Optimal. Leaf size=53 \[ -\frac {a^2 A}{7 x^7}-\frac {a (a B+2 A b)}{4 x^4}-\frac {b (2 a B+A b)}{x}+\frac {1}{2} b^2 B x^2 \]
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Rubi [A] time = 0.03, antiderivative size = 53, 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} \begin {gather*} -\frac {a^2 A}{7 x^7}-\frac {a (a B+2 A b)}{4 x^4}-\frac {b (2 a B+A b)}{x}+\frac {1}{2} b^2 B x^2 \end {gather*}
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^8} \, dx &=\int \left (\frac {a^2 A}{x^8}+\frac {a (2 A b+a B)}{x^5}+\frac {b (A b+2 a B)}{x^2}+b^2 B x\right ) \, dx\\ &=-\frac {a^2 A}{7 x^7}-\frac {a (2 A b+a B)}{4 x^4}-\frac {b (A b+2 a B)}{x}+\frac {1}{2} b^2 B x^2\\ \end {align*}
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Mathematica [A] time = 0.02, size = 54, normalized size = 1.02 \begin {gather*} -\frac {a^2 \left (4 A+7 B x^3\right )+14 a b x^3 \left (A+4 B x^3\right )-14 b^2 x^6 \left (B x^3-2 A\right )}{28 x^7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.80, size = 53, normalized size = 1.00 \begin {gather*} \frac {14 \, B b^{2} x^{9} - 28 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} - 7 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - 4 \, A a^{2}}{28 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 56, normalized size = 1.06 \begin {gather*} \frac {1}{2} \, B b^{2} x^{2} - \frac {56 \, B a b x^{6} + 28 \, A b^{2} x^{6} + 7 \, B a^{2} x^{3} + 14 \, A a b x^{3} + 4 \, A a^{2}}{28 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 48, normalized size = 0.91 \begin {gather*} \frac {B \,b^{2} x^{2}}{2}-\frac {\left (A b +2 B a \right ) b}{x}-\frac {\left (2 A b +B a \right ) a}{4 x^{4}}-\frac {A \,a^{2}}{7 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 54, normalized size = 1.02 \begin {gather*} \frac {1}{2} \, B b^{2} x^{2} - \frac {28 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + 7 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + 4 \, A a^{2}}{28 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 53, normalized size = 1.00 \begin {gather*} \frac {B\,b^2\,x^2}{2}-\frac {x^3\,\left (\frac {B\,a^2}{4}+\frac {A\,b\,a}{2}\right )+x^6\,\left (A\,b^2+2\,B\,a\,b\right )+\frac {A\,a^2}{7}}{x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.87, size = 58, normalized size = 1.09 \begin {gather*} \frac {B b^{2} x^{2}}{2} + \frac {- 4 A a^{2} + x^{6} \left (- 28 A b^{2} - 56 B a b\right ) + x^{3} \left (- 14 A a b - 7 B a^{2}\right )}{28 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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