Optimal. Leaf size=33 \[ \frac {1}{5} x^5 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{8} b B x^8 \]
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Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {448} \[ \frac {1}{5} x^5 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{8} b B x^8 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A x+(A b+a B) x^4+b B x^7\right ) \, dx\\ &=\frac {1}{2} a A x^2+\frac {1}{5} (A b+a B) x^5+\frac {1}{8} b B x^8\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 1.00 \[ \frac {1}{5} x^5 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{8} b B x^8 \]
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 29, normalized size = 0.88 \[ \frac {1}{8} x^{8} b B + \frac {1}{5} x^{5} a B + \frac {1}{5} x^{5} b A + \frac {1}{2} x^{2} a A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 0.88 \[ \frac {1}{8} \, B b x^{8} + \frac {1}{5} \, B a x^{5} + \frac {1}{5} \, A b x^{5} + \frac {1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 0.85 \[ \frac {B b \,x^{8}}{8}+\frac {\left (A b +B a \right ) x^{5}}{5}+\frac {A a \,x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 27, normalized size = 0.82 \[ \frac {1}{8} \, B b x^{8} + \frac {1}{5} \, {\left (B a + A b\right )} x^{5} + \frac {1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.48, size = 28, normalized size = 0.85 \[ \frac {B\,b\,x^8}{8}+\left (\frac {A\,b}{5}+\frac {B\,a}{5}\right )\,x^5+\frac {A\,a\,x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 29, normalized size = 0.88 \[ \frac {A a x^{2}}{2} + \frac {B b x^{8}}{8} + x^{5} \left (\frac {A b}{5} + \frac {B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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