Optimal. Leaf size=34 \[ \frac{\left (a+b x^3\right )^7}{21 b^2}-\frac{a \left (a+b x^3\right )^6}{18 b^2} \]
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Rubi [A] time = 0.0363607, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{\left (a+b x^3\right )^7}{21 b^2}-\frac{a \left (a+b x^3\right )^6}{18 b^2} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^5 \left (a+b x^3\right )^5 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x (a+b x)^5 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (-\frac{a (a+b x)^5}{b}+\frac{(a+b x)^6}{b}\right ) \, dx,x,x^3\right )\\ &=-\frac{a \left (a+b x^3\right )^6}{18 b^2}+\frac{\left (a+b x^3\right )^7}{21 b^2}\\ \end{align*}
Mathematica [B] time = 0.0022518, size = 69, normalized size = 2.03 \[ \frac{2}{3} a^2 b^3 x^{15}+\frac{5}{6} a^3 b^2 x^{12}+\frac{5}{9} a^4 b x^9+\frac{a^5 x^6}{6}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{21}}{21} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 58, normalized size = 1.7 \begin{align*}{\frac{{b}^{5}{x}^{21}}{21}}+{\frac{5\,a{b}^{4}{x}^{18}}{18}}+{\frac{2\,{a}^{2}{b}^{3}{x}^{15}}{3}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{12}}{6}}+{\frac{5\,{a}^{4}b{x}^{9}}{9}}+{\frac{{a}^{5}{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0309, size = 77, normalized size = 2.26 \begin{align*} \frac{1}{21} \, b^{5} x^{21} + \frac{5}{18} \, a b^{4} x^{18} + \frac{2}{3} \, a^{2} b^{3} x^{15} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{5}{9} \, a^{4} b x^{9} + \frac{1}{6} \, a^{5} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46043, size = 136, normalized size = 4. \begin{align*} \frac{1}{21} x^{21} b^{5} + \frac{5}{18} x^{18} b^{4} a + \frac{2}{3} x^{15} b^{3} a^{2} + \frac{5}{6} x^{12} b^{2} a^{3} + \frac{5}{9} x^{9} b a^{4} + \frac{1}{6} x^{6} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.101785, size = 66, normalized size = 1.94 \begin{align*} \frac{a^{5} x^{6}}{6} + \frac{5 a^{4} b x^{9}}{9} + \frac{5 a^{3} b^{2} x^{12}}{6} + \frac{2 a^{2} b^{3} x^{15}}{3} + \frac{5 a b^{4} x^{18}}{18} + \frac{b^{5} x^{21}}{21} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11928, size = 77, normalized size = 2.26 \begin{align*} \frac{1}{21} \, b^{5} x^{21} + \frac{5}{18} \, a b^{4} x^{18} + \frac{2}{3} \, a^{2} b^{3} x^{15} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{5}{9} \, a^{4} b x^{9} + \frac{1}{6} \, a^{5} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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