Integrand size = 20, antiderivative size = 279 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=\frac {3 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) x}{e^7}+\frac {(b d-a e)^6 (B d-A e)}{4 e^8 (d+e x)^4}-\frac {(b d-a e)^5 (7 b B d-6 A b e-a B e)}{3 e^8 (d+e x)^3}+\frac {3 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e)}{2 e^8 (d+e x)^2}-\frac {5 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e)}{e^8 (d+e x)}-\frac {b^5 (7 b B d-A b e-6 a B e) (d+e x)^2}{2 e^8}+\frac {b^6 B (d+e x)^3}{3 e^8}-\frac {5 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) \log (d+e x)}{e^8} \]
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Time = 0.26 (sec) , antiderivative size = 279, 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} \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=-\frac {b^5 (d+e x)^2 (-6 a B e-A b e+7 b B d)}{2 e^8}+\frac {3 b^4 x (b d-a e) (-5 a B e-2 A b e+7 b B d)}{e^7}-\frac {5 b^3 (b d-a e)^2 \log (d+e x) (-4 a B e-3 A b e+7 b B d)}{e^8}-\frac {5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8 (d+e x)}+\frac {3 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{2 e^8 (d+e x)^2}-\frac {(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8 (d+e x)^3}+\frac {(b d-a e)^6 (B d-A e)}{4 e^8 (d+e x)^4}+\frac {b^6 B (d+e x)^3}{3 e^8} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {3 b^4 (b d-a e) (-7 b B d+2 A b e+5 a B e)}{e^7}+\frac {(-b d+a e)^6 (-B d+A e)}{e^7 (d+e x)^5}+\frac {(-b d+a e)^5 (-7 b B d+6 A b e+a B e)}{e^7 (d+e x)^4}+\frac {3 b (b d-a e)^4 (-7 b B d+5 A b e+2 a B e)}{e^7 (d+e x)^3}-\frac {5 b^2 (b d-a e)^3 (-7 b B d+4 A b e+3 a B e)}{e^7 (d+e x)^2}+\frac {5 b^3 (b d-a e)^2 (-7 b B d+3 A b e+4 a B e)}{e^7 (d+e x)}+\frac {b^5 (-7 b B d+A b e+6 a B e) (d+e x)}{e^7}+\frac {b^6 B (d+e x)^2}{e^7}\right ) \, dx \\ & = \frac {3 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) x}{e^7}+\frac {(b d-a e)^6 (B d-A e)}{4 e^8 (d+e x)^4}-\frac {(b d-a e)^5 (7 b B d-6 A b e-a B e)}{3 e^8 (d+e x)^3}+\frac {3 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e)}{2 e^8 (d+e x)^2}-\frac {5 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e)}{e^8 (d+e x)}-\frac {b^5 (7 b B d-A b e-6 a B e) (d+e x)^2}{2 e^8}+\frac {b^6 B (d+e x)^3}{3 e^8}-\frac {5 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) \log (d+e x)}{e^8} \\ \end{align*}
Time = 0.12 (sec) , antiderivative size = 263, normalized size of antiderivative = 0.94 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=\frac {-12 b^4 e \left (-15 a^2 B e^2-6 a b e (-5 B d+A e)+5 b^2 d (-3 B d+A e)\right ) x+6 b^5 e^2 (-5 b B d+A b e+6 a B e) x^2+4 b^6 B e^3 x^3+\frac {3 (b d-a e)^6 (B d-A e)}{(d+e x)^4}-\frac {4 (b d-a e)^5 (7 b B d-6 A b e-a B e)}{(d+e x)^3}+\frac {18 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e)}{(d+e x)^2}-\frac {60 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e)}{d+e x}-60 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) \log (d+e x)}{12 e^8} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(797\) vs. \(2(269)=538\).
Time = 0.70 (sec) , antiderivative size = 798, normalized size of antiderivative = 2.86
method | result | size |
norman | \(\frac {\frac {b^{4} \left (6 A a b \,e^{2}-3 A \,b^{2} d e +15 B \,a^{2} e^{2}-18 B a b d e +7 b^{2} B \,d^{2}\right ) x^{5}}{e^{3}}-\frac {3 A \,a^{6} e^{7}+6 A \,a^{5} b d \,e^{6}+15 A \,a^{4} b^{2} d^{2} e^{5}+60 A \,a^{3} b^{3} d^{3} e^{4}-375 A \,a^{2} b^{4} d^{4} e^{3}+750 A a \,b^{5} d^{5} e^{2}-375 A \,b^{6} d^{6} e +B \,a^{6} d \,e^{6}+6 B \,a^{5} b \,d^{2} e^{5}+45 B \,a^{4} b^{2} d^{3} e^{4}-500 B \,a^{3} b^{3} d^{4} e^{3}+1875 B \,a^{2} b^{4} d^{5} e^{2}-2250 B a \,b^{5} d^{6} e +875 b^{6} B \,d^{7}}{12 e^{8}}-\frac {\left (20 A \,a^{3} b^{3} e^{4}-60 A \,a^{2} b^{4} d \,e^{3}+120 A a \,b^{5} d^{2} e^{2}-60 A \,b^{6} d^{3} e +15 B \,a^{4} b^{2} e^{4}-80 B \,a^{3} b^{3} d \,e^{3}+300 B \,a^{2} b^{4} d^{2} e^{2}-360 B a \,b^{5} d^{3} e +140 b^{6} B \,d^{4}\right ) x^{3}}{e^{5}}-\frac {3 \left (5 A \,a^{4} b^{2} e^{5}+20 A \,a^{3} b^{3} d \,e^{4}-90 A \,a^{2} b^{4} d^{2} e^{3}+180 A a \,b^{5} d^{3} e^{2}-90 A \,b^{6} d^{4} e +2 B \,a^{5} b \,e^{5}+15 B \,a^{4} b^{2} d \,e^{4}-120 B \,a^{3} b^{3} d^{2} e^{3}+450 B \,a^{2} b^{4} d^{3} e^{2}-540 B a \,b^{5} d^{4} e +210 b^{6} B \,d^{5}\right ) x^{2}}{2 e^{6}}-\frac {\left (6 A \,a^{5} b \,e^{6}+15 A \,a^{4} b^{2} d \,e^{5}+60 A \,a^{3} b^{3} d^{2} e^{4}-330 A \,a^{2} b^{4} d^{3} e^{3}+660 A a \,b^{5} d^{4} e^{2}-330 A \,b^{6} d^{5} e +B \,a^{6} e^{6}+6 B \,a^{5} b d \,e^{5}+45 B \,a^{4} b^{2} d^{2} e^{4}-440 B \,a^{3} b^{3} d^{3} e^{3}+1650 B \,a^{2} b^{4} d^{4} e^{2}-1980 B a \,b^{5} d^{5} e +770 b^{6} B \,d^{6}\right ) x}{3 e^{7}}+\frac {b^{5} \left (3 A b e +18 B a e -7 B b d \right ) x^{6}}{6 e^{2}}+\frac {b^{6} B \,x^{7}}{3 e}}{\left (e x +d \right )^{4}}+\frac {5 b^{3} \left (3 A \,a^{2} b \,e^{3}-6 A a \,b^{2} d \,e^{2}+3 A \,b^{3} d^{2} e +4 B \,a^{3} e^{3}-15 B \,a^{2} b d \,e^{2}+18 B a \,b^{2} d^{2} e -7 b^{3} B \,d^{3}\right ) \ln \left (e x +d \right )}{e^{8}}\) | \(798\) |
default | \(\frac {b^{4} \left (\frac {1}{3} b^{2} B \,x^{3} e^{2}+\frac {1}{2} A \,b^{2} e^{2} x^{2}+3 B a b \,e^{2} x^{2}-\frac {5}{2} B \,b^{2} d e \,x^{2}+6 A a b \,e^{2} x -5 A \,b^{2} d e x +15 B \,a^{2} e^{2} x -30 B a b d e x +15 b^{2} B \,d^{2} x \right )}{e^{7}}-\frac {5 b^{2} \left (4 A \,a^{3} b \,e^{4}-12 A \,a^{2} b^{2} d \,e^{3}+12 A a \,b^{3} d^{2} e^{2}-4 A \,b^{4} d^{3} e +3 B \,a^{4} e^{4}-16 B \,a^{3} b d \,e^{3}+30 B \,a^{2} b^{2} d^{2} e^{2}-24 B a \,b^{3} d^{3} e +7 B \,b^{4} d^{4}\right )}{e^{8} \left (e x +d \right )}-\frac {6 A \,a^{5} b \,e^{6}-30 A \,a^{4} b^{2} d \,e^{5}+60 A \,a^{3} b^{3} d^{2} e^{4}-60 A \,a^{2} b^{4} d^{3} e^{3}+30 A a \,b^{5} d^{4} e^{2}-6 A \,b^{6} d^{5} e +B \,a^{6} e^{6}-12 B \,a^{5} b d \,e^{5}+45 B \,a^{4} b^{2} d^{2} e^{4}-80 B \,a^{3} b^{3} d^{3} e^{3}+75 B \,a^{2} b^{4} d^{4} e^{2}-36 B a \,b^{5} d^{5} e +7 b^{6} B \,d^{6}}{3 e^{8} \left (e x +d \right )^{3}}-\frac {3 b \left (5 A \,a^{4} b \,e^{5}-20 A \,a^{3} b^{2} d \,e^{4}+30 A \,a^{2} b^{3} d^{2} e^{3}-20 A a \,b^{4} d^{3} e^{2}+5 A \,b^{5} d^{4} e +2 B \,a^{5} e^{5}-15 B \,a^{4} b d \,e^{4}+40 B \,a^{3} b^{2} d^{2} e^{3}-50 B \,a^{2} b^{3} d^{3} e^{2}+30 B a \,b^{4} d^{4} e -7 B \,b^{5} d^{5}\right )}{2 e^{8} \left (e x +d \right )^{2}}+\frac {5 b^{3} \left (3 A \,a^{2} b \,e^{3}-6 A a \,b^{2} d \,e^{2}+3 A \,b^{3} d^{2} e +4 B \,a^{3} e^{3}-15 B \,a^{2} b d \,e^{2}+18 B a \,b^{2} d^{2} e -7 b^{3} B \,d^{3}\right ) \ln \left (e x +d \right )}{e^{8}}-\frac {A \,a^{6} e^{7}-6 A \,a^{5} b d \,e^{6}+15 A \,a^{4} b^{2} d^{2} e^{5}-20 A \,a^{3} b^{3} d^{3} e^{4}+15 A \,a^{2} b^{4} d^{4} e^{3}-6 A a \,b^{5} d^{5} e^{2}+A \,b^{6} d^{6} e -B \,a^{6} d \,e^{6}+6 B \,a^{5} b \,d^{2} e^{5}-15 B \,a^{4} b^{2} d^{3} e^{4}+20 B \,a^{3} b^{3} d^{4} e^{3}-15 B \,a^{2} b^{4} d^{5} e^{2}+6 B a \,b^{5} d^{6} e -b^{6} B \,d^{7}}{4 e^{8} \left (e x +d \right )^{4}}\) | \(810\) |
risch | \(\frac {b^{6} B \,x^{3}}{3 e^{5}}+\frac {b^{6} A \,x^{2}}{2 e^{5}}+\frac {3 b^{5} B a \,x^{2}}{e^{5}}-\frac {5 b^{6} B d \,x^{2}}{2 e^{6}}+\frac {6 b^{5} A a x}{e^{5}}-\frac {5 b^{6} A d x}{e^{6}}+\frac {15 b^{4} B \,a^{2} x}{e^{5}}-\frac {30 b^{5} B a d x}{e^{6}}+\frac {15 b^{6} B \,d^{2} x}{e^{7}}+\frac {\left (-20 A \,a^{3} b^{3} e^{6}+60 A \,a^{2} b^{4} d \,e^{5}-60 A a \,b^{5} d^{2} e^{4}+20 A \,b^{6} d^{3} e^{3}-15 B \,a^{4} b^{2} e^{6}+80 B \,a^{3} b^{3} d \,e^{5}-150 B \,a^{2} b^{4} d^{2} e^{4}+120 B a \,b^{5} d^{3} e^{3}-35 b^{6} B \,d^{4} e^{2}\right ) x^{3}-\frac {3 e b \left (5 A \,a^{4} b \,e^{5}+20 A \,a^{3} b^{2} d \,e^{4}-90 A \,a^{2} b^{3} d^{2} e^{3}+100 A a \,b^{4} d^{3} e^{2}-35 A \,b^{5} d^{4} e +2 B \,a^{5} e^{5}+15 B \,a^{4} b d \,e^{4}-120 B \,a^{3} b^{2} d^{2} e^{3}+250 B \,a^{2} b^{3} d^{3} e^{2}-210 B a \,b^{4} d^{4} e +63 B \,b^{5} d^{5}\right ) x^{2}}{2}+\left (-2 A \,a^{5} b \,e^{6}-5 A \,a^{4} b^{2} d \,e^{5}-20 A \,a^{3} b^{3} d^{2} e^{4}+110 A \,a^{2} b^{4} d^{3} e^{3}-130 A a \,b^{5} d^{4} e^{2}+47 A \,b^{6} d^{5} e -\frac {1}{3} B \,a^{6} e^{6}-2 B \,a^{5} b d \,e^{5}-15 B \,a^{4} b^{2} d^{2} e^{4}+\frac {440}{3} B \,a^{3} b^{3} d^{3} e^{3}-325 B \,a^{2} b^{4} d^{4} e^{2}+282 B a \,b^{5} d^{5} e -\frac {259}{3} b^{6} B \,d^{6}\right ) x -\frac {3 A \,a^{6} e^{7}+6 A \,a^{5} b d \,e^{6}+15 A \,a^{4} b^{2} d^{2} e^{5}+60 A \,a^{3} b^{3} d^{3} e^{4}-375 A \,a^{2} b^{4} d^{4} e^{3}+462 A a \,b^{5} d^{5} e^{2}-171 A \,b^{6} d^{6} e +B \,a^{6} d \,e^{6}+6 B \,a^{5} b \,d^{2} e^{5}+45 B \,a^{4} b^{2} d^{3} e^{4}-500 B \,a^{3} b^{3} d^{4} e^{3}+1155 B \,a^{2} b^{4} d^{5} e^{2}-1026 B a \,b^{5} d^{6} e +319 b^{6} B \,d^{7}}{12 e}}{e^{7} \left (e x +d \right )^{4}}+\frac {15 b^{4} \ln \left (e x +d \right ) A \,a^{2}}{e^{5}}-\frac {30 b^{5} \ln \left (e x +d \right ) A a d}{e^{6}}+\frac {15 b^{6} \ln \left (e x +d \right ) A \,d^{2}}{e^{7}}+\frac {20 b^{3} \ln \left (e x +d \right ) B \,a^{3}}{e^{5}}-\frac {75 b^{4} \ln \left (e x +d \right ) B \,a^{2} d}{e^{6}}+\frac {90 b^{5} \ln \left (e x +d \right ) B a \,d^{2}}{e^{7}}-\frac {35 b^{6} \ln \left (e x +d \right ) B \,d^{3}}{e^{8}}\) | \(855\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1539\) |
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Leaf count of result is larger than twice the leaf count of optimal. 1222 vs. \(2 (269) = 538\).
Time = 0.24 (sec) , antiderivative size = 1222, normalized size of antiderivative = 4.38 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=\text {Too large to display} \]
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Timed out. \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 801 vs. \(2 (269) = 538\).
Time = 0.27 (sec) , antiderivative size = 801, normalized size of antiderivative = 2.87 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=-\frac {319 \, B b^{6} d^{7} + 3 \, A a^{6} e^{7} - 171 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 231 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} - 125 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 15 \, {\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} + 60 \, {\left (7 \, B b^{6} d^{4} e^{3} - 4 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{4} + 6 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{5} - 4 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{6} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{7}\right )} x^{3} + 18 \, {\left (63 \, B b^{6} d^{5} e^{2} - 35 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e^{3} + 50 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{4} - 30 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{5} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{6} + {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{7}\right )} x^{2} + 4 \, {\left (259 \, B b^{6} d^{6} e - 141 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e^{2} + 195 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{3} - 110 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{4} + 15 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{5} + 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{6} + {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{7}\right )} x}{12 \, {\left (e^{12} x^{4} + 4 \, d e^{11} x^{3} + 6 \, d^{2} e^{10} x^{2} + 4 \, d^{3} e^{9} x + d^{4} e^{8}\right )}} + \frac {2 \, B b^{6} e^{2} x^{3} - 3 \, {\left (5 \, B b^{6} d e - {\left (6 \, B a b^{5} + A b^{6}\right )} e^{2}\right )} x^{2} + 6 \, {\left (15 \, B b^{6} d^{2} - 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{2}\right )} x}{6 \, e^{7}} - \frac {5 \, {\left (7 \, B b^{6} d^{3} - 3 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{2} - {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{3}\right )} \log \left (e x + d\right )}{e^{8}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1175 vs. \(2 (269) = 538\).
Time = 0.29 (sec) , antiderivative size = 1175, normalized size of antiderivative = 4.21 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=\text {Too large to display} \]
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Time = 1.44 (sec) , antiderivative size = 863, normalized size of antiderivative = 3.09 \[ \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx=x^2\,\left (\frac {A\,b^6+6\,B\,a\,b^5}{2\,e^5}-\frac {5\,B\,b^6\,d}{2\,e^6}\right )-\frac {x^3\,\left (15\,B\,a^4\,b^2\,e^6-80\,B\,a^3\,b^3\,d\,e^5+20\,A\,a^3\,b^3\,e^6+150\,B\,a^2\,b^4\,d^2\,e^4-60\,A\,a^2\,b^4\,d\,e^5-120\,B\,a\,b^5\,d^3\,e^3+60\,A\,a\,b^5\,d^2\,e^4+35\,B\,b^6\,d^4\,e^2-20\,A\,b^6\,d^3\,e^3\right )+\frac {B\,a^6\,d\,e^6+3\,A\,a^6\,e^7+6\,B\,a^5\,b\,d^2\,e^5+6\,A\,a^5\,b\,d\,e^6+45\,B\,a^4\,b^2\,d^3\,e^4+15\,A\,a^4\,b^2\,d^2\,e^5-500\,B\,a^3\,b^3\,d^4\,e^3+60\,A\,a^3\,b^3\,d^3\,e^4+1155\,B\,a^2\,b^4\,d^5\,e^2-375\,A\,a^2\,b^4\,d^4\,e^3-1026\,B\,a\,b^5\,d^6\,e+462\,A\,a\,b^5\,d^5\,e^2+319\,B\,b^6\,d^7-171\,A\,b^6\,d^6\,e}{12\,e}+x\,\left (\frac {B\,a^6\,e^6}{3}+2\,B\,a^5\,b\,d\,e^5+2\,A\,a^5\,b\,e^6+15\,B\,a^4\,b^2\,d^2\,e^4+5\,A\,a^4\,b^2\,d\,e^5-\frac {440\,B\,a^3\,b^3\,d^3\,e^3}{3}+20\,A\,a^3\,b^3\,d^2\,e^4+325\,B\,a^2\,b^4\,d^4\,e^2-110\,A\,a^2\,b^4\,d^3\,e^3-282\,B\,a\,b^5\,d^5\,e+130\,A\,a\,b^5\,d^4\,e^2+\frac {259\,B\,b^6\,d^6}{3}-47\,A\,b^6\,d^5\,e\right )+x^2\,\left (3\,B\,a^5\,b\,e^6+\frac {45\,B\,a^4\,b^2\,d\,e^5}{2}+\frac {15\,A\,a^4\,b^2\,e^6}{2}-180\,B\,a^3\,b^3\,d^2\,e^4+30\,A\,a^3\,b^3\,d\,e^5+375\,B\,a^2\,b^4\,d^3\,e^3-135\,A\,a^2\,b^4\,d^2\,e^4-315\,B\,a\,b^5\,d^4\,e^2+150\,A\,a\,b^5\,d^3\,e^3+\frac {189\,B\,b^6\,d^5\,e}{2}-\frac {105\,A\,b^6\,d^4\,e^2}{2}\right )}{d^4\,e^7+4\,d^3\,e^8\,x+6\,d^2\,e^9\,x^2+4\,d\,e^{10}\,x^3+e^{11}\,x^4}-x\,\left (\frac {5\,d\,\left (\frac {A\,b^6+6\,B\,a\,b^5}{e^5}-\frac {5\,B\,b^6\,d}{e^6}\right )}{e}-\frac {3\,a\,b^4\,\left (2\,A\,b+5\,B\,a\right )}{e^5}+\frac {10\,B\,b^6\,d^2}{e^7}\right )+\frac {\ln \left (d+e\,x\right )\,\left (20\,B\,a^3\,b^3\,e^3-75\,B\,a^2\,b^4\,d\,e^2+15\,A\,a^2\,b^4\,e^3+90\,B\,a\,b^5\,d^2\,e-30\,A\,a\,b^5\,d\,e^2-35\,B\,b^6\,d^3+15\,A\,b^6\,d^2\,e\right )}{e^8}+\frac {B\,b^6\,x^3}{3\,e^5} \]
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