Optimal. Leaf size=53 \[ -\frac {a^2 A}{4 x^4}+\frac {1}{2} b x^2 (2 a B+A b)-\frac {a (a B+2 A b)}{x}+\frac {1}{5} b^2 B x^5 \]
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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}{4 x^4}+\frac {1}{2} b x^2 (2 a B+A b)-\frac {a (a B+2 A b)}{x}+\frac {1}{5} b^2 B x^5 \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^5} \, dx &=\int \left (\frac {a^2 A}{x^5}+\frac {a (2 A b+a B)}{x^2}+b (A b+2 a B) x+b^2 B x^4\right ) \, dx\\ &=-\frac {a^2 A}{4 x^4}-\frac {a (2 A b+a B)}{x}+\frac {1}{2} b (A b+2 a B) x^2+\frac {1}{5} b^2 B x^5\\ \end {align*}
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Mathematica [A] time = 0.02, size = 51, normalized size = 0.96 \begin {gather*} \frac {-5 a^2 A+10 b x^6 (2 a B+A b)-20 a x^3 (a B+2 A b)+4 b^2 B x^9}{20 x^4} \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^5} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.72, size = 53, normalized size = 1.00 \begin {gather*} \frac {4 \, B b^{2} x^{9} + 10 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} - 20 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - 5 \, A a^{2}}{20 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 54, normalized size = 1.02 \begin {gather*} \frac {1}{5} \, B b^{2} x^{5} + B a b x^{2} + \frac {1}{2} \, A b^{2} x^{2} - \frac {4 \, B a^{2} x^{3} + 8 \, A a b x^{3} + A a^{2}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 50, normalized size = 0.94 \begin {gather*} \frac {B \,b^{2} x^{5}}{5}+\frac {A \,b^{2} x^{2}}{2}+B a b \,x^{2}-\frac {\left (2 A b +B a \right ) a}{x}-\frac {A \,a^{2}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 53, normalized size = 1.00 \begin {gather*} \frac {1}{5} \, B b^{2} x^{5} + \frac {1}{2} \, {\left (2 \, B a b + A b^{2}\right )} x^{2} - \frac {4 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + A a^{2}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 52, normalized size = 0.98 \begin {gather*} x^2\,\left (\frac {A\,b^2}{2}+B\,a\,b\right )-\frac {x^3\,\left (B\,a^2+2\,A\,b\,a\right )+\frac {A\,a^2}{4}}{x^4}+\frac {B\,b^2\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 53, normalized size = 1.00 \begin {gather*} \frac {B b^{2} x^{5}}{5} + x^{2} \left (\frac {A b^{2}}{2} + B a b\right ) + \frac {- A a^{2} + x^{3} \left (- 8 A a b - 4 B a^{2}\right )}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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