Optimal. Leaf size=28 \[ \frac {1}{3} x^3 (a B+A b)+a A x+\frac {1}{5} b B x^5 \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {373} \begin {gather*} \frac {1}{3} x^3 (a B+A b)+a A x+\frac {1}{5} b B x^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 373
Rubi steps
\begin {align*} \int \left (a+b x^2\right ) \left (A+B x^2\right ) \, dx &=\int \left (a A+(A b+a B) x^2+b B x^4\right ) \, dx\\ &=a A x+\frac {1}{3} (A b+a B) x^3+\frac {1}{5} b B x^5\\ \end {align*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} \frac {1}{3} x^3 (a B+A b)+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 \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 = 0.40, size = 26, normalized size = 0.93 \begin {gather*} \frac {1}{5} x^{5} b B + \frac {1}{3} x^{3} a B + \frac {1}{3} x^{3} b A + x a A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 26, normalized size = 0.93 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{3} \, B a x^{3} + \frac {1}{3} \, A b x^{3} + A a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.89 \begin {gather*} \frac {B b \,x^{5}}{5}+A a x +\frac {\left (A b +B a \right ) x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{3} \, {\left (B a + A b\right )} x^{3} + 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 = 25, normalized size = 0.89 \begin {gather*} \frac {B\,b\,x^5}{5}+\left (\frac {A\,b}{3}+\frac {B\,a}{3}\right )\,x^3+A\,a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 26, normalized size = 0.93 \begin {gather*} A a x + \frac {B b x^{5}}{5} + x^{3} \left (\frac {A b}{3} + \frac {B a}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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