Optimal. Leaf size=35 \[ \frac{3}{2} a^2 b x^2+a^3 x+a b^2 x^3+\frac{b^3 x^4}{4} \]
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Rubi [A] time = 0.0068023, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{3}{2} a^2 b x^2+a^3 x+a b^2 x^3+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right ) \, dx &=a^3 x+\frac{3}{2} a^2 b x^2+a b^2 x^3+\frac{b^3 x^4}{4}\\ \end{align*}
Mathematica [A] time = 0.0000398, size = 35, normalized size = 1. \[ \frac{3}{2} a^2 b x^2+a^3 x+a b^2 x^3+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 32, normalized size = 0.9 \begin{align*}{a}^{3}x+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+a{b}^{2}{x}^{3}+{\frac{{b}^{3}{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09014, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.08271, size = 66, normalized size = 1.89 \begin{align*} \frac{1}{4} x^{4} b^{3} + x^{3} b^{2} a + \frac{3}{2} x^{2} b a^{2} + x a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061812, size = 32, normalized size = 0.91 \begin{align*} a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08373, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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