Optimal. Leaf size=50 \[ -\frac {a^2 A}{2 x^2}+\frac {1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac {1}{7} b^2 B x^7 \]
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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} \begin {gather*} -\frac {a^2 A}{2 x^2}+\frac {1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac {1}{7} b^2 B x^7 \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^3} \, dx &=\int \left (a (2 A b+a B)+\frac {a^2 A}{x^3}+b (A b+2 a B) x^3+b^2 B x^6\right ) \, dx\\ &=-\frac {a^2 A}{2 x^2}+a (2 A b+a B) x+\frac {1}{4} b (A b+2 a B) x^4+\frac {1}{7} b^2 B x^7\\ \end {align*}
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Mathematica [A] time = 0.02, size = 50, normalized size = 1.00 \begin {gather*} -\frac {a^2 A}{2 x^2}+\frac {1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac {1}{7} b^2 B 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^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.83, size = 53, normalized size = 1.06 \begin {gather*} \frac {4 \, B b^{2} x^{9} + 7 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + 28 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - 14 \, A a^{2}}{28 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 48, normalized size = 0.96 \begin {gather*} \frac {1}{7} \, B b^{2} x^{7} + \frac {1}{2} \, B a b x^{4} + \frac {1}{4} \, A b^{2} x^{4} + B a^{2} x + 2 \, A a b x - \frac {A a^{2}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 49, normalized size = 0.98 \begin {gather*} \frac {B \,b^{2} x^{7}}{7}+\frac {A \,b^{2} x^{4}}{4}+\frac {B a b \,x^{4}}{2}+2 A a b x +B \,a^{2} x -\frac {A \,a^{2}}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 48, normalized size = 0.96 \begin {gather*} \frac {1}{7} \, B b^{2} x^{7} + \frac {1}{4} \, {\left (2 \, B a b + A b^{2}\right )} x^{4} + {\left (B a^{2} + 2 \, A a b\right )} x - \frac {A a^{2}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 48, normalized size = 0.96 \begin {gather*} x^4\,\left (\frac {A\,b^2}{4}+\frac {B\,a\,b}{2}\right )+x\,\left (B\,a^2+2\,A\,b\,a\right )-\frac {A\,a^2}{2\,x^2}+\frac {B\,b^2\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 49, normalized size = 0.98 \begin {gather*} - \frac {A a^{2}}{2 x^{2}} + \frac {B b^{2} x^{7}}{7} + x^{4} \left (\frac {A b^{2}}{4} + \frac {B a b}{2}\right ) + x \left (2 A a b + B a^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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