Optimal. Leaf size=28 \[ -\frac {a B+A b}{2 x^2}-\frac {a A}{5 x^5}+b B x \]
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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} \begin {gather*} -\frac {a B+A b}{2 x^2}-\frac {a A}{5 x^5}+b B x \end {gather*}
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^6} \, dx &=\int \left (b B+\frac {a A}{x^6}+\frac {A b+a B}{x^3}\right ) \, dx\\ &=-\frac {a A}{5 x^5}-\frac {A b+a B}{2 x^2}+b B x\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.07 \begin {gather*} \frac {-a B-A b}{2 x^2}-\frac {a A}{5 x^5}+b B x \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 ) \left (A+B x^3\right )}{x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.74, size = 29, normalized size = 1.04 \begin {gather*} \frac {10 \, B b x^{6} - 5 \, {\left (B a + A b\right )} x^{3} - 2 \, A a}{10 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 29, normalized size = 1.04 \begin {gather*} B b x - \frac {5 \, B a x^{3} + 5 \, A b x^{3} + 2 \, A a}{10 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 0.89 \begin {gather*} B b x -\frac {A b +B a}{2 x^{2}}-\frac {A a}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 27, normalized size = 0.96 \begin {gather*} B b x - \frac {5 \, {\left (B a + A b\right )} x^{3} + 2 \, A a}{10 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 28, normalized size = 1.00 \begin {gather*} B\,b\,x-\frac {\left (\frac {A\,b}{2}+\frac {B\,a}{2}\right )\,x^3+\frac {A\,a}{5}}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 29, normalized size = 1.04 \begin {gather*} B b x + \frac {- 2 A a + x^{3} \left (- 5 A b - 5 B a\right )}{10 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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