Optimal. Leaf size=227 \[ -\frac{15 a^7 b^2 (3 a B+8 A b)}{16 x^{16}}-\frac{2 a^6 b^3 (4 a B+7 A b)}{x^{15}}-\frac{3 a^5 b^4 (5 a B+6 A b)}{x^{14}}-\frac{42 a^4 b^5 (6 a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b^6 (7 a B+4 A b)}{2 x^{12}}-\frac{15 a^2 b^7 (8 a B+3 A b)}{11 x^{11}}-\frac{a^9 (a B+10 A b)}{18 x^{18}}-\frac{5 a^8 b (2 a B+9 A b)}{17 x^{17}}-\frac{a^{10} A}{19 x^{19}}-\frac{a b^8 (9 a B+2 A b)}{2 x^{10}}-\frac{b^9 (10 a B+A b)}{9 x^9}-\frac{b^{10} B}{8 x^8} \]
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Rubi [A] time = 0.128833, antiderivative size = 227, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {76} \[ -\frac{15 a^7 b^2 (3 a B+8 A b)}{16 x^{16}}-\frac{2 a^6 b^3 (4 a B+7 A b)}{x^{15}}-\frac{3 a^5 b^4 (5 a B+6 A b)}{x^{14}}-\frac{42 a^4 b^5 (6 a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b^6 (7 a B+4 A b)}{2 x^{12}}-\frac{15 a^2 b^7 (8 a B+3 A b)}{11 x^{11}}-\frac{a^9 (a B+10 A b)}{18 x^{18}}-\frac{5 a^8 b (2 a B+9 A b)}{17 x^{17}}-\frac{a^{10} A}{19 x^{19}}-\frac{a b^8 (9 a B+2 A b)}{2 x^{10}}-\frac{b^9 (10 a B+A b)}{9 x^9}-\frac{b^{10} B}{8 x^8} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x)^{10} (A+B x)}{x^{20}} \, dx &=\int \left (\frac{a^{10} A}{x^{20}}+\frac{a^9 (10 A b+a B)}{x^{19}}+\frac{5 a^8 b (9 A b+2 a B)}{x^{18}}+\frac{15 a^7 b^2 (8 A b+3 a B)}{x^{17}}+\frac{30 a^6 b^3 (7 A b+4 a B)}{x^{16}}+\frac{42 a^5 b^4 (6 A b+5 a B)}{x^{15}}+\frac{42 a^4 b^5 (5 A b+6 a B)}{x^{14}}+\frac{30 a^3 b^6 (4 A b+7 a B)}{x^{13}}+\frac{15 a^2 b^7 (3 A b+8 a B)}{x^{12}}+\frac{5 a b^8 (2 A b+9 a B)}{x^{11}}+\frac{b^9 (A b+10 a B)}{x^{10}}+\frac{b^{10} B}{x^9}\right ) \, dx\\ &=-\frac{a^{10} A}{19 x^{19}}-\frac{a^9 (10 A b+a B)}{18 x^{18}}-\frac{5 a^8 b (9 A b+2 a B)}{17 x^{17}}-\frac{15 a^7 b^2 (8 A b+3 a B)}{16 x^{16}}-\frac{2 a^6 b^3 (7 A b+4 a B)}{x^{15}}-\frac{3 a^5 b^4 (6 A b+5 a B)}{x^{14}}-\frac{42 a^4 b^5 (5 A b+6 a B)}{13 x^{13}}-\frac{5 a^3 b^6 (4 A b+7 a B)}{2 x^{12}}-\frac{15 a^2 b^7 (3 A b+8 a B)}{11 x^{11}}-\frac{a b^8 (2 A b+9 a B)}{2 x^{10}}-\frac{b^9 (A b+10 a B)}{9 x^9}-\frac{b^{10} B}{8 x^8}\\ \end{align*}
Mathematica [A] time = 0.0643007, size = 220, normalized size = 0.97 \[ -\frac{45 a^8 b^2 (16 A+17 B x)}{272 x^{17}}-\frac{a^7 b^3 (15 A+16 B x)}{2 x^{16}}-\frac{a^6 b^4 (14 A+15 B x)}{x^{15}}-\frac{18 a^5 b^5 (13 A+14 B x)}{13 x^{14}}-\frac{35 a^4 b^6 (12 A+13 B x)}{26 x^{13}}-\frac{10 a^3 b^7 (11 A+12 B x)}{11 x^{12}}-\frac{9 a^2 b^8 (10 A+11 B x)}{22 x^{11}}-\frac{5 a^9 b (17 A+18 B x)}{153 x^{18}}-\frac{a^{10} (18 A+19 B x)}{342 x^{19}}-\frac{a b^9 (9 A+10 B x)}{9 x^{10}}-\frac{b^{10} (8 A+9 B x)}{72 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 208, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{10}}{19\,{x}^{19}}}-{\frac{{a}^{9} \left ( 10\,Ab+Ba \right ) }{18\,{x}^{18}}}-{\frac{5\,{a}^{8}b \left ( 9\,Ab+2\,Ba \right ) }{17\,{x}^{17}}}-{\frac{15\,{a}^{7}{b}^{2} \left ( 8\,Ab+3\,Ba \right ) }{16\,{x}^{16}}}-2\,{\frac{{a}^{6}{b}^{3} \left ( 7\,Ab+4\,Ba \right ) }{{x}^{15}}}-3\,{\frac{{a}^{5}{b}^{4} \left ( 6\,Ab+5\,Ba \right ) }{{x}^{14}}}-{\frac{42\,{a}^{4}{b}^{5} \left ( 5\,Ab+6\,Ba \right ) }{13\,{x}^{13}}}-{\frac{5\,{a}^{3}{b}^{6} \left ( 4\,Ab+7\,Ba \right ) }{2\,{x}^{12}}}-{\frac{15\,{a}^{2}{b}^{7} \left ( 3\,Ab+8\,Ba \right ) }{11\,{x}^{11}}}-{\frac{a{b}^{8} \left ( 2\,Ab+9\,Ba \right ) }{2\,{x}^{10}}}-{\frac{{b}^{9} \left ( Ab+10\,Ba \right ) }{9\,{x}^{9}}}-{\frac{B{b}^{10}}{8\,{x}^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03018, size = 328, normalized size = 1.44 \begin{align*} -\frac{831402 \, B b^{10} x^{11} + 350064 \, A a^{10} + 739024 \,{\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 3325608 \,{\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 9069840 \,{\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 16628040 \,{\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 21488544 \,{\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 19953648 \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 13302432 \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 6235515 \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 1956240 \,{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 369512 \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x}{6651216 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40274, size = 620, normalized size = 2.73 \begin{align*} -\frac{831402 \, B b^{10} x^{11} + 350064 \, A a^{10} + 739024 \,{\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 3325608 \,{\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 9069840 \,{\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 16628040 \,{\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 21488544 \,{\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 19953648 \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 13302432 \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 6235515 \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 1956240 \,{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 369512 \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x}{6651216 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19935, size = 328, normalized size = 1.44 \begin{align*} -\frac{831402 \, B b^{10} x^{11} + 7390240 \, B a b^{9} x^{10} + 739024 \, A b^{10} x^{10} + 29930472 \, B a^{2} b^{8} x^{9} + 6651216 \, A a b^{9} x^{9} + 72558720 \, B a^{3} b^{7} x^{8} + 27209520 \, A a^{2} b^{8} x^{8} + 116396280 \, B a^{4} b^{6} x^{7} + 66512160 \, A a^{3} b^{7} x^{7} + 128931264 \, B a^{5} b^{5} x^{6} + 107442720 \, A a^{4} b^{6} x^{6} + 99768240 \, B a^{6} b^{4} x^{5} + 119721888 \, A a^{5} b^{5} x^{5} + 53209728 \, B a^{7} b^{3} x^{4} + 93117024 \, A a^{6} b^{4} x^{4} + 18706545 \, B a^{8} b^{2} x^{3} + 49884120 \, A a^{7} b^{3} x^{3} + 3912480 \, B a^{9} b x^{2} + 17606160 \, A a^{8} b^{2} x^{2} + 369512 \, B a^{10} x + 3695120 \, A a^{9} b x + 350064 \, A a^{10}}{6651216 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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