Optimal. Leaf size=37 \[ \frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} A c x^4+\frac {1}{5} B c x^5 \]
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Rubi [A] time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {766} \[ \frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} A c x^4+\frac {1}{5} B c x^5 \]
Antiderivative was successfully verified.
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Rule 766
Rubi steps
\begin {align*} \int x (A+B x) \left (a+c x^2\right ) \, dx &=\int \left (a A x+a B x^2+A c x^3+B c x^4\right ) \, dx\\ &=\frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} A c x^4+\frac {1}{5} B c x^5\\ \end {align*}
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Mathematica [A] time = 0.00, size = 37, normalized size = 1.00 \[ \frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} A c x^4+\frac {1}{5} B c x^5 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 29, normalized size = 0.78 \[ \frac {1}{5} x^{5} c B + \frac {1}{4} x^{4} c A + \frac {1}{3} x^{3} a B + \frac {1}{2} x^{2} a A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 29, normalized size = 0.78 \[ \frac {1}{5} \, B c x^{5} + \frac {1}{4} \, A c x^{4} + \frac {1}{3} \, B a x^{3} + \frac {1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 30, normalized size = 0.81 \[ \frac {1}{5} B c \,x^{5}+\frac {1}{4} A c \,x^{4}+\frac {1}{3} B a \,x^{3}+\frac {1}{2} A a \,x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 29, normalized size = 0.78 \[ \frac {1}{5} \, B c x^{5} + \frac {1}{4} \, A c x^{4} + \frac {1}{3} \, B a x^{3} + \frac {1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 29, normalized size = 0.78 \[ \frac {B\,c\,x^5}{5}+\frac {A\,c\,x^4}{4}+\frac {B\,a\,x^3}{3}+\frac {A\,a\,x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 32, normalized size = 0.86 \[ \frac {A a x^{2}}{2} + \frac {A c x^{4}}{4} + \frac {B a x^{3}}{3} + \frac {B c x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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