Integrand size = 15, antiderivative size = 89 \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {(c+d x)^8}{10 (b c-a d) (a+b x)^{10}}+\frac {d (c+d x)^8}{45 (b c-a d)^2 (a+b x)^9}-\frac {d^2 (c+d x)^8}{360 (b c-a d)^3 (a+b x)^8} \]
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Time = 0.02 (sec) , antiderivative size = 89, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {47, 37} \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {d^2 (c+d x)^8}{360 (a+b x)^8 (b c-a d)^3}+\frac {d (c+d x)^8}{45 (a+b x)^9 (b c-a d)^2}-\frac {(c+d x)^8}{10 (a+b x)^{10} (b c-a d)} \]
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Rule 37
Rule 47
Rubi steps \begin{align*} \text {integral}& = -\frac {(c+d x)^8}{10 (b c-a d) (a+b x)^{10}}-\frac {d \int \frac {(c+d x)^7}{(a+b x)^{10}} \, dx}{5 (b c-a d)} \\ & = -\frac {(c+d x)^8}{10 (b c-a d) (a+b x)^{10}}+\frac {d (c+d x)^8}{45 (b c-a d)^2 (a+b x)^9}+\frac {d^2 \int \frac {(c+d x)^7}{(a+b x)^9} \, dx}{45 (b c-a d)^2} \\ & = -\frac {(c+d x)^8}{10 (b c-a d) (a+b x)^{10}}+\frac {d (c+d x)^8}{45 (b c-a d)^2 (a+b x)^9}-\frac {d^2 (c+d x)^8}{360 (b c-a d)^3 (a+b x)^8} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(371\) vs. \(2(89)=178\).
Time = 0.08 (sec) , antiderivative size = 371, normalized size of antiderivative = 4.17 \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {a^7 d^7+a^6 b d^6 (3 c+10 d x)+3 a^5 b^2 d^5 \left (2 c^2+10 c d x+15 d^2 x^2\right )+5 a^4 b^3 d^4 \left (2 c^3+12 c^2 d x+27 c d^2 x^2+24 d^3 x^3\right )+5 a^3 b^4 d^3 \left (3 c^4+20 c^3 d x+54 c^2 d^2 x^2+72 c d^3 x^3+42 d^4 x^4\right )+3 a^2 b^5 d^2 \left (7 c^5+50 c^4 d x+150 c^3 d^2 x^2+240 c^2 d^3 x^3+210 c d^4 x^4+84 d^5 x^5\right )+a b^6 d \left (28 c^6+210 c^5 d x+675 c^4 d^2 x^2+1200 c^3 d^3 x^3+1260 c^2 d^4 x^4+756 c d^5 x^5+210 d^6 x^6\right )+b^7 \left (36 c^7+280 c^6 d x+945 c^5 d^2 x^2+1800 c^4 d^3 x^3+2100 c^3 d^4 x^4+1512 c^2 d^5 x^5+630 c d^6 x^6+120 d^7 x^7\right )}{360 b^8 (a+b x)^{10}} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(437\) vs. \(2(83)=166\).
Time = 0.22 (sec) , antiderivative size = 438, normalized size of antiderivative = 4.92
method | result | size |
risch | \(\frac {-\frac {d^{7} x^{7}}{3 b}-\frac {7 d^{6} \left (a d +3 b c \right ) x^{6}}{12 b^{2}}-\frac {7 d^{5} \left (a^{2} d^{2}+3 a b c d +6 b^{2} c^{2}\right ) x^{5}}{10 b^{3}}-\frac {7 d^{4} \left (a^{3} d^{3}+3 a^{2} b c \,d^{2}+6 a \,b^{2} c^{2} d +10 b^{3} c^{3}\right ) x^{4}}{12 b^{4}}-\frac {d^{3} \left (a^{4} d^{4}+3 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}+10 a \,b^{3} c^{3} d +15 b^{4} c^{4}\right ) x^{3}}{3 b^{5}}-\frac {d^{2} \left (a^{5} d^{5}+3 a^{4} b c \,d^{4}+6 a^{3} b^{2} c^{2} d^{3}+10 a^{2} b^{3} c^{3} d^{2}+15 a \,b^{4} c^{4} d +21 b^{5} c^{5}\right ) x^{2}}{8 b^{6}}-\frac {d \left (a^{6} d^{6}+3 a^{5} b c \,d^{5}+6 a^{4} b^{2} c^{2} d^{4}+10 a^{3} b^{3} c^{3} d^{3}+15 a^{2} b^{4} c^{4} d^{2}+21 a \,b^{5} c^{5} d +28 b^{6} c^{6}\right ) x}{36 b^{7}}-\frac {a^{7} d^{7}+3 a^{6} b c \,d^{6}+6 a^{5} b^{2} c^{2} d^{5}+10 a^{4} b^{3} c^{3} d^{4}+15 a^{3} b^{4} c^{4} d^{3}+21 a^{2} b^{5} c^{5} d^{2}+28 a \,b^{6} c^{6} d +36 b^{7} c^{7}}{360 b^{8}}}{\left (b x +a \right )^{10}}\) | \(438\) |
default | \(-\frac {d^{7}}{3 b^{8} \left (b x +a \right )^{3}}-\frac {7 d \left (a^{6} d^{6}-6 a^{5} b c \,d^{5}+15 a^{4} b^{2} c^{2} d^{4}-20 a^{3} b^{3} c^{3} d^{3}+15 a^{2} b^{4} c^{4} d^{2}-6 a \,b^{5} c^{5} d +b^{6} c^{6}\right )}{9 b^{8} \left (b x +a \right )^{9}}+\frac {35 d^{4} \left (a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right )}{6 b^{8} \left (b x +a \right )^{6}}+\frac {21 d^{2} \left (a^{5} d^{5}-5 a^{4} b c \,d^{4}+10 a^{3} b^{2} c^{2} d^{3}-10 a^{2} b^{3} c^{3} d^{2}+5 a \,b^{4} c^{4} d -b^{5} c^{5}\right )}{8 b^{8} \left (b x +a \right )^{8}}+\frac {7 d^{6} \left (a d -b c \right )}{4 b^{8} \left (b x +a \right )^{4}}-\frac {5 d^{3} \left (a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right )}{b^{8} \left (b x +a \right )^{7}}-\frac {-a^{7} d^{7}+7 a^{6} b c \,d^{6}-21 a^{5} b^{2} c^{2} d^{5}+35 a^{4} b^{3} c^{3} d^{4}-35 a^{3} b^{4} c^{4} d^{3}+21 a^{2} b^{5} c^{5} d^{2}-7 a \,b^{6} c^{6} d +b^{7} c^{7}}{10 b^{8} \left (b x +a \right )^{10}}-\frac {21 d^{5} \left (a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right )}{5 b^{8} \left (b x +a \right )^{5}}\) | \(464\) |
norman | \(\frac {-\frac {d^{7} x^{7}}{3 b}+\frac {7 \left (-a \,b^{2} d^{7}-3 b^{3} c \,d^{6}\right ) x^{6}}{12 b^{4}}+\frac {7 \left (-a^{2} b^{2} d^{7}-3 a \,b^{3} c \,d^{6}-6 b^{4} c^{2} d^{5}\right ) x^{5}}{10 b^{5}}+\frac {7 \left (-a^{3} b^{2} d^{7}-3 a^{2} b^{3} c \,d^{6}-6 a \,b^{4} c^{2} d^{5}-10 b^{5} c^{3} d^{4}\right ) x^{4}}{12 b^{6}}+\frac {\left (-a^{4} b^{2} d^{7}-3 a^{3} b^{3} c \,d^{6}-6 a^{2} b^{4} c^{2} d^{5}-10 a \,b^{5} c^{3} d^{4}-15 b^{6} c^{4} d^{3}\right ) x^{3}}{3 b^{7}}+\frac {\left (-a^{5} b^{2} d^{7}-3 a^{4} b^{3} c \,d^{6}-6 a^{3} b^{4} c^{2} d^{5}-10 a^{2} b^{5} c^{3} d^{4}-15 a \,b^{6} c^{4} d^{3}-21 b^{7} c^{5} d^{2}\right ) x^{2}}{8 b^{8}}+\frac {\left (-a^{6} b^{2} d^{7}-3 a^{5} b^{3} c \,d^{6}-6 a^{4} b^{4} c^{2} d^{5}-10 a^{3} b^{5} c^{3} d^{4}-15 a^{2} b^{6} c^{4} d^{3}-21 a \,b^{7} c^{5} d^{2}-28 b^{8} c^{6} d \right ) x}{36 b^{9}}+\frac {-a^{7} b^{2} d^{7}-3 a^{6} b^{3} c \,d^{6}-6 a^{5} b^{4} c^{2} d^{5}-10 a^{4} b^{5} c^{3} d^{4}-15 a^{3} b^{6} c^{4} d^{3}-21 a^{2} b^{7} c^{5} d^{2}-28 a \,b^{8} c^{6} d -36 b^{9} c^{7}}{360 b^{10}}}{\left (b x +a \right )^{10}}\) | \(492\) |
gosper | \(-\frac {120 x^{7} d^{7} b^{7}+210 x^{6} a \,b^{6} d^{7}+630 x^{6} b^{7} c \,d^{6}+252 x^{5} a^{2} b^{5} d^{7}+756 x^{5} a \,b^{6} c \,d^{6}+1512 x^{5} b^{7} c^{2} d^{5}+210 x^{4} a^{3} b^{4} d^{7}+630 x^{4} a^{2} b^{5} c \,d^{6}+1260 x^{4} a \,b^{6} c^{2} d^{5}+2100 x^{4} b^{7} c^{3} d^{4}+120 x^{3} a^{4} b^{3} d^{7}+360 x^{3} a^{3} b^{4} c \,d^{6}+720 x^{3} a^{2} b^{5} c^{2} d^{5}+1200 x^{3} a \,b^{6} c^{3} d^{4}+1800 x^{3} b^{7} c^{4} d^{3}+45 x^{2} a^{5} b^{2} d^{7}+135 x^{2} a^{4} b^{3} c \,d^{6}+270 x^{2} a^{3} b^{4} c^{2} d^{5}+450 x^{2} a^{2} b^{5} c^{3} d^{4}+675 x^{2} a \,b^{6} c^{4} d^{3}+945 x^{2} b^{7} c^{5} d^{2}+10 x \,a^{6} b \,d^{7}+30 x \,a^{5} b^{2} c \,d^{6}+60 x \,a^{4} b^{3} c^{2} d^{5}+100 x \,a^{3} b^{4} c^{3} d^{4}+150 x \,a^{2} b^{5} c^{4} d^{3}+210 x a \,b^{6} c^{5} d^{2}+280 x \,b^{7} c^{6} d +a^{7} d^{7}+3 a^{6} b c \,d^{6}+6 a^{5} b^{2} c^{2} d^{5}+10 a^{4} b^{3} c^{3} d^{4}+15 a^{3} b^{4} c^{4} d^{3}+21 a^{2} b^{5} c^{5} d^{2}+28 a \,b^{6} c^{6} d +36 b^{7} c^{7}}{360 b^{8} \left (b x +a \right )^{10}}\) | \(497\) |
parallelrisch | \(\frac {-120 d^{7} x^{7} b^{9}-210 a \,b^{8} d^{7} x^{6}-630 b^{9} c \,d^{6} x^{6}-252 a^{2} b^{7} d^{7} x^{5}-756 a \,b^{8} c \,d^{6} x^{5}-1512 b^{9} c^{2} d^{5} x^{5}-210 a^{3} b^{6} d^{7} x^{4}-630 a^{2} b^{7} c \,d^{6} x^{4}-1260 a \,b^{8} c^{2} d^{5} x^{4}-2100 b^{9} c^{3} d^{4} x^{4}-120 a^{4} b^{5} d^{7} x^{3}-360 a^{3} b^{6} c \,d^{6} x^{3}-720 a^{2} b^{7} c^{2} d^{5} x^{3}-1200 a \,b^{8} c^{3} d^{4} x^{3}-1800 b^{9} c^{4} d^{3} x^{3}-45 a^{5} b^{4} d^{7} x^{2}-135 a^{4} b^{5} c \,d^{6} x^{2}-270 a^{3} b^{6} c^{2} d^{5} x^{2}-450 a^{2} b^{7} c^{3} d^{4} x^{2}-675 a \,b^{8} c^{4} d^{3} x^{2}-945 b^{9} c^{5} d^{2} x^{2}-10 a^{6} b^{3} d^{7} x -30 a^{5} b^{4} c \,d^{6} x -60 a^{4} b^{5} c^{2} d^{5} x -100 a^{3} b^{6} c^{3} d^{4} x -150 a^{2} b^{7} c^{4} d^{3} x -210 a \,b^{8} c^{5} d^{2} x -280 b^{9} c^{6} d x -a^{7} b^{2} d^{7}-3 a^{6} b^{3} c \,d^{6}-6 a^{5} b^{4} c^{2} d^{5}-10 a^{4} b^{5} c^{3} d^{4}-15 a^{3} b^{6} c^{4} d^{3}-21 a^{2} b^{7} c^{5} d^{2}-28 a \,b^{8} c^{6} d -36 b^{9} c^{7}}{360 b^{10} \left (b x +a \right )^{10}}\) | \(505\) |
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Leaf count of result is larger than twice the leaf count of optimal. 559 vs. \(2 (83) = 166\).
Time = 0.23 (sec) , antiderivative size = 559, normalized size of antiderivative = 6.28 \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {120 \, b^{7} d^{7} x^{7} + 36 \, b^{7} c^{7} + 28 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} + 15 \, a^{3} b^{4} c^{4} d^{3} + 10 \, a^{4} b^{3} c^{3} d^{4} + 6 \, a^{5} b^{2} c^{2} d^{5} + 3 \, a^{6} b c d^{6} + a^{7} d^{7} + 210 \, {\left (3 \, b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{6} + 252 \, {\left (6 \, b^{7} c^{2} d^{5} + 3 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right )} x^{5} + 210 \, {\left (10 \, b^{7} c^{3} d^{4} + 6 \, a b^{6} c^{2} d^{5} + 3 \, a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right )} x^{4} + 120 \, {\left (15 \, b^{7} c^{4} d^{3} + 10 \, a b^{6} c^{3} d^{4} + 6 \, a^{2} b^{5} c^{2} d^{5} + 3 \, a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right )} x^{3} + 45 \, {\left (21 \, b^{7} c^{5} d^{2} + 15 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} + 6 \, a^{3} b^{4} c^{2} d^{5} + 3 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right )} x^{2} + 10 \, {\left (28 \, b^{7} c^{6} d + 21 \, a b^{6} c^{5} d^{2} + 15 \, a^{2} b^{5} c^{4} d^{3} + 10 \, a^{3} b^{4} c^{3} d^{4} + 6 \, a^{4} b^{3} c^{2} d^{5} + 3 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x}{360 \, {\left (b^{18} x^{10} + 10 \, a b^{17} x^{9} + 45 \, a^{2} b^{16} x^{8} + 120 \, a^{3} b^{15} x^{7} + 210 \, a^{4} b^{14} x^{6} + 252 \, a^{5} b^{13} x^{5} + 210 \, a^{6} b^{12} x^{4} + 120 \, a^{7} b^{11} x^{3} + 45 \, a^{8} b^{10} x^{2} + 10 \, a^{9} b^{9} x + a^{10} b^{8}\right )}} \]
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Timed out. \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 559 vs. \(2 (83) = 166\).
Time = 0.24 (sec) , antiderivative size = 559, normalized size of antiderivative = 6.28 \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {120 \, b^{7} d^{7} x^{7} + 36 \, b^{7} c^{7} + 28 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} + 15 \, a^{3} b^{4} c^{4} d^{3} + 10 \, a^{4} b^{3} c^{3} d^{4} + 6 \, a^{5} b^{2} c^{2} d^{5} + 3 \, a^{6} b c d^{6} + a^{7} d^{7} + 210 \, {\left (3 \, b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{6} + 252 \, {\left (6 \, b^{7} c^{2} d^{5} + 3 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right )} x^{5} + 210 \, {\left (10 \, b^{7} c^{3} d^{4} + 6 \, a b^{6} c^{2} d^{5} + 3 \, a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right )} x^{4} + 120 \, {\left (15 \, b^{7} c^{4} d^{3} + 10 \, a b^{6} c^{3} d^{4} + 6 \, a^{2} b^{5} c^{2} d^{5} + 3 \, a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right )} x^{3} + 45 \, {\left (21 \, b^{7} c^{5} d^{2} + 15 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} + 6 \, a^{3} b^{4} c^{2} d^{5} + 3 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right )} x^{2} + 10 \, {\left (28 \, b^{7} c^{6} d + 21 \, a b^{6} c^{5} d^{2} + 15 \, a^{2} b^{5} c^{4} d^{3} + 10 \, a^{3} b^{4} c^{3} d^{4} + 6 \, a^{4} b^{3} c^{2} d^{5} + 3 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x}{360 \, {\left (b^{18} x^{10} + 10 \, a b^{17} x^{9} + 45 \, a^{2} b^{16} x^{8} + 120 \, a^{3} b^{15} x^{7} + 210 \, a^{4} b^{14} x^{6} + 252 \, a^{5} b^{13} x^{5} + 210 \, a^{6} b^{12} x^{4} + 120 \, a^{7} b^{11} x^{3} + 45 \, a^{8} b^{10} x^{2} + 10 \, a^{9} b^{9} x + a^{10} b^{8}\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 496 vs. \(2 (83) = 166\).
Time = 0.28 (sec) , antiderivative size = 496, normalized size of antiderivative = 5.57 \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {120 \, b^{7} d^{7} x^{7} + 630 \, b^{7} c d^{6} x^{6} + 210 \, a b^{6} d^{7} x^{6} + 1512 \, b^{7} c^{2} d^{5} x^{5} + 756 \, a b^{6} c d^{6} x^{5} + 252 \, a^{2} b^{5} d^{7} x^{5} + 2100 \, b^{7} c^{3} d^{4} x^{4} + 1260 \, a b^{6} c^{2} d^{5} x^{4} + 630 \, a^{2} b^{5} c d^{6} x^{4} + 210 \, a^{3} b^{4} d^{7} x^{4} + 1800 \, b^{7} c^{4} d^{3} x^{3} + 1200 \, a b^{6} c^{3} d^{4} x^{3} + 720 \, a^{2} b^{5} c^{2} d^{5} x^{3} + 360 \, a^{3} b^{4} c d^{6} x^{3} + 120 \, a^{4} b^{3} d^{7} x^{3} + 945 \, b^{7} c^{5} d^{2} x^{2} + 675 \, a b^{6} c^{4} d^{3} x^{2} + 450 \, a^{2} b^{5} c^{3} d^{4} x^{2} + 270 \, a^{3} b^{4} c^{2} d^{5} x^{2} + 135 \, a^{4} b^{3} c d^{6} x^{2} + 45 \, a^{5} b^{2} d^{7} x^{2} + 280 \, b^{7} c^{6} d x + 210 \, a b^{6} c^{5} d^{2} x + 150 \, a^{2} b^{5} c^{4} d^{3} x + 100 \, a^{3} b^{4} c^{3} d^{4} x + 60 \, a^{4} b^{3} c^{2} d^{5} x + 30 \, a^{5} b^{2} c d^{6} x + 10 \, a^{6} b d^{7} x + 36 \, b^{7} c^{7} + 28 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} + 15 \, a^{3} b^{4} c^{4} d^{3} + 10 \, a^{4} b^{3} c^{3} d^{4} + 6 \, a^{5} b^{2} c^{2} d^{5} + 3 \, a^{6} b c d^{6} + a^{7} d^{7}}{360 \, {\left (b x + a\right )}^{10} b^{8}} \]
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Time = 0.64 (sec) , antiderivative size = 600, normalized size of antiderivative = 6.74 \[ \int \frac {(c+d x)^7}{(a+b x)^{11}} \, dx=-\frac {a^7\,d^7+3\,a^6\,b\,c\,d^6+10\,a^6\,b\,d^7\,x+6\,a^5\,b^2\,c^2\,d^5+30\,a^5\,b^2\,c\,d^6\,x+45\,a^5\,b^2\,d^7\,x^2+10\,a^4\,b^3\,c^3\,d^4+60\,a^4\,b^3\,c^2\,d^5\,x+135\,a^4\,b^3\,c\,d^6\,x^2+120\,a^4\,b^3\,d^7\,x^3+15\,a^3\,b^4\,c^4\,d^3+100\,a^3\,b^4\,c^3\,d^4\,x+270\,a^3\,b^4\,c^2\,d^5\,x^2+360\,a^3\,b^4\,c\,d^6\,x^3+210\,a^3\,b^4\,d^7\,x^4+21\,a^2\,b^5\,c^5\,d^2+150\,a^2\,b^5\,c^4\,d^3\,x+450\,a^2\,b^5\,c^3\,d^4\,x^2+720\,a^2\,b^5\,c^2\,d^5\,x^3+630\,a^2\,b^5\,c\,d^6\,x^4+252\,a^2\,b^5\,d^7\,x^5+28\,a\,b^6\,c^6\,d+210\,a\,b^6\,c^5\,d^2\,x+675\,a\,b^6\,c^4\,d^3\,x^2+1200\,a\,b^6\,c^3\,d^4\,x^3+1260\,a\,b^6\,c^2\,d^5\,x^4+756\,a\,b^6\,c\,d^6\,x^5+210\,a\,b^6\,d^7\,x^6+36\,b^7\,c^7+280\,b^7\,c^6\,d\,x+945\,b^7\,c^5\,d^2\,x^2+1800\,b^7\,c^4\,d^3\,x^3+2100\,b^7\,c^3\,d^4\,x^4+1512\,b^7\,c^2\,d^5\,x^5+630\,b^7\,c\,d^6\,x^6+120\,b^7\,d^7\,x^7}{360\,a^{10}\,b^8+3600\,a^9\,b^9\,x+16200\,a^8\,b^{10}\,x^2+43200\,a^7\,b^{11}\,x^3+75600\,a^6\,b^{12}\,x^4+90720\,a^5\,b^{13}\,x^5+75600\,a^4\,b^{14}\,x^6+43200\,a^3\,b^{15}\,x^7+16200\,a^2\,b^{16}\,x^8+3600\,a\,b^{17}\,x^9+360\,b^{18}\,x^{10}} \]
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