Integrand size = 20, antiderivative size = 277 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=-\frac {3 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e) x}{e^7}+\frac {(b d-a e)^6 (B d-A e)}{e^8 (d+e x)}+\frac {5 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e) (d+e x)^2}{2 e^8}-\frac {5 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) (d+e x)^3}{3 e^8}+\frac {3 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) (d+e x)^4}{4 e^8}-\frac {b^5 (7 b B d-A b e-6 a B e) (d+e x)^5}{5 e^8}+\frac {b^6 B (d+e x)^6}{6 e^8}+\frac {(b d-a e)^5 (7 b B d-6 A b e-a B e) \log (d+e x)}{e^8} \]
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Time = 0.42 (sec) , antiderivative size = 277, 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} \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=-\frac {b^5 (d+e x)^5 (-6 a B e-A b e+7 b B d)}{5 e^8}+\frac {3 b^4 (d+e x)^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{4 e^8}-\frac {5 b^3 (d+e x)^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac {5 b^2 (d+e x)^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{2 e^8}+\frac {(b d-a e)^6 (B d-A e)}{e^8 (d+e x)}+\frac {(b d-a e)^5 \log (d+e x) (-a B e-6 A b e+7 b B d)}{e^8}-\frac {3 b x (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^7}+\frac {b^6 B (d+e x)^6}{6 e^8} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {3 b (b d-a e)^4 (-7 b B d+5 A b e+2 a B e)}{e^7}+\frac {(-b d+a e)^6 (-B d+A e)}{e^7 (d+e x)^2}+\frac {(-b d+a e)^5 (-7 b B d+6 A b e+a B e)}{e^7 (d+e x)}-\frac {5 b^2 (b d-a e)^3 (-7 b B d+4 A b e+3 a B e) (d+e x)}{e^7}+\frac {5 b^3 (b d-a e)^2 (-7 b B d+3 A b e+4 a B e) (d+e x)^2}{e^7}-\frac {3 b^4 (b d-a e) (-7 b B d+2 A b e+5 a B e) (d+e x)^3}{e^7}+\frac {b^5 (-7 b B d+A b e+6 a B e) (d+e x)^4}{e^7}+\frac {b^6 B (d+e x)^5}{e^7}\right ) \, dx \\ & = -\frac {3 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e) x}{e^7}+\frac {(b d-a e)^6 (B d-A e)}{e^8 (d+e x)}+\frac {5 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e) (d+e x)^2}{2 e^8}-\frac {5 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) (d+e x)^3}{3 e^8}+\frac {3 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) (d+e x)^4}{4 e^8}-\frac {b^5 (7 b B d-A b e-6 a B e) (d+e x)^5}{5 e^8}+\frac {b^6 B (d+e x)^6}{6 e^8}+\frac {(b d-a e)^5 (7 b B d-6 A b e-a B e) \log (d+e x)}{e^8} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(643\) vs. \(2(277)=554\).
Time = 0.18 (sec) , antiderivative size = 643, normalized size of antiderivative = 2.32 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=\frac {60 a^6 e^6 (B d-A e)+360 a^5 b e^5 \left (A d e+B \left (-d^2+d e x+e^2 x^2\right )\right )+450 a^4 b^2 e^4 \left (2 A e \left (-d^2+d e x+e^2 x^2\right )+B \left (2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right )\right )+200 a^3 b^3 e^3 \left (3 A e \left (2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right )+2 B \left (-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right )\right )+75 a^2 b^4 e^2 \left (4 A e \left (-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right )+B \left (12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right )\right )+6 a b^5 e \left (5 A e \left (12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right )-6 B \left (10 d^6-50 d^5 e x-30 d^4 e^2 x^2+10 d^3 e^3 x^3-5 d^2 e^4 x^4+3 d e^5 x^5-2 e^6 x^6\right )\right )+b^6 \left (6 A e \left (-10 d^6+50 d^5 e x+30 d^4 e^2 x^2-10 d^3 e^3 x^3+5 d^2 e^4 x^4-3 d e^5 x^5+2 e^6 x^6\right )+B \left (60 d^7-360 d^6 e x-210 d^5 e^2 x^2+70 d^4 e^3 x^3-35 d^3 e^4 x^4+21 d^2 e^5 x^5-14 d e^6 x^6+10 e^7 x^7\right )\right )+60 (b d-a e)^5 (7 b B d-6 A b e-a B e) (d+e x) \log (d+e x)}{60 e^8 (d+e x)} \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. \(794\) vs. \(2(267)=534\).
Time = 0.70 (sec) , antiderivative size = 795, normalized size of antiderivative = 2.87
method | result | size |
norman | \(\frac {\frac {\left (A \,a^{6} e^{7}-6 A \,a^{5} b d \,e^{6}+30 A \,a^{4} b^{2} d^{2} e^{5}-60 A \,a^{3} b^{3} d^{3} e^{4}+60 A \,a^{2} b^{4} d^{4} e^{3}-30 A a \,b^{5} d^{5} e^{2}+6 A \,b^{6} d^{6} e -B \,a^{6} d \,e^{6}+12 B \,a^{5} b \,d^{2} e^{5}-45 B \,a^{4} b^{2} d^{3} e^{4}+80 B \,a^{3} b^{3} d^{4} e^{3}-75 B \,a^{2} b^{4} d^{5} e^{2}+36 B a \,b^{5} d^{6} e -7 b^{6} B \,d^{7}\right ) x}{e^{7} d}+\frac {b \left (30 A \,a^{4} b \,e^{5}-60 A \,a^{3} b^{2} d \,e^{4}+60 A \,a^{2} b^{3} d^{2} e^{3}-30 A a \,b^{4} d^{3} e^{2}+6 A \,b^{5} d^{4} e +12 B \,a^{5} e^{5}-45 B \,a^{4} b d \,e^{4}+80 B \,a^{3} b^{2} d^{2} e^{3}-75 B \,a^{2} b^{3} d^{3} e^{2}+36 B a \,b^{4} d^{4} e -7 B \,b^{5} d^{5}\right ) x^{2}}{2 e^{6}}+\frac {b^{2} \left (60 A \,a^{3} b \,e^{4}-60 A \,a^{2} b^{2} d \,e^{3}+30 A a \,b^{3} d^{2} e^{2}-6 A \,b^{4} d^{3} e +45 B \,a^{4} e^{4}-80 B \,a^{3} b d \,e^{3}+75 B \,a^{2} b^{2} d^{2} e^{2}-36 B a \,b^{3} d^{3} e +7 B \,b^{4} d^{4}\right ) x^{3}}{6 e^{5}}+\frac {b^{3} \left (60 A \,a^{2} b \,e^{3}-30 A a \,b^{2} d \,e^{2}+6 A \,b^{3} d^{2} e +80 B \,a^{3} e^{3}-75 B \,a^{2} b d \,e^{2}+36 B a \,b^{2} d^{2} e -7 b^{3} B \,d^{3}\right ) x^{4}}{12 e^{4}}+\frac {b^{4} \left (30 A a b \,e^{2}-6 A \,b^{2} d e +75 B \,a^{2} e^{2}-36 B a b d e +7 b^{2} B \,d^{2}\right ) x^{5}}{20 e^{3}}+\frac {b^{5} \left (6 A b e +36 B a e -7 B b d \right ) x^{6}}{30 e^{2}}+\frac {b^{6} B \,x^{7}}{6 e}}{e x +d}+\frac {\left (6 A \,a^{5} b \,e^{6}-30 A \,a^{4} b^{2} d \,e^{5}+60 A \,a^{3} b^{3} d^{2} e^{4}-60 A \,a^{2} b^{4} d^{3} e^{3}+30 A a \,b^{5} d^{4} e^{2}-6 A \,b^{6} d^{5} e +B \,a^{6} e^{6}-12 B \,a^{5} b d \,e^{5}+45 B \,a^{4} b^{2} d^{2} e^{4}-80 B \,a^{3} b^{3} d^{3} e^{3}+75 B \,a^{2} b^{4} d^{4} e^{2}-36 B a \,b^{5} d^{5} e +7 b^{6} B \,d^{6}\right ) \ln \left (e x +d \right )}{e^{8}}\) | \(795\) |
default | \(\frac {b \left (60 B \,a^{3} b^{2} d^{2} e^{3} x -60 B \,a^{2} b^{3} d^{3} e^{2} x +30 B a \,b^{4} d^{4} e x +\frac {45}{2} B \,a^{2} b^{3} d^{2} e^{3} x^{2}-12 B a \,b^{4} d^{3} e^{2} x^{2}-40 A \,a^{3} b^{2} d \,e^{4} x +45 A \,a^{2} b^{3} d^{2} e^{3} x -24 A a \,b^{4} d^{3} e^{2} x -30 B \,a^{4} b d \,e^{4} x +\frac {15}{4} B \,a^{2} b^{3} e^{5} x^{4}+6 B \,a^{5} e^{5} x -6 B \,b^{5} d^{5} x +\frac {6}{5} B a \,b^{4} e^{5} x^{5}-\frac {2}{5} B \,b^{5} d \,e^{4} x^{5}+\frac {3}{4} B \,b^{5} d^{2} e^{3} x^{4}+5 A \,a^{2} b^{3} e^{5} x^{3}+\frac {20}{3} B \,a^{3} b^{2} e^{5} x^{3}-\frac {4}{3} B \,b^{5} d^{3} e^{2} x^{3}-\frac {1}{2} A \,b^{5} d \,e^{4} x^{4}-2 A \,b^{5} d^{3} e^{2} x^{2}+\frac {15}{2} B \,a^{4} b \,e^{5} x^{2}+\frac {5}{2} B \,b^{5} d^{4} e \,x^{2}+15 A \,a^{4} b \,e^{5} x +5 A \,b^{5} d^{4} e x +10 A \,a^{3} b^{2} e^{5} x^{2}+\frac {3}{2} A a \,b^{4} e^{5} x^{4}-10 B \,a^{2} b^{3} d \,e^{4} x^{3}+6 B a \,b^{4} d^{2} e^{3} x^{3}-15 A \,a^{2} b^{3} d \,e^{4} x^{2}+9 A a \,b^{4} d^{2} e^{3} x^{2}-20 B \,a^{3} b^{2} d \,e^{4} x^{2}+A \,b^{5} d^{2} e^{3} x^{3}+\frac {1}{5} A \,b^{5} e^{5} x^{5}+\frac {1}{6} b^{5} B \,x^{6} e^{5}-3 B a \,b^{4} d \,e^{4} x^{4}-4 A a \,b^{4} d \,e^{4} x^{3}\right )}{e^{7}}-\frac {A \,a^{6} e^{7}-6 A \,a^{5} b d \,e^{6}+15 A \,a^{4} b^{2} d^{2} e^{5}-20 A \,a^{3} b^{3} d^{3} e^{4}+15 A \,a^{2} b^{4} d^{4} e^{3}-6 A a \,b^{5} d^{5} e^{2}+A \,b^{6} d^{6} e -B \,a^{6} d \,e^{6}+6 B \,a^{5} b \,d^{2} e^{5}-15 B \,a^{4} b^{2} d^{3} e^{4}+20 B \,a^{3} b^{3} d^{4} e^{3}-15 B \,a^{2} b^{4} d^{5} e^{2}+6 B a \,b^{5} d^{6} e -b^{6} B \,d^{7}}{e^{8} \left (e x +d \right )}+\frac {\left (6 A \,a^{5} b \,e^{6}-30 A \,a^{4} b^{2} d \,e^{5}+60 A \,a^{3} b^{3} d^{2} e^{4}-60 A \,a^{2} b^{4} d^{3} e^{3}+30 A a \,b^{5} d^{4} e^{2}-6 A \,b^{6} d^{5} e +B \,a^{6} e^{6}-12 B \,a^{5} b d \,e^{5}+45 B \,a^{4} b^{2} d^{2} e^{4}-80 B \,a^{3} b^{3} d^{3} e^{3}+75 B \,a^{2} b^{4} d^{4} e^{2}-36 B a \,b^{5} d^{5} e +7 b^{6} B \,d^{6}\right ) \ln \left (e x +d \right )}{e^{8}}\) | \(871\) |
risch | \(\text {Expression too large to display}\) | \(1047\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1236\) |
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Leaf count of result is larger than twice the leaf count of optimal. 1067 vs. \(2 (267) = 534\).
Time = 0.24 (sec) , antiderivative size = 1067, normalized size of antiderivative = 3.85 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=\text {Too large to display} \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. 782 vs. \(2 (284) = 568\).
Time = 1.95 (sec) , antiderivative size = 782, normalized size of antiderivative = 2.82 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=\frac {B b^{6} x^{6}}{6 e^{2}} + x^{5} \left (\frac {A b^{6}}{5 e^{2}} + \frac {6 B a b^{5}}{5 e^{2}} - \frac {2 B b^{6} d}{5 e^{3}}\right ) + x^{4} \cdot \left (\frac {3 A a b^{5}}{2 e^{2}} - \frac {A b^{6} d}{2 e^{3}} + \frac {15 B a^{2} b^{4}}{4 e^{2}} - \frac {3 B a b^{5} d}{e^{3}} + \frac {3 B b^{6} d^{2}}{4 e^{4}}\right ) + x^{3} \cdot \left (\frac {5 A a^{2} b^{4}}{e^{2}} - \frac {4 A a b^{5} d}{e^{3}} + \frac {A b^{6} d^{2}}{e^{4}} + \frac {20 B a^{3} b^{3}}{3 e^{2}} - \frac {10 B a^{2} b^{4} d}{e^{3}} + \frac {6 B a b^{5} d^{2}}{e^{4}} - \frac {4 B b^{6} d^{3}}{3 e^{5}}\right ) + x^{2} \cdot \left (\frac {10 A a^{3} b^{3}}{e^{2}} - \frac {15 A a^{2} b^{4} d}{e^{3}} + \frac {9 A a b^{5} d^{2}}{e^{4}} - \frac {2 A b^{6} d^{3}}{e^{5}} + \frac {15 B a^{4} b^{2}}{2 e^{2}} - \frac {20 B a^{3} b^{3} d}{e^{3}} + \frac {45 B a^{2} b^{4} d^{2}}{2 e^{4}} - \frac {12 B a b^{5} d^{3}}{e^{5}} + \frac {5 B b^{6} d^{4}}{2 e^{6}}\right ) + x \left (\frac {15 A a^{4} b^{2}}{e^{2}} - \frac {40 A a^{3} b^{3} d}{e^{3}} + \frac {45 A a^{2} b^{4} d^{2}}{e^{4}} - \frac {24 A a b^{5} d^{3}}{e^{5}} + \frac {5 A b^{6} d^{4}}{e^{6}} + \frac {6 B a^{5} b}{e^{2}} - \frac {30 B a^{4} b^{2} d}{e^{3}} + \frac {60 B a^{3} b^{3} d^{2}}{e^{4}} - \frac {60 B a^{2} b^{4} d^{3}}{e^{5}} + \frac {30 B a b^{5} d^{4}}{e^{6}} - \frac {6 B b^{6} d^{5}}{e^{7}}\right ) + \frac {- A a^{6} e^{7} + 6 A a^{5} b d e^{6} - 15 A a^{4} b^{2} d^{2} e^{5} + 20 A a^{3} b^{3} d^{3} e^{4} - 15 A a^{2} b^{4} d^{4} e^{3} + 6 A a b^{5} d^{5} e^{2} - A b^{6} d^{6} e + B a^{6} d e^{6} - 6 B a^{5} b d^{2} e^{5} + 15 B a^{4} b^{2} d^{3} e^{4} - 20 B a^{3} b^{3} d^{4} e^{3} + 15 B a^{2} b^{4} d^{5} e^{2} - 6 B a b^{5} d^{6} e + B b^{6} d^{7}}{d e^{8} + e^{9} x} + \frac {\left (a e - b d\right )^{5} \cdot \left (6 A b e + B a e - 7 B b d\right ) \log {\left (d + e x \right )}}{e^{8}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 771 vs. \(2 (267) = 534\).
Time = 0.21 (sec) , antiderivative size = 771, normalized size of antiderivative = 2.78 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=\frac {B b^{6} d^{7} - A a^{6} e^{7} - {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} - 5 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} - 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} + {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6}}{e^{9} x + d e^{8}} + \frac {10 \, B b^{6} e^{5} x^{6} - 12 \, {\left (2 \, B b^{6} d e^{4} - {\left (6 \, B a b^{5} + A b^{6}\right )} e^{5}\right )} x^{5} + 15 \, {\left (3 \, B b^{6} d^{2} e^{3} - 2 \, {\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^{4} - 20 \, {\left (4 \, B b^{6} d^{3} e^{2} - 3 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{3} + 6 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{4} - 5 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{5}\right )} x^{3} + 30 \, {\left (5 \, B b^{6} d^{4} e - 4 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{2} + 9 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{3} - 10 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{4} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{5}\right )} x^{2} - 60 \, {\left (6 \, B b^{6} d^{5} - 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e + 12 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{2} - 15 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{3} + 10 \, {\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}{60 \, e^{7}} + \frac {{\left (7 \, B b^{6} d^{6} - 6 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e + 15 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{2} - 20 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{3} + 15 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{4} - 6 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{5} + {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{6}\right )} \log \left (e x + d\right )}{e^{8}} \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. 979 vs. \(2 (267) = 534\).
Time = 0.29 (sec) , antiderivative size = 979, normalized size of antiderivative = 3.53 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=\frac {{\left (10 \, B b^{6} - \frac {12 \, {\left (7 \, B b^{6} d e - 6 \, B a b^{5} e^{2} - A b^{6} e^{2}\right )}}{{\left (e x + d\right )} e} + \frac {45 \, {\left (7 \, B b^{6} d^{2} e^{2} - 12 \, B a b^{5} d e^{3} - 2 \, A b^{6} d e^{3} + 5 \, B a^{2} b^{4} e^{4} + 2 \, A a b^{5} e^{4}\right )}}{{\left (e x + d\right )}^{2} e^{2}} - \frac {100 \, {\left (7 \, B b^{6} d^{3} e^{3} - 18 \, B a b^{5} d^{2} e^{4} - 3 \, A b^{6} d^{2} e^{4} + 15 \, B a^{2} b^{4} d e^{5} + 6 \, A a b^{5} d e^{5} - 4 \, B a^{3} b^{3} e^{6} - 3 \, A a^{2} b^{4} e^{6}\right )}}{{\left (e x + d\right )}^{3} e^{3}} + \frac {150 \, {\left (7 \, B b^{6} d^{4} e^{4} - 24 \, B a b^{5} d^{3} e^{5} - 4 \, A b^{6} d^{3} e^{5} + 30 \, B a^{2} b^{4} d^{2} e^{6} + 12 \, A a b^{5} d^{2} e^{6} - 16 \, B a^{3} b^{3} d e^{7} - 12 \, A a^{2} b^{4} d e^{7} + 3 \, B a^{4} b^{2} e^{8} + 4 \, A a^{3} b^{3} e^{8}\right )}}{{\left (e x + d\right )}^{4} e^{4}} - \frac {180 \, {\left (7 \, B b^{6} d^{5} e^{5} - 30 \, B a b^{5} d^{4} e^{6} - 5 \, A b^{6} d^{4} e^{6} + 50 \, B a^{2} b^{4} d^{3} e^{7} + 20 \, A a b^{5} d^{3} e^{7} - 40 \, B a^{3} b^{3} d^{2} e^{8} - 30 \, A a^{2} b^{4} d^{2} e^{8} + 15 \, B a^{4} b^{2} d e^{9} + 20 \, A a^{3} b^{3} d e^{9} - 2 \, B a^{5} b e^{10} - 5 \, A a^{4} b^{2} e^{10}\right )}}{{\left (e x + d\right )}^{5} e^{5}}\right )} {\left (e x + d\right )}^{6}}{60 \, e^{8}} - \frac {{\left (7 \, B b^{6} d^{6} - 36 \, B a b^{5} d^{5} e - 6 \, A b^{6} d^{5} e + 75 \, B a^{2} b^{4} d^{4} e^{2} + 30 \, A a b^{5} d^{4} e^{2} - 80 \, B a^{3} b^{3} d^{3} e^{3} - 60 \, A a^{2} b^{4} d^{3} e^{3} + 45 \, B a^{4} b^{2} d^{2} e^{4} + 60 \, A a^{3} b^{3} d^{2} e^{4} - 12 \, B a^{5} b d e^{5} - 30 \, A a^{4} b^{2} d e^{5} + B a^{6} e^{6} + 6 \, A a^{5} b e^{6}\right )} \log \left (\frac {{\left | e x + d \right |}}{{\left (e x + d\right )}^{2} {\left | e \right |}}\right )}{e^{8}} + \frac {\frac {B b^{6} d^{7} e^{6}}{e x + d} - \frac {6 \, B a b^{5} d^{6} e^{7}}{e x + d} - \frac {A b^{6} d^{6} e^{7}}{e x + d} + \frac {15 \, B a^{2} b^{4} d^{5} e^{8}}{e x + d} + \frac {6 \, A a b^{5} d^{5} e^{8}}{e x + d} - \frac {20 \, B a^{3} b^{3} d^{4} e^{9}}{e x + d} - \frac {15 \, A a^{2} b^{4} d^{4} e^{9}}{e x + d} + \frac {15 \, B a^{4} b^{2} d^{3} e^{10}}{e x + d} + \frac {20 \, A a^{3} b^{3} d^{3} e^{10}}{e x + d} - \frac {6 \, B a^{5} b d^{2} e^{11}}{e x + d} - \frac {15 \, A a^{4} b^{2} d^{2} e^{11}}{e x + d} + \frac {B a^{6} d e^{12}}{e x + d} + \frac {6 \, A a^{5} b d e^{12}}{e x + d} - \frac {A a^{6} e^{13}}{e x + d}}{e^{14}} \]
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Time = 1.30 (sec) , antiderivative size = 1228, normalized size of antiderivative = 4.43 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx=\text {Too large to display} \]
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