Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^6}{12 b} \]
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Rubi [A] time = 0.0024507, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \frac{\left (a+b x^2\right )^6}{12 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \left (a+b x^2\right )^5 \, dx &=\frac{\left (a+b x^2\right )^6}{12 b}\\ \end{align*}
Mathematica [A] time = 0.0023003, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^6}{12 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 58, normalized size = 3.6 \begin{align*}{\frac{{b}^{5}{x}^{12}}{12}}+{\frac{a{b}^{4}{x}^{10}}{2}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{8}}{4}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{6}}{3}}+{\frac{5\,{a}^{4}b{x}^{4}}{4}}+{\frac{{a}^{5}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.05634, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{6}}{12 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.09957, size = 132, normalized size = 8.25 \begin{align*} \frac{1}{12} x^{12} b^{5} + \frac{1}{2} x^{10} b^{4} a + \frac{5}{4} x^{8} b^{3} a^{2} + \frac{5}{3} x^{6} b^{2} a^{3} + \frac{5}{4} x^{4} b a^{4} + \frac{1}{2} x^{2} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.067715, size = 65, normalized size = 4.06 \begin{align*} \frac{a^{5} x^{2}}{2} + \frac{5 a^{4} b x^{4}}{4} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{12}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.02084, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{6}}{12 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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