Optimal. Leaf size=31 \[ \frac {1}{2} x^2 (a B+A b)-\frac {a A}{x}+\frac {1}{5} b B x^5 \]
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Rubi [A] time = 0.02, antiderivative size = 31, 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 {1}{2} x^2 (a B+A b)-\frac {a A}{x}+\frac {1}{5} b B x^5 \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^2} \, dx &=\int \left (\frac {a A}{x^2}+(A b+a B) x+b B x^4\right ) \, dx\\ &=-\frac {a A}{x}+\frac {1}{2} (A b+a B) x^2+\frac {1}{5} b B x^5\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \begin {gather*} \frac {1}{2} x^2 (a B+A b)-\frac {a A}{x}+\frac {1}{5} b B x^5 \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^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.73, size = 29, normalized size = 0.94 \begin {gather*} \frac {2 \, B b x^{6} + 5 \, {\left (B a + A b\right )} x^{3} - 10 \, A a}{10 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 0.94 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{2} \, B a x^{2} + \frac {1}{2} \, A b x^{2} - \frac {A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 30, normalized size = 0.97 \begin {gather*} \frac {B b \,x^{5}}{5}+\frac {A b \,x^{2}}{2}+\frac {B a \,x^{2}}{2}-\frac {A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 27, normalized size = 0.87 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{2} \, {\left (B a + A b\right )} x^{2} - \frac {A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.90 \begin {gather*} x^2\,\left (\frac {A\,b}{2}+\frac {B\,a}{2}\right )-\frac {A\,a}{x}+\frac {B\,b\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 26, normalized size = 0.84 \begin {gather*} - \frac {A a}{x} + \frac {B b x^{5}}{5} + x^{2} \left (\frac {A b}{2} + \frac {B a}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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