Optimal. Leaf size=115 \[ -\frac {a^5 A}{9 x^9}-\frac {a^4 (a B+5 A b)}{8 x^8}-\frac {5 a^3 b (a B+2 A b)}{7 x^7}-\frac {5 a^2 b^2 (a B+A b)}{3 x^6}-\frac {b^4 (5 a B+A b)}{4 x^4}-\frac {a b^3 (2 a B+A b)}{x^5}-\frac {b^5 B}{3 x^3} \]
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Rubi [A] time = 0.05, antiderivative size = 115, normalized size of antiderivative = 1.00, 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} \[ -\frac {5 a^2 b^2 (a B+A b)}{3 x^6}-\frac {a^4 (a B+5 A b)}{8 x^8}-\frac {5 a^3 b (a B+2 A b)}{7 x^7}-\frac {a^5 A}{9 x^9}-\frac {a b^3 (2 a B+A b)}{x^5}-\frac {b^4 (5 a B+A b)}{4 x^4}-\frac {b^5 B}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int \frac {(a+b x)^5 (A+B x)}{x^{10}} \, dx &=\int \left (\frac {a^5 A}{x^{10}}+\frac {a^4 (5 A b+a B)}{x^9}+\frac {5 a^3 b (2 A b+a B)}{x^8}+\frac {10 a^2 b^2 (A b+a B)}{x^7}+\frac {5 a b^3 (A b+2 a B)}{x^6}+\frac {b^4 (A b+5 a B)}{x^5}+\frac {b^5 B}{x^4}\right ) \, dx\\ &=-\frac {a^5 A}{9 x^9}-\frac {a^4 (5 A b+a B)}{8 x^8}-\frac {5 a^3 b (2 A b+a B)}{7 x^7}-\frac {5 a^2 b^2 (A b+a B)}{3 x^6}-\frac {a b^3 (A b+2 a B)}{x^5}-\frac {b^4 (A b+5 a B)}{4 x^4}-\frac {b^5 B}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 107, normalized size = 0.93 \[ -\frac {7 a^5 (8 A+9 B x)+45 a^4 b x (7 A+8 B x)+120 a^3 b^2 x^2 (6 A+7 B x)+168 a^2 b^3 x^3 (5 A+6 B x)+126 a b^4 x^4 (4 A+5 B x)+42 b^5 x^5 (3 A+4 B x)}{504 x^9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 119, normalized size = 1.03 \[ -\frac {168 \, B b^{5} x^{6} + 56 \, A a^{5} + 126 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 504 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 840 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 360 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 63 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 123, normalized size = 1.07 \[ -\frac {168 \, B b^{5} x^{6} + 630 \, B a b^{4} x^{5} + 126 \, A b^{5} x^{5} + 1008 \, B a^{2} b^{3} x^{4} + 504 \, A a b^{4} x^{4} + 840 \, B a^{3} b^{2} x^{3} + 840 \, A a^{2} b^{3} x^{3} + 360 \, B a^{4} b x^{2} + 720 \, A a^{3} b^{2} x^{2} + 63 \, B a^{5} x + 315 \, A a^{4} b x + 56 \, A a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 104, normalized size = 0.90 \[ -\frac {B \,b^{5}}{3 x^{3}}-\frac {\left (A b +5 B a \right ) b^{4}}{4 x^{4}}-\frac {\left (A b +2 B a \right ) a \,b^{3}}{x^{5}}-\frac {5 \left (A b +B a \right ) a^{2} b^{2}}{3 x^{6}}-\frac {A \,a^{5}}{9 x^{9}}-\frac {5 \left (2 A b +B a \right ) a^{3} b}{7 x^{7}}-\frac {\left (5 A b +B a \right ) a^{4}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 119, normalized size = 1.03 \[ -\frac {168 \, B b^{5} x^{6} + 56 \, A a^{5} + 126 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 504 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 840 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 360 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 63 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 119, normalized size = 1.03 \[ -\frac {x\,\left (\frac {B\,a^5}{8}+\frac {5\,A\,b\,a^4}{8}\right )+\frac {A\,a^5}{9}+x^4\,\left (2\,B\,a^2\,b^3+A\,a\,b^4\right )+x^2\,\left (\frac {5\,B\,a^4\,b}{7}+\frac {10\,A\,a^3\,b^2}{7}\right )+x^5\,\left (\frac {A\,b^5}{4}+\frac {5\,B\,a\,b^4}{4}\right )+x^3\,\left (\frac {5\,B\,a^3\,b^2}{3}+\frac {5\,A\,a^2\,b^3}{3}\right )+\frac {B\,b^5\,x^6}{3}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.13, size = 133, normalized size = 1.16 \[ \frac {- 56 A a^{5} - 168 B b^{5} x^{6} + x^{5} \left (- 126 A b^{5} - 630 B a b^{4}\right ) + x^{4} \left (- 504 A a b^{4} - 1008 B a^{2} b^{3}\right ) + x^{3} \left (- 840 A a^{2} b^{3} - 840 B a^{3} b^{2}\right ) + x^{2} \left (- 720 A a^{3} b^{2} - 360 B a^{4} b\right ) + x \left (- 315 A a^{4} b - 63 B a^{5}\right )}{504 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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