Optimal. Leaf size=14 \[ \frac{(a+b x)^6}{6 b} \]
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Rubi [A] time = 0.0026455, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {27, 32} \[ \frac{(a+b x)^6}{6 b} \]
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 )^2 \, dx &=\int (a+b x)^5 \, dx\\ &=\frac{(a+b x)^6}{6 b}\\ \end{align*}
Mathematica [A] time = 0.0013097, size = 14, normalized size = 1. \[ \frac{(a+b x)^6}{6 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 54, normalized size = 3.9 \begin{align*}{\frac{{b}^{5}{x}^{6}}{6}}+a{b}^{4}{x}^{5}+{\frac{5\,{a}^{2}{b}^{3}{x}^{4}}{2}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{3}}{3}}+{\frac{5\,{a}^{4}b{x}^{2}}{2}}+{a}^{5}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967306, size = 31, normalized size = 2.21 \begin{align*} \frac{{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{3}}{6 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.383, size = 116, normalized size = 8.29 \begin{align*} \frac{1}{6} x^{6} b^{5} + x^{5} b^{4} a + \frac{5}{2} x^{4} b^{3} a^{2} + \frac{10}{3} x^{3} b^{2} a^{3} + \frac{5}{2} x^{2} b a^{4} + x a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.070088, size = 60, normalized size = 4.29 \begin{align*} a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.10072, size = 72, normalized size = 5.14 \begin{align*} \frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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