Optimal. Leaf size=75 \[ -\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{a^3 A}{8 x^8}-\frac{b^2 (3 a B+A b)}{5 x^5}-\frac{a b (a B+A b)}{2 x^6}-\frac{b^3 B}{4 x^4} \]
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Rubi [A] time = 0.0339948, antiderivative size = 75, 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} \[ -\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{a^3 A}{8 x^8}-\frac{b^2 (3 a B+A b)}{5 x^5}-\frac{a b (a B+A b)}{2 x^6}-\frac{b^3 B}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x)^3 (A+B x)}{x^9} \, dx &=\int \left (\frac{a^3 A}{x^9}+\frac{a^2 (3 A b+a B)}{x^8}+\frac{3 a b (A b+a B)}{x^7}+\frac{b^2 (A b+3 a B)}{x^6}+\frac{b^3 B}{x^5}\right ) \, dx\\ &=-\frac{a^3 A}{8 x^8}-\frac{a^2 (3 A b+a B)}{7 x^7}-\frac{a b (A b+a B)}{2 x^6}-\frac{b^2 (A b+3 a B)}{5 x^5}-\frac{b^3 B}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.0195082, size = 69, normalized size = 0.92 \[ -\frac{20 a^2 b x (6 A+7 B x)+5 a^3 (7 A+8 B x)+28 a b^2 x^2 (5 A+6 B x)+14 b^3 x^3 (4 A+5 B x)}{280 x^8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 66, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{3}}{8\,{x}^{8}}}-{\frac{{a}^{2} \left ( 3\,Ab+Ba \right ) }{7\,{x}^{7}}}-{\frac{ab \left ( Ab+Ba \right ) }{2\,{x}^{6}}}-{\frac{{b}^{2} \left ( Ab+3\,Ba \right ) }{5\,{x}^{5}}}-{\frac{B{b}^{3}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02713, size = 99, normalized size = 1.32 \begin{align*} -\frac{70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 140 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 40 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{280 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.90523, size = 167, normalized size = 2.23 \begin{align*} -\frac{70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 140 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 40 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{280 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.05672, size = 78, normalized size = 1.04 \begin{align*} - \frac{35 A a^{3} + 70 B b^{3} x^{4} + x^{3} \left (56 A b^{3} + 168 B a b^{2}\right ) + x^{2} \left (140 A a b^{2} + 140 B a^{2} b\right ) + x \left (120 A a^{2} b + 40 B a^{3}\right )}{280 x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21269, size = 101, normalized size = 1.35 \begin{align*} -\frac{70 \, B b^{3} x^{4} + 168 \, B a b^{2} x^{3} + 56 \, A b^{3} x^{3} + 140 \, B a^{2} b x^{2} + 140 \, A a b^{2} x^{2} + 40 \, B a^{3} x + 120 \, A a^{2} b x + 35 \, A a^{3}}{280 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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