3+70 a^4 b d e^4+8 a^5 e^5\right )\right ) x^9+\frac {1}{2} a b^3 \left (3 a B \left (3 b^5 d^5+40 a b^4 d^4 e+140 a^2 b^3 d^3 e^2+168 a^3 b^2 d^2 e^3+70 a^4 b d e^4+8 a^5 e^5\right )+A b \left (2 b^5 d^5+45 a b^4 d^4 e+240 a^2 b^3 d^3 e^2+420 a^3 b^2 d^2 e^3+252 a^4 b d e^4+42 a^5 e^5\right )\right ) x^{10}+\frac {1}{11} b^4 \left (5 a B \left (2 b^5 d^5+45 a b^4 d^4 e+240 a^2 b^3 d^3 e^2+420 a^3 b^2 d^2 e^3+252 a^4 b d e^4+42 a^5 e^5\right )+A b \left (b^5 d^5+50 a b^4 d^4 e+450 a^2 b^3 d^3 e^2+1200 a^3 b^2 d^2 e^3+1050 a^4 b d e^4+252 a^5 e^5\right )\right ) x^{11}+\frac {1}{12} b^5 \left (252 a^5 B e^5+450 a^2 b^3 d^2 e^2 (B d+A e)+600 a^3 b^2 d e^3 (2 B d+A e)+210 a^4 b e^4 (5 B d+A e)+50 a b^4 d^3 e (B d+2 A e)+b^5 d^4 (B d+5 A e)\right ) x^{12}+\frac {5}{13} b^6 e \left (42 a^4 B e^4+20 a b^3 d^2 e (B d+A e)+45 a^2 b^2 d e^2 (2 B d+A e)+24 a^3 b e^3 (5 B d+A e)+b^4 d^3 (B d+2 A e)\right ) x^{13}+\frac {5}{14} b^7 e^2 \left (24 a^3 B e^3+2 b^3 d^2 (B d+A e)+10 a b^2 d e (2 B d+A e)+9 a^2 b e^2 (5 B d+A e)\right ) x^{14}+\frac {1}{3} b^8 e^3 \left (9 a^2 B e^2+b^2 d (2 B d+A e)+2 a b e (5 B d+A e)\right ) x^{15}+\frac {1}{16} b^9 e^4 (5 b B d+A b e+10 a B e) x^{16}+\frac {1}{17} b^{10} B e^5 x^{17} \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. \(1620\) vs.
\(2(229)=458\).
time = 0.09, size = 1621, normalized size = 6.67
method | result | size |
default | \(\text {Expression too large to display}\) | \(1621\) |
norman | \(\text {Expression too large to display}\) | \(1718\) |
gosper | \(\text {Expression too large to display}\) | \(2033\) |
risch | \(\text {Expression too large to display}\) | \(2033\) |
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. 1664 vs.
\(2 (241) = 482\).
time = 0.32, size = 1664, normalized size = 6.85 \begin {gather*} \frac {1}{17} \, B b^{10} x^{17} e^{5} + A a^{10} d^{5} x + \frac {1}{16} \, {\left (5 \, B b^{10} d e^{4} + 10 \, B a b^{9} e^{5} + A b^{10} e^{5}\right )} x^{16} + \frac {1}{3} \, {\left (2 \, B b^{10} d^{2} e^{3} + 9 \, B a^{2} b^{8} e^{5} + 2 \, A a b^{9} e^{5} + {\left (10 \, B a b^{9} e^{4} + A b^{10} e^{4}\right )} d\right )} x^{15} + \frac {5}{14} \, {\left (2 \, B b^{10} d^{3} e^{2} + 24 \, B a^{3} b^{7} e^{5} + 9 \, A a^{2} b^{8} e^{5} + 2 \, {\left (10 \, B a b^{9} e^{3} + A b^{10} e^{3}\right )} d^{2} + 5 \, {\left (9 \, B a^{2} b^{8} e^{4} + 2 \, A a b^{9} e^{4}\right )} d\right )} x^{14} + \frac {5}{13} \, {\left (B b^{10} d^{4} e + 42 \, B a^{4} b^{6} e^{5} + 24 \, A a^{3} b^{7} e^{5} + 2 \, {\left (10 \, B a b^{9} e^{2} + A b^{10} e^{2}\right )} d^{3} + 10 \, {\left (9 \, B a^{2} b^{8} e^{3} + 2 \, A a b^{9} e^{3}\right )} d^{2} + 15 \, {\left (8 \, B a^{3} b^{7} e^{4} + 3 \, A a^{2} b^{8} e^{4}\right )} d\right )} x^{13} + \frac {1}{12} \, {\left (B b^{10} d^{5} + 252 \, B a^{5} b^{5} e^{5} + 210 \, A a^{4} b^{6} e^{5} + 5 \, {\left (10 \, B a b^{9} e + A b^{10} e\right )} d^{4} + 50 \, {\left (9 \, B a^{2} b^{8} e^{2} + 2 \, A a b^{9} e^{2}\right )} d^{3} + 150 \, {\left (8 \, B a^{3} b^{7} e^{3} + 3 \, A a^{2} b^{8} e^{3}\right )} d^{2} + 150 \, {\left (7 \, B a^{4} b^{6} e^{4} + 4 \, A a^{3} b^{7} e^{4}\right )} d\right )} x^{12} + \frac {1}{11} \, {\left (210 \, B a^{6} b^{4} e^{5} + 252 \, A a^{5} b^{5} e^{5} + {\left (10 \, B a b^{9} + A b^{10}\right )} d^{5} + 25 \, {\left (9 \, B a^{2} b^{8} e + 2 \, A a b^{9} e\right )} d^{4} + 150 \, {\left (8 \, B a^{3} b^{7} e^{2} + 3 \, A a^{2} b^{8} e^{2}\right )} d^{3} + 300 \, {\left (7 \, B a^{4} b^{6} e^{3} + 4 \, A a^{3} b^{7} e^{3}\right )} d^{2} + 210 \, {\left (6 \, B a^{5} b^{5} e^{4} + 5 \, A a^{4} b^{6} e^{4}\right )} d\right )} x^{11} + \frac {1}{2} \, {\left (24 \, B a^{7} b^{3} e^{5} + 42 \, A a^{6} b^{4} e^{5} + {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} d^{5} + 15 \, {\left (8 \, B a^{3} b^{7} e + 3 \, A a^{2} b^{8} e\right )} d^{4} + 60 \, {\left (7 \, B a^{4} b^{6} e^{2} + 4 \, A a^{3} b^{7} e^{2}\right )} d^{3} + 84 \, {\left (6 \, B a^{5} b^{5} e^{3} + 5 \, A a^{4} b^{6} e^{3}\right )} d^{2} + 42 \, {\left (5 \, B a^{6} b^{4} e^{4} + 6 \, A a^{5} b^{5} e^{4}\right )} d\right )} x^{10} + \frac {5}{3} \, {\left (3 \, B a^{8} b^{2} e^{5} + 8 \, A a^{7} b^{3} e^{5} + {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} d^{5} + 10 \, {\left (7 \, B a^{4} b^{6} e + 4 \, A a^{3} b^{7} e\right )} d^{4} + 28 \, {\left (6 \, B a^{5} b^{5} e^{2} + 5 \, A a^{4} b^{6} e^{2}\right )} d^{3} + 28 \, {\left (5 \, B a^{6} b^{4} e^{3} + 6 \, A a^{5} b^{5} e^{3}\right )} d^{2} + 10 \, {\left (4 \, B a^{7} b^{3} e^{4} + 7 \, A a^{6} b^{4} e^{4}\right )} d\right )} x^{9} + \frac {5}{8} \, {\left (2 \, B a^{9} b e^{5} + 9 \, A a^{8} b^{2} e^{5} + 6 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} d^{5} + 42 \, {\left (6 \, B a^{5} b^{5} e + 5 \, A a^{4} b^{6} e\right )} d^{4} + 84 \, {\left (5 \, B a^{6} b^{4} e^{2} + 6 \, A a^{5} b^{5} e^{2}\right )} d^{3} + 60 \, {\left (4 \, B a^{7} b^{3} e^{3} + 7 \, A a^{6} b^{4} e^{3}\right )} d^{2} + 15 \, {\left (3 \, B a^{8} b^{2} e^{4} + 8 \, A a^{7} b^{3} e^{4}\right )} d\right )} x^{8} + \frac {1}{7} \, {\left (B a^{10} e^{5} + 10 \, A a^{9} b e^{5} + 42 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} d^{5} + 210 \, {\left (5 \, B a^{6} b^{4} e + 6 \, A a^{5} b^{5} e\right )} d^{4} + 300 \, {\left (4 \, B a^{7} b^{3} e^{2} + 7 \, A a^{6} b^{4} e^{2}\right )} d^{3} + 150 \, {\left (3 \, B a^{8} b^{2} e^{3} + 8 \, A a^{7} b^{3} e^{3}\right )} d^{2} + 25 \, {\left (2 \, B a^{9} b e^{4} + 9 \, A a^{8} b^{2} e^{4}\right )} d\right )} x^{7} + \frac {1}{6} \, {\left (A a^{10} e^{5} + 42 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} d^{5} + 150 \, {\left (4 \, B a^{7} b^{3} e + 7 \, A a^{6} b^{4} e\right )} d^{4} + 150 \, {\left (3 \, B a^{8} b^{2} e^{2} + 8 \, A a^{7} b^{3} e^{2}\right )} d^{3} + 50 \, {\left (2 \, B a^{9} b e^{3} + 9 \, A a^{8} b^{2} e^{3}\right )} d^{2} + 5 \, {\left (B a^{10} e^{4} + 10 \, A a^{9} b e^{4}\right )} d\right )} x^{6} + {\left (A a^{10} d e^{4} + 6 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} d^{5} + 15 \, {\left (3 \, B a^{8} b^{2} e + 8 \, A a^{7} b^{3} e\right )} d^{4} + 10 \, {\left (2 \, B a^{9} b e^{2} + 9 \, A a^{8} b^{2} e^{2}\right )} d^{3} + 2 \, {\left (B a^{10} e^{3} + 10 \, A a^{9} b e^{3}\right )} d^{2}\right )} x^{5} + \frac {5}{4} \, {\left (2 \, A a^{10} d^{2} e^{3} + 3 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} d^{5} + 5 \, {\left (2 \, B a^{9} b e + 9 \, A a^{8} b^{2} e\right )} d^{4} + 2 \, {\left (B a^{10} e^{2} + 10 \, A a^{9} b e^{2}\right )} d^{3}\right )} x^{4} + \frac {5}{3} \, {\left (2 \, A a^{10} d^{3} e^{2} + {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} d^{5} + {\left (B a^{10} e + 10 \, A a^{9} b e\right )} d^{4}\right )} x^{3} + \frac {1}{2} \, {\left (5 \, A a^{10} d^{4} e + {\left (B a^{10} + 10 \, A a^{9} b\right )} d^{5}\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. 1631 vs.
\(2 (241) = 482\).
time = 0.71, size = 1631, normalized size = 6.71 \begin {gather*} \frac {1}{12} \, B b^{10} d^{5} x^{12} + A a^{10} d^{5} x + \frac {1}{11} \, {\left (10 \, B a b^{9} + A b^{10}\right )} d^{5} x^{11} + \frac {1}{2} \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} d^{5} x^{10} + \frac {5}{3} \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} d^{5} x^{9} + \frac {15}{4} \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} d^{5} x^{8} + 6 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} d^{5} x^{7} + 7 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} d^{5} x^{6} + 6 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} d^{5} x^{5} + \frac {15}{4} \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} d^{5} x^{4} + \frac {5}{3} \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} d^{5} x^{3} + \frac {1}{2} \, {\left (B a^{10} + 10 \, A a^{9} b\right )} d^{5} x^{2} + \frac {1}{816816} \, {\left (48048 \, B b^{10} x^{17} + 136136 \, A a^{10} x^{6} + 51051 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{16} + 272272 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{15} + 875160 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{14} + 1884960 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{13} + 2858856 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{12} + 3118752 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{11} + 2450448 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{10} + 1361360 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{9} + 510510 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{8} + 116688 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x^{7}\right )} e^{5} + \frac {1}{48048} \, {\left (15015 \, B b^{10} d x^{16} + 48048 \, A a^{10} d x^{5} + 16016 \, {\left (10 \, B a b^{9} + A b^{10}\right )} d x^{15} + 85800 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} d x^{14} + 277200 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} d x^{13} + 600600 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} d x^{12} + 917280 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} d x^{11} + 1009008 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} d x^{10} + 800800 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} d x^{9} + 450450 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} d x^{8} + 171600 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} d x^{7} + 40040 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} d x^{6}\right )} e^{4} + \frac {1}{6006} \, {\left (4004 \, B b^{10} d^{2} x^{15} + 15015 \, A a^{10} d^{2} x^{4} + 4290 \, {\left (10 \, B a b^{9} + A b^{10}\right )} d^{2} x^{14} + 23100 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} d^{2} x^{13} + 75075 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} d^{2} x^{12} + 163800 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} d^{2} x^{11} + 252252 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} d^{2} x^{10} + 280280 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} d^{2} x^{9} + 225225 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} d^{2} x^{8} + 128700 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} d^{2} x^{7} + 50050 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} d^{2} x^{6} + 12012 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} d^{2} x^{5}\right )} e^{3} + \frac {5}{6006} \, {\left (858 \, B b^{10} d^{3} x^{14} + 4004 \, A a^{10} d^{3} x^{3} + 924 \, {\left (10 \, B a b^{9} + A b^{10}\right )} d^{3} x^{13} + 5005 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} d^{3} x^{12} + 16380 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} d^{3} x^{11} + 36036 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} d^{3} x^{10} + 56056 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} d^{3} x^{9} + 63063 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} d^{3} x^{8} + 51480 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} d^{3} x^{7} + 30030 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} d^{3} x^{6} + 12012 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} d^{3} x^{5} + 3003 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} d^{3} x^{4}\right )} e^{2} + \frac {5}{1716} \, {\left (132 \, B b^{10} d^{4} x^{13} + 858 \, A a^{10} d^{4} x^{2} + 143 \, {\left (10 \, B a b^{9} + A b^{10}\right )} d^{4} x^{12} + 780 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} d^{4} x^{11} + 2574 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} d^{4} x^{10} + 5720 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} d^{4} x^{9} + 9009 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} d^{4} x^{8} + 10296 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} d^{4} x^{7} + 8580 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} d^{4} x^{6} + 5148 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} d^{4} x^{5} + 2145 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} d^{4} x^{4} + 572 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} d^{4} 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. 2076 vs.
\(2 (243) = 486\).
time = 0.13, size = 2076, normalized size = 8.54 \begin {gather*} A a^{10} d^{5} x + \frac {B b^{10} e^{5} x^{17}}{17} + x^{16} \left (\frac {A b^{10} e^{5}}{16} + \frac {5 B a b^{9} e^{5}}{8} + \frac {5 B b^{10} d e^{4}}{16}\right ) + x^{15} \cdot \left (\frac {2 A a b^{9} e^{5}}{3} + \frac {A b^{10} d e^{4}}{3} + 3 B a^{2} b^{8} e^{5} + \frac {10 B a b^{9} d e^{4}}{3} + \frac {2 B b^{10} d^{2} e^{3}}{3}\right ) + x^{14} \cdot \left (\frac {45 A a^{2} b^{8} e^{5}}{14} + \frac {25 A a b^{9} d e^{4}}{7} + \frac {5 A b^{10} d^{2} e^{3}}{7} + \frac {60 B a^{3} b^{7} e^{5}}{7} + \frac {225 B a^{2} b^{8} d e^{4}}{14} + \frac {50 B a b^{9} d^{2} e^{3}}{7} + \frac {5 B b^{10} d^{3} e^{2}}{7}\right ) + x^{13} \cdot \left (\frac {120 A a^{3} b^{7} e^{5}}{13} + \frac {225 A a^{2} b^{8} d e^{4}}{13} + \frac {100 A a b^{9} d^{2} e^{3}}{13} + \frac {10 A b^{10} d^{3} e^{2}}{13} + \frac {210 B a^{4} b^{6} e^{5}}{13} + \frac {600 B a^{3} b^{7} d e^{4}}{13} + \frac {450 B a^{2} b^{8} d^{2} e^{3}}{13} + \frac {100 B a b^{9} d^{3} e^{2}}{13} + \frac {5 B b^{10} d^{4} e}{13}\right ) + x^{12} \cdot \left (\frac {35 A a^{4} b^{6} e^{5}}{2} + 50 A a^{3} b^{7} d e^{4} + \frac {75 A a^{2} b^{8} d^{2} e^{3}}{2} + \frac {25 A a b^{9} d^{3} e^{2}}{3} + \frac {5 A b^{10} d^{4} e}{12} + 21 B a^{5} b^{5} e^{5} + \frac {175 B a^{4} b^{6} d e^{4}}{2} + 100 B a^{3} b^{7} d^{2} e^{3} + \frac {75 B a^{2} b^{8} d^{3} e^{2}}{2} + \frac {25 B a b^{9} d^{4} e}{6} + \frac {B b^{10} d^{5}}{12}\right ) + x^{11} \cdot \left (\frac {252 A a^{5} b^{5} e^{5}}{11} + \frac {1050 A a^{4} b^{6} d e^{4}}{11} + \frac {1200 A a^{3} b^{7} d^{2} e^{3}}{11} + \frac {450 A a^{2} b^{8} d^{3} e^{2}}{11} + \frac {50 A a b^{9} d^{4} e}{11} + \frac {A b^{10} d^{5}}{11} + \frac {210 B a^{6} b^{4} e^{5}}{11} + \frac {1260 B a^{5} b^{5} d e^{4}}{11} + \frac {2100 B a^{4} b^{6} d^{2} e^{3}}{11} + \frac {1200 B a^{3} b^{7} d^{3} e^{2}}{11} + \frac {225 B a^{2} b^{8} d^{4} e}{11} + \frac {10 B a b^{9} d^{5}}{11}\right ) + x^{10} \cdot \left (21 A a^{6} b^{4} e^{5} + 126 A a^{5} b^{5} d e^{4} + 210 A a^{4} b^{6} d^{2} e^{3} + 120 A a^{3} b^{7} d^{3} e^{2} + \frac {45 A a^{2} b^{8} d^{4} e}{2} + A a b^{9} d^{5} + 12 B a^{7} b^{3} e^{5} + 105 B a^{6} b^{4} d e^{4} + 252 B a^{5} b^{5} d^{2} e^{3} + 210 B a^{4} b^{6} d^{3} e^{2} + 60 B a^{3} b^{7} d^{4} e + \frac {9 B a^{2} b^{8} d^{5}}{2}\right ) + x^{9} \cdot \left (\frac {40 A a^{7} b^{3} e^{5}}{3} + \frac {350 A a^{6} b^{4} d e^{4}}{3} + 280 A a^{5} b^{5} d^{2} e^{3} + \frac {700 A a^{4} b^{6} d^{3} e^{2}}{3} + \frac {200 A a^{3} b^{7} d^{4} e}{3} + 5 A a^{2} b^{8} d^{5} + 5 B a^{8} b^{2} e^{5} + \frac {200 B a^{7} b^{3} d e^{4}}{3} + \frac {700 B a^{6} b^{4} d^{2} e^{3}}{3} + 280 B a^{5} b^{5} d^{3} e^{2} + \frac {350 B a^{4} b^{6} d^{4} e}{3} + \frac {40 B a^{3} b^{7} d^{5}}{3}\right ) + x^{8} \cdot \left (\frac {45 A a^{8} b^{2} e^{5}}{8} + 75 A a^{7} b^{3} d e^{4} + \frac {525 A a^{6} b^{4} d^{2} e^{3}}{2} + 315 A a^{5} b^{5} d^{3} e^{2} + \frac {525 A a^{4} b^{6} d^{4} e}{4} + 15 A a^{3} b^{7} d^{5} + \frac {5 B a^{9} b e^{5}}{4} + \frac {225 B a^{8} b^{2} d e^{4}}{8} + 150 B a^{7} b^{3} d^{2} e^{3} + \frac {525 B a^{6} b^{4} d^{3} e^{2}}{2} + \frac {315 B a^{5} b^{5} d^{4} e}{2} + \frac {105 B a^{4} b^{6} d^{5}}{4}\right ) + x^{7} \cdot \left (\frac {10 A a^{9} b e^{5}}{7} + \frac {225 A a^{8} b^{2} d e^{4}}{7} + \frac {1200 A a^{7} b^{3} d^{2} e^{3}}{7} + 300 A a^{6} b^{4} d^{3} e^{2} + 180 A a^{5} b^{5} d^{4} e + 30 A a^{4} b^{6} d^{5} + \frac {B a^{10} e^{5}}{7} + \frac {50 B a^{9} b d e^{4}}{7} + \frac {450 B a^{8} b^{2} d^{2} e^{3}}{7} + \frac {1200 B a^{7} b^{3} d^{3} e^{2}}{7} + 150 B a^{6} b^{4} d^{4} e + 36 B a^{5} b^{5} d^{5}\right ) + x^{6} \left (\frac {A a^{10} e^{5}}{6} + \frac {25 A a^{9} b d e^{4}}{3} + 75 A a^{8} b^{2} d^{2} e^{3} + 200 A a^{7} b^{3} d^{3} e^{2} + 175 A a^{6} b^{4} d^{4} e + 42 A a^{5} b^{5} d^{5} + \frac {5 B a^{10} d e^{4}}{6} + \frac {50 B a^{9} b d^{2} e^{3}}{3} + 75 B a^{8} b^{2} d^{3} e^{2} + 100 B a^{7} b^{3} d^{4} e + 35 B a^{6} b^{4} d^{5}\right ) + x^{5} \left (A a^{10} d e^{4} + 20 A a^{9} b d^{2} e^{3} + 90 A a^{8} b^{2} d^{3} e^{2} + 120 A a^{7} b^{3} d^{4} e + 42 A a^{6} b^{4} d^{5} + 2 B a^{10} d^{2} e^{3} + 20 B a^{9} b d^{3} e^{2} + 45 B a^{8} b^{2} d^{4} e + 24 B a^{7} b^{3} d^{5}\right ) + x^{4} \cdot \left (\frac {5 A a^{10} d^{2} e^{3}}{2} + 25 A a^{9} b d^{3} e^{2} + \frac {225 A a^{8} b^{2} d^{4} e}{4} + 30 A a^{7} b^{3} d^{5} + \frac {5 B a^{10} d^{3} e^{2}}{2} + \frac {25 B a^{9} b d^{4} e}{2} + \frac {45 B a^{8} b^{2} d^{5}}{4}\right ) + x^{3} \cdot \left (\frac {10 A a^{10} d^{3} e^{2}}{3} + \frac {50 A a^{9} b d^{4} e}{3} + 15 A a^{8} b^{2} d^{5} + \frac {5 B a^{10} d^{4} e}{3} + \frac {10 B a^{9} b d^{5}}{3}\right ) + x^{2} \cdot \left (\frac {5 A a^{10} d^{4} e}{2} + 5 A a^{9} b d^{5} + \frac {B a^{10} d^{5}}{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. 1966 vs.
\(2 (241) = 482\).
time = 1.50, size = 1966, normalized size = 8.09 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.62, size = 1685, normalized size = 6.93 \begin {gather*} x^9\,\left (5\,B\,a^8\,b^2\,e^5+\frac {200\,B\,a^7\,b^3\,d\,e^4}{3}+\frac {40\,A\,a^7\,b^3\,e^5}{3}+\frac {700\,B\,a^6\,b^4\,d^2\,e^3}{3}+\frac {350\,A\,a^6\,b^4\,d\,e^4}{3}+280\,B\,a^5\,b^5\,d^3\,e^2+280\,A\,a^5\,b^5\,d^2\,e^3+\frac {350\,B\,a^4\,b^6\,d^4\,e}{3}+\frac {700\,A\,a^4\,b^6\,d^3\,e^2}{3}+\frac {40\,B\,a^3\,b^7\,d^5}{3}+\frac {200\,A\,a^3\,b^7\,d^4\,e}{3}+5\,A\,a^2\,b^8\,d^5\right )+x^7\,\left (\frac {B\,a^{10}\,e^5}{7}+\frac {50\,B\,a^9\,b\,d\,e^4}{7}+\frac {10\,A\,a^9\,b\,e^5}{7}+\frac {450\,B\,a^8\,b^2\,d^2\,e^3}{7}+\frac {225\,A\,a^8\,b^2\,d\,e^4}{7}+\frac {1200\,B\,a^7\,b^3\,d^3\,e^2}{7}+\frac {1200\,A\,a^7\,b^3\,d^2\,e^3}{7}+150\,B\,a^6\,b^4\,d^4\,e+300\,A\,a^6\,b^4\,d^3\,e^2+36\,B\,a^5\,b^5\,d^5+180\,A\,a^5\,b^5\,d^4\,e+30\,A\,a^4\,b^6\,d^5\right )+x^{11}\,\left (\frac {210\,B\,a^6\,b^4\,e^5}{11}+\frac {1260\,B\,a^5\,b^5\,d\,e^4}{11}+\frac {252\,A\,a^5\,b^5\,e^5}{11}+\frac {2100\,B\,a^4\,b^6\,d^2\,e^3}{11}+\frac {1050\,A\,a^4\,b^6\,d\,e^4}{11}+\frac {1200\,B\,a^3\,b^7\,d^3\,e^2}{11}+\frac {1200\,A\,a^3\,b^7\,d^2\,e^3}{11}+\frac {225\,B\,a^2\,b^8\,d^4\,e}{11}+\frac {450\,A\,a^2\,b^8\,d^3\,e^2}{11}+\frac {10\,B\,a\,b^9\,d^5}{11}+\frac {50\,A\,a\,b^9\,d^4\,e}{11}+\frac {A\,b^{10}\,d^5}{11}\right )+x^{10}\,\left (12\,B\,a^7\,b^3\,e^5+105\,B\,a^6\,b^4\,d\,e^4+21\,A\,a^6\,b^4\,e^5+252\,B\,a^5\,b^5\,d^2\,e^3+126\,A\,a^5\,b^5\,d\,e^4+210\,B\,a^4\,b^6\,d^3\,e^2+210\,A\,a^4\,b^6\,d^2\,e^3+60\,B\,a^3\,b^7\,d^4\,e+120\,A\,a^3\,b^7\,d^3\,e^2+\frac {9\,B\,a^2\,b^8\,d^5}{2}+\frac {45\,A\,a^2\,b^8\,d^4\,e}{2}+A\,a\,b^9\,d^5\right )+x^8\,\left (\frac {5\,B\,a^9\,b\,e^5}{4}+\frac {225\,B\,a^8\,b^2\,d\,e^4}{8}+\frac {45\,A\,a^8\,b^2\,e^5}{8}+150\,B\,a^7\,b^3\,d^2\,e^3+75\,A\,a^7\,b^3\,d\,e^4+\frac {525\,B\,a^6\,b^4\,d^3\,e^2}{2}+\frac {525\,A\,a^6\,b^4\,d^2\,e^3}{2}+\frac {315\,B\,a^5\,b^5\,d^4\,e}{2}+315\,A\,a^5\,b^5\,d^3\,e^2+\frac {105\,B\,a^4\,b^6\,d^5}{4}+\frac {525\,A\,a^4\,b^6\,d^4\,e}{4}+15\,A\,a^3\,b^7\,d^5\right )+x^5\,\left (2\,B\,a^{10}\,d^2\,e^3+A\,a^{10}\,d\,e^4+20\,B\,a^9\,b\,d^3\,e^2+20\,A\,a^9\,b\,d^2\,e^3+45\,B\,a^8\,b^2\,d^4\,e+90\,A\,a^8\,b^2\,d^3\,e^2+24\,B\,a^7\,b^3\,d^5+120\,A\,a^7\,b^3\,d^4\,e+42\,A\,a^6\,b^4\,d^5\right )+x^{13}\,\left (\frac {210\,B\,a^4\,b^6\,e^5}{13}+\frac {600\,B\,a^3\,b^7\,d\,e^4}{13}+\frac {120\,A\,a^3\,b^7\,e^5}{13}+\frac {450\,B\,a^2\,b^8\,d^2\,e^3}{13}+\frac {225\,A\,a^2\,b^8\,d\,e^4}{13}+\frac {100\,B\,a\,b^9\,d^3\,e^2}{13}+\frac {100\,A\,a\,b^9\,d^2\,e^3}{13}+\frac {5\,B\,b^{10}\,d^4\,e}{13}+\frac {10\,A\,b^{10}\,d^3\,e^2}{13}\right )+x^4\,\left (\frac {5\,B\,a^{10}\,d^3\,e^2}{2}+\frac {5\,A\,a^{10}\,d^2\,e^3}{2}+\frac {25\,B\,a^9\,b\,d^4\,e}{2}+25\,A\,a^9\,b\,d^3\,e^2+\frac {45\,B\,a^8\,b^2\,d^5}{4}+\frac {225\,A\,a^8\,b^2\,d^4\,e}{4}+30\,A\,a^7\,b^3\,d^5\right )+x^{14}\,\left (\frac {60\,B\,a^3\,b^7\,e^5}{7}+\frac {225\,B\,a^2\,b^8\,d\,e^4}{14}+\frac {45\,A\,a^2\,b^8\,e^5}{14}+\frac {50\,B\,a\,b^9\,d^2\,e^3}{7}+\frac {25\,A\,a\,b^9\,d\,e^4}{7}+\frac {5\,B\,b^{10}\,d^3\,e^2}{7}+\frac {5\,A\,b^{10}\,d^2\,e^3}{7}\right )+x^6\,\left (\frac {5\,B\,a^{10}\,d\,e^4}{6}+\frac {A\,a^{10}\,e^5}{6}+\frac {50\,B\,a^9\,b\,d^2\,e^3}{3}+\frac {25\,A\,a^9\,b\,d\,e^4}{3}+75\,B\,a^8\,b^2\,d^3\,e^2+75\,A\,a^8\,b^2\,d^2\,e^3+100\,B\,a^7\,b^3\,d^4\,e+200\,A\,a^7\,b^3\,d^3\,e^2+35\,B\,a^6\,b^4\,d^5+175\,A\,a^6\,b^4\,d^4\,e+42\,A\,a^5\,b^5\,d^5\right )+x^{12}\,\left (21\,B\,a^5\,b^5\,e^5+\frac {175\,B\,a^4\,b^6\,d\,e^4}{2}+\frac {35\,A\,a^4\,b^6\,e^5}{2}+100\,B\,a^3\,b^7\,d^2\,e^3+50\,A\,a^3\,b^7\,d\,e^4+\frac {75\,B\,a^2\,b^8\,d^3\,e^2}{2}+\frac {75\,A\,a^2\,b^8\,d^2\,e^3}{2}+\frac {25\,B\,a\,b^9\,d^4\,e}{6}+\frac {25\,A\,a\,b^9\,d^3\,e^2}{3}+\frac {B\,b^{10}\,d^5}{12}+\frac {5\,A\,b^{10}\,d^4\,e}{12}\right )+\frac {a^9\,d^4\,x^2\,\left (5\,A\,a\,e+10\,A\,b\,d+B\,a\,d\right )}{2}+\frac {b^9\,e^4\,x^{16}\,\left (A\,b\,e+10\,B\,a\,e+5\,B\,b\,d\right )}{16}+A\,a^{10}\,d^5\,x+\frac {5\,a^8\,d^3\,x^3\,\left (B\,a^2\,d\,e+2\,A\,a^2\,e^2+2\,B\,a\,b\,d^2+10\,A\,a\,b\,d\,e+9\,A\,b^2\,d^2\right )}{3}+\frac {b^8\,e^3\,x^{15}\,\left (9\,B\,a^2\,e^2+10\,B\,a\,b\,d\,e+2\,A\,a\,b\,e^2+2\,B\,b^2\,d^2+A\,b^2\,d\,e\right )}{3}+\frac {B\,b^{10}\,e^5\,x^{17}}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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