Optimal. Leaf size=33 \[ \frac {1}{4} x^4 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{6} b B x^6 \]
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Rubi [A] time = 0.03, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {444, 43} \begin {gather*} \frac {1}{4} x^4 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{6} b B x^6 \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 444
Rubi steps
\begin {align*} \int x \left (a+b x^2\right ) \left (A+B x^2\right ) \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int (a+b x) (A+B x) \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (a A+(A b+a B) x+b B x^2\right ) \, dx,x,x^2\right )\\ &=\frac {1}{2} a A x^2+\frac {1}{4} (A b+a B) x^4+\frac {1}{6} b B x^6\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 1.00 \begin {gather*} \frac {1}{4} x^4 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{6} b B x^6 \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x \left (a+b x^2\right ) \left (A+B x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.37, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{6} x^{6} b B + \frac {1}{4} x^{4} a B + \frac {1}{4} x^{4} b A + \frac {1}{2} x^{2} a A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{6} \, B b x^{6} + \frac {1}{4} \, B a x^{4} + \frac {1}{4} \, A b x^{4} + \frac {1}{2} \, A a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 0.85 \begin {gather*} \frac {B b \,x^{6}}{6}+\frac {A a \,x^{2}}{2}+\frac {\left (A b +B a \right ) x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{6} \, B b x^{6} + \frac {1}{4} \, {\left (B a + A b\right )} x^{4} + \frac {1}{2} \, A a x^{2} \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 = 0.85 \begin {gather*} \frac {B\,b\,x^6}{6}+\left (\frac {A\,b}{4}+\frac {B\,a}{4}\right )\,x^4+\frac {A\,a\,x^2}{2} \end {gather*}
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 \begin {gather*} \frac {A a x^{2}}{2} + \frac {B b x^{6}}{6} + x^{4} \left (\frac {A b}{4} + \frac {B a}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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