Optimal. Leaf size=75 \[ -\frac {a^3 A}{9 x^9}-\frac {a^2 (a B+3 A b)}{8 x^8}-\frac {b^2 (3 a B+A b)}{6 x^6}-\frac {3 a b (a B+A b)}{7 x^7}-\frac {b^3 B}{5 x^5} \]
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Rubi [A] time = 0.03, antiderivative size = 75, 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} \[ -\frac {a^2 (a B+3 A b)}{8 x^8}-\frac {a^3 A}{9 x^9}-\frac {b^2 (3 a B+A b)}{6 x^6}-\frac {3 a b (a B+A b)}{7 x^7}-\frac {b^3 B}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int \frac {(a+b x)^3 (A+B x)}{x^{10}} \, dx &=\int \left (\frac {a^3 A}{x^{10}}+\frac {a^2 (3 A b+a B)}{x^9}+\frac {3 a b (A b+a B)}{x^8}+\frac {b^2 (A b+3 a B)}{x^7}+\frac {b^3 B}{x^6}\right ) \, dx\\ &=-\frac {a^3 A}{9 x^9}-\frac {a^2 (3 A b+a B)}{8 x^8}-\frac {3 a b (A b+a B)}{7 x^7}-\frac {b^2 (A b+3 a B)}{6 x^6}-\frac {b^3 B}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 69, normalized size = 0.92 \[ -\frac {35 a^3 (8 A+9 B x)+135 a^2 b x (7 A+8 B x)+180 a b^2 x^2 (6 A+7 B x)+84 b^3 x^3 (5 A+6 B x)}{2520 x^9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 73, normalized size = 0.97 \[ -\frac {504 \, B b^{3} x^{4} + 280 \, A a^{3} + 420 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 1080 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 315 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{2520 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 75, normalized size = 1.00 \[ -\frac {504 \, B b^{3} x^{4} + 1260 \, B a b^{2} x^{3} + 420 \, A b^{3} x^{3} + 1080 \, B a^{2} b x^{2} + 1080 \, A a b^{2} x^{2} + 315 \, B a^{3} x + 945 \, A a^{2} b x + 280 \, A a^{3}}{2520 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 66, normalized size = 0.88 \[ -\frac {B \,b^{3}}{5 x^{5}}-\frac {\left (A b +3 B a \right ) b^{2}}{6 x^{6}}-\frac {A \,a^{3}}{9 x^{9}}-\frac {3 \left (A b +B a \right ) a b}{7 x^{7}}-\frac {\left (3 A b +B a \right ) a^{2}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.04, size = 73, normalized size = 0.97 \[ -\frac {504 \, B b^{3} x^{4} + 280 \, A a^{3} + 420 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 1080 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 315 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{2520 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 74, normalized size = 0.99 \[ -\frac {x^2\,\left (\frac {3\,B\,a^2\,b}{7}+\frac {3\,A\,a\,b^2}{7}\right )+x\,\left (\frac {B\,a^3}{8}+\frac {3\,A\,b\,a^2}{8}\right )+\frac {A\,a^3}{9}+x^3\,\left (\frac {A\,b^3}{6}+\frac {B\,a\,b^2}{2}\right )+\frac {B\,b^3\,x^4}{5}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.09, size = 82, normalized size = 1.09 \[ \frac {- 280 A a^{3} - 504 B b^{3} x^{4} + x^{3} \left (- 420 A b^{3} - 1260 B a b^{2}\right ) + x^{2} \left (- 1080 A a b^{2} - 1080 B a^{2} b\right ) + x \left (- 945 A a^{2} b - 315 B a^{3}\right )}{2520 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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