Optimal. Leaf size=14 \[ \frac{(a+b x)^4}{4 b} \]
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Rubi [A] time = 0.0023068, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {27, 32} \[ \frac{(a+b x)^4}{4 b} \]
Antiderivative was successfully verified.
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Rule 27
Rule 32
Rubi steps
\begin{align*} \int (a+b x) \left (a^2+2 a b x+b^2 x^2\right ) \, dx &=\int (a+b x)^3 \, dx\\ &=\frac{(a+b x)^4}{4 b}\\ \end{align*}
Mathematica [A] time = 0.0011029, size = 14, normalized size = 1. \[ \frac{(a+b x)^4}{4 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0., size = 32, normalized size = 2.3 \begin{align*}{\frac{{b}^{3}{x}^{4}}{4}}+{b}^{2}a{x}^{3}+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+{a}^{3}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952269, size = 31, normalized size = 2.21 \begin{align*} \frac{{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{2}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.34458, size = 66, normalized size = 4.71 \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 [B] time = 0.060346, size = 32, normalized size = 2.29 \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 [B] time = 1.136, size = 42, normalized size = 3. \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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