Optimal. Leaf size=42 \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4 \]
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Rubi [A] time = 0.0277259, antiderivative size = 42, normalized size of antiderivative = 1., 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 = {631} \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4 \]
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin{align*} \int (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A+(A b+a B) x+(b B+A c) x^2+B c x^3\right ) \, dx\\ &=a A x+\frac{1}{2} (A b+a B) x^2+\frac{1}{3} (b B+A c) x^3+\frac{1}{4} B c x^4\\ \end{align*}
Mathematica [A] time = 0.013361, size = 42, normalized size = 1. \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 37, normalized size = 0.9 \begin{align*} aAx+{\frac{ \left ( Ab+aB \right ){x}^{2}}{2}}+{\frac{ \left ( Ac+bB \right ){x}^{3}}{3}}+{\frac{Bc{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03019, size = 49, normalized size = 1.17 \begin{align*} \frac{1}{4} \, B c x^{4} + \frac{1}{3} \,{\left (B b + A c\right )} x^{3} + A a x + \frac{1}{2} \,{\left (B a + A b\right )} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.08533, size = 104, normalized size = 2.48 \begin{align*} \frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.143956, size = 39, normalized size = 0.93 \begin{align*} A a x + \frac{B c x^{4}}{4} + x^{3} \left (\frac{A c}{3} + \frac{B b}{3}\right ) + x^{2} \left (\frac{A b}{2} + \frac{B a}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21008, size = 54, normalized size = 1.29 \begin{align*} \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} + A a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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