Integrand size = 20, antiderivative size = 240 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=\frac {(A b-a B) (b d-a e)^5 (a+b x)^7}{7 b^7}+\frac {(b d-a e)^4 (b B d+5 A b e-6 a B e) (a+b x)^8}{8 b^7}+\frac {5 e (b d-a e)^3 (b B d+2 A b e-3 a B e) (a+b x)^9}{9 b^7}+\frac {e^2 (b d-a e)^2 (b B d+A b e-2 a B e) (a+b x)^{10}}{b^7}+\frac {5 e^3 (b d-a e) (2 b B d+A b e-3 a B e) (a+b x)^{11}}{11 b^7}+\frac {e^4 (5 b B d+A b e-6 a B e) (a+b x)^{12}}{12 b^7}+\frac {B e^5 (a+b x)^{13}}{13 b^7} \]
[Out]
Time = 0.52 (sec) , antiderivative size = 240, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=\frac {e^4 (a+b x)^{12} (-6 a B e+A b e+5 b B d)}{12 b^7}+\frac {5 e^3 (a+b x)^{11} (b d-a e) (-3 a B e+A b e+2 b B d)}{11 b^7}+\frac {e^2 (a+b x)^{10} (b d-a e)^2 (-2 a B e+A b e+b B d)}{b^7}+\frac {5 e (a+b x)^9 (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{9 b^7}+\frac {(a+b x)^8 (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{8 b^7}+\frac {(a+b x)^7 (A b-a B) (b d-a e)^5}{7 b^7}+\frac {B e^5 (a+b x)^{13}}{13 b^7} \]
[In]
[Out]
Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {(A b-a B) (b d-a e)^5 (a+b x)^6}{b^6}+\frac {(b d-a e)^4 (b B d+5 A b e-6 a B e) (a+b x)^7}{b^6}+\frac {5 e (b d-a e)^3 (b B d+2 A b e-3 a B e) (a+b x)^8}{b^6}+\frac {10 e^2 (b d-a e)^2 (b B d+A b e-2 a B e) (a+b x)^9}{b^6}+\frac {5 e^3 (b d-a e) (2 b B d+A b e-3 a B e) (a+b x)^{10}}{b^6}+\frac {e^4 (5 b B d+A b e-6 a B e) (a+b x)^{11}}{b^6}+\frac {B e^5 (a+b x)^{12}}{b^6}\right ) \, dx \\ & = \frac {(A b-a B) (b d-a e)^5 (a+b x)^7}{7 b^7}+\frac {(b d-a e)^4 (b B d+5 A b e-6 a B e) (a+b x)^8}{8 b^7}+\frac {5 e (b d-a e)^3 (b B d+2 A b e-3 a B e) (a+b x)^9}{9 b^7}+\frac {e^2 (b d-a e)^2 (b B d+A b e-2 a B e) (a+b x)^{10}}{b^7}+\frac {5 e^3 (b d-a e) (2 b B d+A b e-3 a B e) (a+b x)^{11}}{11 b^7}+\frac {e^4 (5 b B d+A b e-6 a B e) (a+b x)^{12}}{12 b^7}+\frac {B e^5 (a+b x)^{13}}{13 b^7} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(907\) vs. \(2(240)=480\).
Time = 0.20 (sec) , antiderivative size = 907, normalized size of antiderivative = 3.78 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=a^6 A d^5 x+\frac {1}{2} a^5 d^4 (6 A b d+a B d+5 a A e) x^2+\frac {1}{3} a^4 d^3 \left (a B d (6 b d+5 a e)+5 A \left (3 b^2 d^2+6 a b d e+2 a^2 e^2\right )\right ) x^3+\frac {5}{4} a^3 d^2 \left (a B d \left (3 b^2 d^2+6 a b d e+2 a^2 e^2\right )+A \left (4 b^3 d^3+15 a b^2 d^2 e+12 a^2 b d e^2+2 a^3 e^3\right )\right ) x^4+a^2 d \left (a B d \left (4 b^3 d^3+15 a b^2 d^2 e+12 a^2 b d e^2+2 a^3 e^3\right )+A \left (3 b^4 d^4+20 a b^3 d^3 e+30 a^2 b^2 d^2 e^2+12 a^3 b d e^3+a^4 e^4\right )\right ) x^5+\frac {1}{6} a \left (5 a B d \left (3 b^4 d^4+20 a b^3 d^3 e+30 a^2 b^2 d^2 e^2+12 a^3 b d e^3+a^4 e^4\right )+A \left (6 b^5 d^5+75 a b^4 d^4 e+200 a^2 b^3 d^3 e^2+150 a^3 b^2 d^2 e^3+30 a^4 b d e^4+a^5 e^5\right )\right ) x^6+\frac {1}{7} \left (a B \left (6 b^5 d^5+75 a b^4 d^4 e+200 a^2 b^3 d^3 e^2+150 a^3 b^2 d^2 e^3+30 a^4 b d e^4+a^5 e^5\right )+A b \left (b^5 d^5+30 a b^4 d^4 e+150 a^2 b^3 d^3 e^2+200 a^3 b^2 d^2 e^3+75 a^4 b d e^4+6 a^5 e^5\right )\right ) x^7+\frac {1}{8} b \left (6 a^5 B e^5+150 a^2 b^3 d^2 e^2 (B d+A e)+100 a^3 b^2 d e^3 (2 B d+A e)+15 a^4 b e^4 (5 B d+A e)+30 a b^4 d^3 e (B d+2 A e)+b^5 d^4 (B d+5 A e)\right ) x^8+\frac {5}{9} b^2 e \left (3 a^4 B e^4+12 a b^3 d^2 e (B d+A e)+15 a^2 b^2 d e^2 (2 B d+A e)+4 a^3 b e^3 (5 B d+A e)+b^4 d^3 (B d+2 A e)\right ) x^9+\frac {1}{2} b^3 e^2 \left (4 a^3 B e^3+2 b^3 d^2 (B d+A e)+6 a b^2 d e (2 B d+A e)+3 a^2 b e^2 (5 B d+A e)\right ) x^{10}+\frac {1}{11} b^4 e^3 \left (15 a^2 B e^2+5 b^2 d (2 B d+A e)+6 a b e (5 B d+A e)\right ) x^{11}+\frac {1}{12} b^5 e^4 (5 b B d+A b e+6 a B e) x^{12}+\frac {1}{13} b^6 B e^5 x^{13} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(996\) vs. \(2(228)=456\).
Time = 1.67 (sec) , antiderivative size = 997, normalized size of antiderivative = 4.15
method | result | size |
default | \(\frac {b^{6} B \,e^{5} x^{13}}{13}+\frac {\left (\left (b^{6} A +6 a \,b^{5} B \right ) e^{5}+5 b^{6} B d \,e^{4}\right ) x^{12}}{12}+\frac {\left (\left (6 a \,b^{5} A +15 a^{2} b^{4} B \right ) e^{5}+5 \left (b^{6} A +6 a \,b^{5} B \right ) d \,e^{4}+10 b^{6} B \,d^{2} e^{3}\right ) x^{11}}{11}+\frac {\left (\left (15 a^{2} b^{4} A +20 a^{3} b^{3} B \right ) e^{5}+5 \left (6 a \,b^{5} A +15 a^{2} b^{4} B \right ) d \,e^{4}+10 \left (b^{6} A +6 a \,b^{5} B \right ) d^{2} e^{3}+10 b^{6} B \,d^{3} e^{2}\right ) x^{10}}{10}+\frac {\left (\left (20 a^{3} b^{3} A +15 a^{4} b^{2} B \right ) e^{5}+5 \left (15 a^{2} b^{4} A +20 a^{3} b^{3} B \right ) d \,e^{4}+10 \left (6 a \,b^{5} A +15 a^{2} b^{4} B \right ) d^{2} e^{3}+10 \left (b^{6} A +6 a \,b^{5} B \right ) d^{3} e^{2}+5 b^{6} B \,d^{4} e \right ) x^{9}}{9}+\frac {\left (\left (15 a^{4} b^{2} A +6 a^{5} b B \right ) e^{5}+5 \left (20 a^{3} b^{3} A +15 a^{4} b^{2} B \right ) d \,e^{4}+10 \left (15 a^{2} b^{4} A +20 a^{3} b^{3} B \right ) d^{2} e^{3}+10 \left (6 a \,b^{5} A +15 a^{2} b^{4} B \right ) d^{3} e^{2}+5 \left (b^{6} A +6 a \,b^{5} B \right ) d^{4} e +b^{6} B \,d^{5}\right ) x^{8}}{8}+\frac {\left (\left (6 A \,a^{5} b +B \,a^{6}\right ) e^{5}+5 \left (15 a^{4} b^{2} A +6 a^{5} b B \right ) d \,e^{4}+10 \left (20 a^{3} b^{3} A +15 a^{4} b^{2} B \right ) d^{2} e^{3}+10 \left (15 a^{2} b^{4} A +20 a^{3} b^{3} B \right ) d^{3} e^{2}+5 \left (6 a \,b^{5} A +15 a^{2} b^{4} B \right ) d^{4} e +\left (b^{6} A +6 a \,b^{5} B \right ) d^{5}\right ) x^{7}}{7}+\frac {\left (A \,a^{6} e^{5}+5 \left (6 A \,a^{5} b +B \,a^{6}\right ) d \,e^{4}+10 \left (15 a^{4} b^{2} A +6 a^{5} b B \right ) d^{2} e^{3}+10 \left (20 a^{3} b^{3} A +15 a^{4} b^{2} B \right ) d^{3} e^{2}+5 \left (15 a^{2} b^{4} A +20 a^{3} b^{3} B \right ) d^{4} e +\left (6 a \,b^{5} A +15 a^{2} b^{4} B \right ) d^{5}\right ) x^{6}}{6}+\frac {\left (5 A \,a^{6} d \,e^{4}+10 \left (6 A \,a^{5} b +B \,a^{6}\right ) d^{2} e^{3}+10 \left (15 a^{4} b^{2} A +6 a^{5} b B \right ) d^{3} e^{2}+5 \left (20 a^{3} b^{3} A +15 a^{4} b^{2} B \right ) d^{4} e +\left (15 a^{2} b^{4} A +20 a^{3} b^{3} B \right ) d^{5}\right ) x^{5}}{5}+\frac {\left (10 A \,a^{6} d^{2} e^{3}+10 \left (6 A \,a^{5} b +B \,a^{6}\right ) d^{3} e^{2}+5 \left (15 a^{4} b^{2} A +6 a^{5} b B \right ) d^{4} e +\left (20 a^{3} b^{3} A +15 a^{4} b^{2} B \right ) d^{5}\right ) x^{4}}{4}+\frac {\left (10 A \,a^{6} d^{3} e^{2}+5 \left (6 A \,a^{5} b +B \,a^{6}\right ) d^{4} e +\left (15 a^{4} b^{2} A +6 a^{5} b B \right ) d^{5}\right ) x^{3}}{3}+\frac {\left (5 A \,a^{6} d^{4} e +\left (6 A \,a^{5} b +B \,a^{6}\right ) d^{5}\right ) x^{2}}{2}+A \,a^{6} d^{5} x\) | \(997\) |
norman | \(\text {Expression too large to display}\) | \(1056\) |
gosper | \(\text {Expression too large to display}\) | \(1247\) |
risch | \(\text {Expression too large to display}\) | \(1247\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1247\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 997 vs. \(2 (228) = 456\).
Time = 0.23 (sec) , antiderivative size = 997, normalized size of antiderivative = 4.15 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=\frac {1}{13} \, B b^{6} e^{5} x^{13} + A a^{6} d^{5} x + \frac {1}{12} \, {\left (5 \, B b^{6} d e^{4} + {\left (6 \, B a b^{5} + A b^{6}\right )} e^{5}\right )} x^{12} + \frac {1}{11} \, {\left (10 \, B b^{6} d^{2} e^{3} + 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e^{4} + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{5}\right )} x^{11} + \frac {1}{2} \, {\left (2 \, B b^{6} d^{3} e^{2} + 2 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{3} + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{4} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{5}\right )} x^{10} + \frac {5}{9} \, {\left (B b^{6} d^{4} e + 2 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{2} + 6 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{3} + 5 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{4} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{5}\right )} x^{9} + \frac {1}{8} \, {\left (B b^{6} d^{5} + 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e + 30 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{2} + 50 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{3} + 25 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{4} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{5}\right )} x^{8} + \frac {1}{7} \, {\left ({\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} + 15 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e + 50 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{2} + 50 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{3} + 15 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{4} + {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{5}\right )} x^{7} + \frac {1}{6} \, {\left (A a^{6} e^{5} + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} + 25 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e + 50 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{2} + 30 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{3} + 5 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{4}\right )} x^{6} + {\left (A a^{6} d e^{4} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{5} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{4} e + 6 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{3} e^{2} + 2 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{2} e^{3}\right )} x^{5} + \frac {5}{4} \, {\left (2 \, A a^{6} d^{2} e^{3} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{5} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{4} e + 2 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{3} e^{2}\right )} x^{4} + \frac {1}{3} \, {\left (10 \, A a^{6} d^{3} e^{2} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{5} + 5 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{4} e\right )} x^{3} + \frac {1}{2} \, {\left (5 \, A a^{6} d^{4} e + {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{5}\right )} x^{2} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 1278 vs. \(2 (241) = 482\).
Time = 0.08 (sec) , antiderivative size = 1278, normalized size of antiderivative = 5.32 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=A a^{6} d^{5} x + \frac {B b^{6} e^{5} x^{13}}{13} + x^{12} \left (\frac {A b^{6} e^{5}}{12} + \frac {B a b^{5} e^{5}}{2} + \frac {5 B b^{6} d e^{4}}{12}\right ) + x^{11} \cdot \left (\frac {6 A a b^{5} e^{5}}{11} + \frac {5 A b^{6} d e^{4}}{11} + \frac {15 B a^{2} b^{4} e^{5}}{11} + \frac {30 B a b^{5} d e^{4}}{11} + \frac {10 B b^{6} d^{2} e^{3}}{11}\right ) + x^{10} \cdot \left (\frac {3 A a^{2} b^{4} e^{5}}{2} + 3 A a b^{5} d e^{4} + A b^{6} d^{2} e^{3} + 2 B a^{3} b^{3} e^{5} + \frac {15 B a^{2} b^{4} d e^{4}}{2} + 6 B a b^{5} d^{2} e^{3} + B b^{6} d^{3} e^{2}\right ) + x^{9} \cdot \left (\frac {20 A a^{3} b^{3} e^{5}}{9} + \frac {25 A a^{2} b^{4} d e^{4}}{3} + \frac {20 A a b^{5} d^{2} e^{3}}{3} + \frac {10 A b^{6} d^{3} e^{2}}{9} + \frac {5 B a^{4} b^{2} e^{5}}{3} + \frac {100 B a^{3} b^{3} d e^{4}}{9} + \frac {50 B a^{2} b^{4} d^{2} e^{3}}{3} + \frac {20 B a b^{5} d^{3} e^{2}}{3} + \frac {5 B b^{6} d^{4} e}{9}\right ) + x^{8} \cdot \left (\frac {15 A a^{4} b^{2} e^{5}}{8} + \frac {25 A a^{3} b^{3} d e^{4}}{2} + \frac {75 A a^{2} b^{4} d^{2} e^{3}}{4} + \frac {15 A a b^{5} d^{3} e^{2}}{2} + \frac {5 A b^{6} d^{4} e}{8} + \frac {3 B a^{5} b e^{5}}{4} + \frac {75 B a^{4} b^{2} d e^{4}}{8} + 25 B a^{3} b^{3} d^{2} e^{3} + \frac {75 B a^{2} b^{4} d^{3} e^{2}}{4} + \frac {15 B a b^{5} d^{4} e}{4} + \frac {B b^{6} d^{5}}{8}\right ) + x^{7} \cdot \left (\frac {6 A a^{5} b e^{5}}{7} + \frac {75 A a^{4} b^{2} d e^{4}}{7} + \frac {200 A a^{3} b^{3} d^{2} e^{3}}{7} + \frac {150 A a^{2} b^{4} d^{3} e^{2}}{7} + \frac {30 A a b^{5} d^{4} e}{7} + \frac {A b^{6} d^{5}}{7} + \frac {B a^{6} e^{5}}{7} + \frac {30 B a^{5} b d e^{4}}{7} + \frac {150 B a^{4} b^{2} d^{2} e^{3}}{7} + \frac {200 B a^{3} b^{3} d^{3} e^{2}}{7} + \frac {75 B a^{2} b^{4} d^{4} e}{7} + \frac {6 B a b^{5} d^{5}}{7}\right ) + x^{6} \left (\frac {A a^{6} e^{5}}{6} + 5 A a^{5} b d e^{4} + 25 A a^{4} b^{2} d^{2} e^{3} + \frac {100 A a^{3} b^{3} d^{3} e^{2}}{3} + \frac {25 A a^{2} b^{4} d^{4} e}{2} + A a b^{5} d^{5} + \frac {5 B a^{6} d e^{4}}{6} + 10 B a^{5} b d^{2} e^{3} + 25 B a^{4} b^{2} d^{3} e^{2} + \frac {50 B a^{3} b^{3} d^{4} e}{3} + \frac {5 B a^{2} b^{4} d^{5}}{2}\right ) + x^{5} \left (A a^{6} d e^{4} + 12 A a^{5} b d^{2} e^{3} + 30 A a^{4} b^{2} d^{3} e^{2} + 20 A a^{3} b^{3} d^{4} e + 3 A a^{2} b^{4} d^{5} + 2 B a^{6} d^{2} e^{3} + 12 B a^{5} b d^{3} e^{2} + 15 B a^{4} b^{2} d^{4} e + 4 B a^{3} b^{3} d^{5}\right ) + x^{4} \cdot \left (\frac {5 A a^{6} d^{2} e^{3}}{2} + 15 A a^{5} b d^{3} e^{2} + \frac {75 A a^{4} b^{2} d^{4} e}{4} + 5 A a^{3} b^{3} d^{5} + \frac {5 B a^{6} d^{3} e^{2}}{2} + \frac {15 B a^{5} b d^{4} e}{2} + \frac {15 B a^{4} b^{2} d^{5}}{4}\right ) + x^{3} \cdot \left (\frac {10 A a^{6} d^{3} e^{2}}{3} + 10 A a^{5} b d^{4} e + 5 A a^{4} b^{2} d^{5} + \frac {5 B a^{6} d^{4} e}{3} + 2 B a^{5} b d^{5}\right ) + x^{2} \cdot \left (\frac {5 A a^{6} d^{4} e}{2} + 3 A a^{5} b d^{5} + \frac {B a^{6} d^{5}}{2}\right ) \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. 997 vs. \(2 (228) = 456\).
Time = 0.26 (sec) , antiderivative size = 997, normalized size of antiderivative = 4.15 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=\frac {1}{13} \, B b^{6} e^{5} x^{13} + A a^{6} d^{5} x + \frac {1}{12} \, {\left (5 \, B b^{6} d e^{4} + {\left (6 \, B a b^{5} + A b^{6}\right )} e^{5}\right )} x^{12} + \frac {1}{11} \, {\left (10 \, B b^{6} d^{2} e^{3} + 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e^{4} + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{5}\right )} x^{11} + \frac {1}{2} \, {\left (2 \, B b^{6} d^{3} e^{2} + 2 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{3} + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{4} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{5}\right )} x^{10} + \frac {5}{9} \, {\left (B b^{6} d^{4} e + 2 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{2} + 6 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{3} + 5 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{4} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{5}\right )} x^{9} + \frac {1}{8} \, {\left (B b^{6} d^{5} + 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e + 30 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{2} + 50 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{3} + 25 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{4} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{5}\right )} x^{8} + \frac {1}{7} \, {\left ({\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} + 15 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e + 50 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{2} + 50 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{3} + 15 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{4} + {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{5}\right )} x^{7} + \frac {1}{6} \, {\left (A a^{6} e^{5} + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} + 25 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e + 50 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{2} + 30 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{3} + 5 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{4}\right )} x^{6} + {\left (A a^{6} d e^{4} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{5} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{4} e + 6 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{3} e^{2} + 2 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{2} e^{3}\right )} x^{5} + \frac {5}{4} \, {\left (2 \, A a^{6} d^{2} e^{3} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{5} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{4} e + 2 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{3} e^{2}\right )} x^{4} + \frac {1}{3} \, {\left (10 \, A a^{6} d^{3} e^{2} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{5} + 5 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{4} e\right )} x^{3} + \frac {1}{2} \, {\left (5 \, A a^{6} d^{4} e + {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{5}\right )} x^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1246 vs. \(2 (228) = 456\).
Time = 0.27 (sec) , antiderivative size = 1246, normalized size of antiderivative = 5.19 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=\text {Too large to display} \]
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Time = 1.64 (sec) , antiderivative size = 1039, normalized size of antiderivative = 4.33 \[ \int (a+b x)^6 (A+B x) (d+e x)^5 \, dx=x^7\,\left (\frac {B\,a^6\,e^5}{7}+\frac {30\,B\,a^5\,b\,d\,e^4}{7}+\frac {6\,A\,a^5\,b\,e^5}{7}+\frac {150\,B\,a^4\,b^2\,d^2\,e^3}{7}+\frac {75\,A\,a^4\,b^2\,d\,e^4}{7}+\frac {200\,B\,a^3\,b^3\,d^3\,e^2}{7}+\frac {200\,A\,a^3\,b^3\,d^2\,e^3}{7}+\frac {75\,B\,a^2\,b^4\,d^4\,e}{7}+\frac {150\,A\,a^2\,b^4\,d^3\,e^2}{7}+\frac {6\,B\,a\,b^5\,d^5}{7}+\frac {30\,A\,a\,b^5\,d^4\,e}{7}+\frac {A\,b^6\,d^5}{7}\right )+x^3\,\left (\frac {5\,B\,a^6\,d^4\,e}{3}+\frac {10\,A\,a^6\,d^3\,e^2}{3}+2\,B\,a^5\,b\,d^5+10\,A\,a^5\,b\,d^4\,e+5\,A\,a^4\,b^2\,d^5\right )+x^{11}\,\left (\frac {15\,B\,a^2\,b^4\,e^5}{11}+\frac {30\,B\,a\,b^5\,d\,e^4}{11}+\frac {6\,A\,a\,b^5\,e^5}{11}+\frac {10\,B\,b^6\,d^2\,e^3}{11}+\frac {5\,A\,b^6\,d\,e^4}{11}\right )+x^6\,\left (\frac {5\,B\,a^6\,d\,e^4}{6}+\frac {A\,a^6\,e^5}{6}+10\,B\,a^5\,b\,d^2\,e^3+5\,A\,a^5\,b\,d\,e^4+25\,B\,a^4\,b^2\,d^3\,e^2+25\,A\,a^4\,b^2\,d^2\,e^3+\frac {50\,B\,a^3\,b^3\,d^4\,e}{3}+\frac {100\,A\,a^3\,b^3\,d^3\,e^2}{3}+\frac {5\,B\,a^2\,b^4\,d^5}{2}+\frac {25\,A\,a^2\,b^4\,d^4\,e}{2}+A\,a\,b^5\,d^5\right )+x^8\,\left (\frac {3\,B\,a^5\,b\,e^5}{4}+\frac {75\,B\,a^4\,b^2\,d\,e^4}{8}+\frac {15\,A\,a^4\,b^2\,e^5}{8}+25\,B\,a^3\,b^3\,d^2\,e^3+\frac {25\,A\,a^3\,b^3\,d\,e^4}{2}+\frac {75\,B\,a^2\,b^4\,d^3\,e^2}{4}+\frac {75\,A\,a^2\,b^4\,d^2\,e^3}{4}+\frac {15\,B\,a\,b^5\,d^4\,e}{4}+\frac {15\,A\,a\,b^5\,d^3\,e^2}{2}+\frac {B\,b^6\,d^5}{8}+\frac {5\,A\,b^6\,d^4\,e}{8}\right )+x^5\,\left (2\,B\,a^6\,d^2\,e^3+A\,a^6\,d\,e^4+12\,B\,a^5\,b\,d^3\,e^2+12\,A\,a^5\,b\,d^2\,e^3+15\,B\,a^4\,b^2\,d^4\,e+30\,A\,a^4\,b^2\,d^3\,e^2+4\,B\,a^3\,b^3\,d^5+20\,A\,a^3\,b^3\,d^4\,e+3\,A\,a^2\,b^4\,d^5\right )+x^9\,\left (\frac {5\,B\,a^4\,b^2\,e^5}{3}+\frac {100\,B\,a^3\,b^3\,d\,e^4}{9}+\frac {20\,A\,a^3\,b^3\,e^5}{9}+\frac {50\,B\,a^2\,b^4\,d^2\,e^3}{3}+\frac {25\,A\,a^2\,b^4\,d\,e^4}{3}+\frac {20\,B\,a\,b^5\,d^3\,e^2}{3}+\frac {20\,A\,a\,b^5\,d^2\,e^3}{3}+\frac {5\,B\,b^6\,d^4\,e}{9}+\frac {10\,A\,b^6\,d^3\,e^2}{9}\right )+x^4\,\left (\frac {5\,B\,a^6\,d^3\,e^2}{2}+\frac {5\,A\,a^6\,d^2\,e^3}{2}+\frac {15\,B\,a^5\,b\,d^4\,e}{2}+15\,A\,a^5\,b\,d^3\,e^2+\frac {15\,B\,a^4\,b^2\,d^5}{4}+\frac {75\,A\,a^4\,b^2\,d^4\,e}{4}+5\,A\,a^3\,b^3\,d^5\right )+x^{10}\,\left (2\,B\,a^3\,b^3\,e^5+\frac {15\,B\,a^2\,b^4\,d\,e^4}{2}+\frac {3\,A\,a^2\,b^4\,e^5}{2}+6\,B\,a\,b^5\,d^2\,e^3+3\,A\,a\,b^5\,d\,e^4+B\,b^6\,d^3\,e^2+A\,b^6\,d^2\,e^3\right )+\frac {a^5\,d^4\,x^2\,\left (5\,A\,a\,e+6\,A\,b\,d+B\,a\,d\right )}{2}+\frac {b^5\,e^4\,x^{12}\,\left (A\,b\,e+6\,B\,a\,e+5\,B\,b\,d\right )}{12}+A\,a^6\,d^5\,x+\frac {B\,b^6\,e^5\,x^{13}}{13} \]
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