Optimal. Leaf size=50 \[ -\frac {a^2 A}{8 x^8}-\frac {a (a B+2 A b)}{5 x^5}-\frac {b (2 a B+A b)}{2 x^2}+b^2 B x \]
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Rubi [A] time = 0.03, antiderivative size = 50, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \[ -\frac {a^2 A}{8 x^8}-\frac {a (a B+2 A b)}{5 x^5}-\frac {b (2 a B+A b)}{2 x^2}+b^2 B x \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^9} \, dx &=\int \left (b^2 B+\frac {a^2 A}{x^9}+\frac {a (2 A b+a B)}{x^6}+\frac {b (A b+2 a B)}{x^3}\right ) \, dx\\ &=-\frac {a^2 A}{8 x^8}-\frac {a (2 A b+a B)}{5 x^5}-\frac {b (A b+2 a B)}{2 x^2}+b^2 B x\\ \end {align*}
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Mathematica [A] time = 0.03, size = 50, normalized size = 1.00 \[ -\frac {a^2 A}{8 x^8}-\frac {a (a B+2 A b)}{5 x^5}-\frac {b (2 a B+A b)}{2 x^2}+b^2 B x \]
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 53, normalized size = 1.06 \[ \frac {40 \, B b^{2} x^{9} - 20 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} - 8 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - 5 \, A a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 53, normalized size = 1.06 \[ B b^{2} x - \frac {40 \, B a b x^{6} + 20 \, A b^{2} x^{6} + 8 \, B a^{2} x^{3} + 16 \, A a b x^{3} + 5 \, A a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 45, normalized size = 0.90 \[ B \,b^{2} x -\frac {\left (A b +2 B a \right ) b}{2 x^{2}}-\frac {\left (2 A b +B a \right ) a}{5 x^{5}}-\frac {A \,a^{2}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 51, normalized size = 1.02 \[ B b^{2} x - \frac {20 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + 8 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + 5 \, A a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.34, size = 50, normalized size = 1.00 \[ B\,b^2\,x-\frac {x^3\,\left (\frac {B\,a^2}{5}+\frac {2\,A\,b\,a}{5}\right )+x^6\,\left (\frac {A\,b^2}{2}+B\,a\,b\right )+\frac {A\,a^2}{8}}{x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.99, size = 54, normalized size = 1.08 \[ B b^{2} x + \frac {- 5 A a^{2} + x^{6} \left (- 20 A b^{2} - 40 B a b\right ) + x^{3} \left (- 16 A a b - 8 B a^{2}\right )}{40 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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