Optimal. Leaf size=47 \[ \frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} x^4 (A c+b B)+\frac{1}{5} B c x^5 \]
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Rubi [A] time = 0.0369795, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {765} \[ \frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} x^4 (A c+b B)+\frac{1}{5} B c x^5 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int x (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A x+(A b+a B) x^2+(b B+A c) x^3+B c x^4\right ) \, dx\\ &=\frac{1}{2} a A x^2+\frac{1}{3} (A b+a B) x^3+\frac{1}{4} (b B+A c) x^4+\frac{1}{5} B c x^5\\ \end{align*}
Mathematica [A] time = 0.013442, size = 41, normalized size = 0.87 \[ \frac{1}{60} x^2 \left (20 x (a B+A b)+30 a A+15 x^2 (A c+b B)+12 B c x^3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 40, normalized size = 0.9 \begin{align*}{\frac{aA{x}^{2}}{2}}+{\frac{ \left ( Ab+aB \right ){x}^{3}}{3}}+{\frac{ \left ( Ac+bB \right ){x}^{4}}{4}}+{\frac{Bc{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.18031, size = 53, normalized size = 1.13 \begin{align*} \frac{1}{5} \, B c x^{5} + \frac{1}{4} \,{\left (B b + A c\right )} x^{4} + \frac{1}{2} \, A a x^{2} + \frac{1}{3} \,{\left (B a + A b\right )} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.16329, size = 112, normalized size = 2.38 \begin{align*} \frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} b B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} a B + \frac{1}{3} x^{3} b A + \frac{1}{2} x^{2} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.203798, size = 42, normalized size = 0.89 \begin{align*} \frac{A a x^{2}}{2} + \frac{B c x^{5}}{5} + x^{4} \left (\frac{A c}{4} + \frac{B b}{4}\right ) + x^{3} \left (\frac{A b}{3} + \frac{B a}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26496, size = 58, normalized size = 1.23 \begin{align*} \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, B b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{3} \, A b x^{3} + \frac{1}{2} \, A a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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