Optimal. Leaf size=50 \[ -\frac {a^2 A}{5 x^5}-\frac {a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac {1}{4} b^2 B x^4 \]
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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} \[ -\frac {a^2 A}{5 x^5}-\frac {a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac {1}{4} b^2 B x^4 \]
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^6} \, dx &=\int \left (b (A b+2 a B)+\frac {a^2 A}{x^6}+\frac {a (2 A b+a B)}{x^3}+b^2 B x^3\right ) \, dx\\ &=-\frac {a^2 A}{5 x^5}-\frac {a (2 A b+a B)}{2 x^2}+b (A b+2 a B) x+\frac {1}{4} b^2 B x^4\\ \end {align*}
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Mathematica [A] time = 0.02, size = 50, normalized size = 1.00 \[ -\frac {a^2 A}{5 x^5}-\frac {a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac {1}{4} b^2 B x^4 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 53, normalized size = 1.06 \[ \frac {5 \, B b^{2} x^{9} + 20 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} - 10 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - 4 \, A a^{2}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 51, normalized size = 1.02 \[ \frac {1}{4} \, B b^{2} x^{4} + 2 \, B a b x + A b^{2} x - \frac {5 \, B a^{2} x^{3} + 10 \, A a b x^{3} + 2 \, A a^{2}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 46, normalized size = 0.92 \[ \frac {B \,b^{2} x^{4}}{4}+A \,b^{2} x +2 B a b x -\frac {\left (2 A b +B a \right ) a}{2 x^{2}}-\frac {A \,a^{2}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 51, normalized size = 1.02 \[ \frac {1}{4} \, B b^{2} x^{4} + {\left (2 \, B a b + A b^{2}\right )} x - \frac {5 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + 2 \, A a^{2}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.37, size = 50, normalized size = 1.00 \[ x\,\left (A\,b^2+2\,B\,a\,b\right )-\frac {x^3\,\left (\frac {B\,a^2}{2}+A\,b\,a\right )+\frac {A\,a^2}{5}}{x^5}+\frac {B\,b^2\,x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 53, normalized size = 1.06 \[ \frac {B b^{2} x^{4}}{4} + x \left (A b^{2} + 2 B a b\right ) + \frac {- 2 A a^{2} + x^{3} \left (- 10 A a b - 5 B a^{2}\right )}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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