Optimal. Leaf size=28 \[ x (a B+A b)-\frac {a A}{2 x^2}+\frac {1}{4} b B x^4 \]
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Rubi [A] time = 0.02, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {448} \[ x (a B+A b)-\frac {a A}{2 x^2}+\frac {1}{4} b B x^4 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right ) \left (A+B x^3\right )}{x^3} \, dx &=\int \left (A b \left (1+\frac {a B}{A b}\right )+\frac {a A}{x^3}+b B x^3\right ) \, dx\\ &=-\frac {a A}{2 x^2}+(A b+a B) x+\frac {1}{4} b B x^4\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.00 \[ x (a B+A b)-\frac {a A}{2 x^2}+\frac {1}{4} b B x^4 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 28, normalized size = 1.00 \[ \frac {B b x^{6} + 4 \, {\left (B a + A b\right )} x^{3} - 2 \, A a}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 23, normalized size = 0.82 \[ \frac {1}{4} \, B b x^{4} + B a x + A b x - \frac {A a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 0.86 \[ \frac {B b \,x^{4}}{4}+A b x +B a x -\frac {A a}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 24, normalized size = 0.86 \[ \frac {1}{4} \, B b x^{4} + {\left (B a + A b\right )} x - \frac {A a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.34, size = 24, normalized size = 0.86 \[ x\,\left (A\,b+B\,a\right )-\frac {A\,a}{2\,x^2}+\frac {B\,b\,x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 24, normalized size = 0.86 \[ - \frac {A a}{2 x^{2}} + \frac {B b x^{4}}{4} + x \left (A b + B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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