Optimal. Leaf size=53 \[ -\frac {a^2 A}{x}+\frac {1}{5} b x^5 (2 a B+A b)+\frac {1}{2} a x^2 (a B+2 A b)+\frac {1}{8} b^2 B x^8 \]
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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} \[ -\frac {a^2 A}{x}+\frac {1}{5} b x^5 (2 a B+A b)+\frac {1}{2} a x^2 (a B+2 A b)+\frac {1}{8} b^2 B x^8 \]
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^2} \, dx &=\int \left (\frac {a^2 A}{x^2}+a (2 A b+a B) x+b (A b+2 a B) x^4+b^2 B x^7\right ) \, dx\\ &=-\frac {a^2 A}{x}+\frac {1}{2} a (2 A b+a B) x^2+\frac {1}{5} b (A b+2 a B) x^5+\frac {1}{8} b^2 B x^8\\ \end {align*}
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Mathematica [A] time = 0.02, size = 53, normalized size = 1.00 \[ -\frac {a^2 A}{x}+\frac {1}{5} b x^5 (2 a B+A b)+\frac {1}{2} a x^2 (a B+2 A b)+\frac {1}{8} b^2 B x^8 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 53, normalized size = 1.00 \[ \frac {5 \, B b^{2} x^{9} + 8 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + 20 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - 40 \, A a^{2}}{40 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 52, normalized size = 0.98 \[ \frac {1}{8} \, B b^{2} x^{8} + \frac {2}{5} \, B a b x^{5} + \frac {1}{5} \, A b^{2} x^{5} + \frac {1}{2} \, B a^{2} x^{2} + A a b x^{2} - \frac {A a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 53, normalized size = 1.00 \[ \frac {B \,b^{2} x^{8}}{8}+\frac {A \,b^{2} x^{5}}{5}+\frac {2 B a b \,x^{5}}{5}+A a b \,x^{2}+\frac {B \,a^{2} x^{2}}{2}-\frac {A \,a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 51, normalized size = 0.96 \[ \frac {1}{8} \, B b^{2} x^{8} + \frac {1}{5} \, {\left (2 \, B a b + A b^{2}\right )} x^{5} + \frac {1}{2} \, {\left (B a^{2} + 2 \, A a b\right )} x^{2} - \frac {A a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 50, normalized size = 0.94 \[ x^2\,\left (\frac {B\,a^2}{2}+A\,b\,a\right )+x^5\,\left (\frac {A\,b^2}{5}+\frac {2\,B\,a\,b}{5}\right )-\frac {A\,a^2}{x}+\frac {B\,b^2\,x^8}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 49, normalized size = 0.92 \[ - \frac {A a^{2}}{x} + \frac {B b^{2} x^{8}}{8} + x^{5} \left (\frac {A b^{2}}{5} + \frac {2 B a b}{5}\right ) + x^{2} \left (A a b + \frac {B a^{2}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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