Problem number 166

5.5 Problem number 166

$\int \frac{(a + b x)^{10} (A + B x)}{x^{19}} d x$

Optimal antiderivative $- \frac{a^{10} A}{18 x^{18}} - \frac{a^{9} (10 A b + a B)}{17 x^{17}} - \frac{5 a^{8} b (9 A b + 2 a B)}{16 x^{16}} - \frac{a^{7} b^{2} (8 A b + 3 a B)}{x^{15}} - \frac{15 a^{6} b^{3} (7 A b + 4 a B)}{7 x^{14}} - \frac{42 a^{5} b^{4} (6 A b + 5 a B)}{13 x^{13}} - \frac{7 a^{4} b^{5} (5 A b + 6 a B)}{2 x^{12}} - \frac{30 a^{3} b^{6} (4 A b + 7 a B)}{11 x^{11}} - \frac{3 a^{2} b^{7} (3 A b + 8 a B)}{2 x^{10}} - \frac{5 a b^{8} (2 A b + 9 a B)}{9 x^{9}} - \frac{b^{9} (A b + 10 a B)}{8 x^{8}} - \frac{b^{10} B}{7 x^{7}}$

command

integrate((b*x+a)**10*(B*x+A)/x**19,x)

Sympy 1.10.1 under Python 3.10.4 output

$Timed out$

Sympy 1.8 under Python 3.8.8 output

$\frac{- 136136 A a^{10} - 350064 B b^{10} x^{11} + x^{10} (- 306306 A b^{10} - 3063060 B a b^{9}) + x^{9} (- 2722720 A a b^{9} - 12252240 B a^{2} b^{8}) + x^{8} (- 11027016 A a^{2} b^{8} - 29405376 B a^{3} b^{7}) + x^{7} (- 26732160 A a^{3} b^{7} - 46781280 B a^{4} b^{6}) + x^{6} (- 42882840 A a^{4} b^{6} - 51459408 B a^{5} b^{5}) + x^{5} (- 47500992 A a^{5} b^{5} - 39584160 B a^{6} b^{4}) + x^{4} (- 36756720 A a^{6} b^{4} - 21003840 B a^{7} b^{3}) + x^{3} (- 19603584 A a^{7} b^{3} - 7351344 B a^{8} b^{2}) + x^{2} (- 6891885 A a^{8} b^{2} - 1531530 B a^{9} b) + x (- 1441440 A a^{9} b - 144144 B a^{10})}{2450448 x^{18}}$

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