Optimal. Leaf size=69 \[ \frac{10}{9} a^2 b^3 x^9+\frac{5}{4} a^3 b^2 x^8+\frac{5}{7} a^4 b x^7+\frac{a^5 x^6}{6}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11} \]
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Rubi [A] time = 0.0276943, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{10}{9} a^2 b^3 x^9+\frac{5}{4} a^3 b^2 x^8+\frac{5}{7} a^4 b x^7+\frac{a^5 x^6}{6}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^5 (a+b x)^5 \, dx &=\int \left (a^5 x^5+5 a^4 b x^6+10 a^3 b^2 x^7+10 a^2 b^3 x^8+5 a b^4 x^9+b^5 x^{10}\right ) \, dx\\ &=\frac{a^5 x^6}{6}+\frac{5}{7} a^4 b x^7+\frac{5}{4} a^3 b^2 x^8+\frac{10}{9} a^2 b^3 x^9+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11}\\ \end{align*}
Mathematica [A] time = 0.002325, size = 69, normalized size = 1. \[ \frac{10}{9} a^2 b^3 x^9+\frac{5}{4} a^3 b^2 x^8+\frac{5}{7} a^4 b x^7+\frac{a^5 x^6}{6}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 58, normalized size = 0.8 \begin{align*}{\frac{{a}^{5}{x}^{6}}{6}}+{\frac{5\,{a}^{4}b{x}^{7}}{7}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{8}}{4}}+{\frac{10\,{a}^{2}{b}^{3}{x}^{9}}{9}}+{\frac{a{b}^{4}{x}^{10}}{2}}+{\frac{{b}^{5}{x}^{11}}{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02887, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{11} \, b^{5} x^{11} + \frac{1}{2} \, a b^{4} x^{10} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{4} \, a^{3} b^{2} x^{8} + \frac{5}{7} \, a^{4} b x^{7} + \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 = 1.32468, size = 134, normalized size = 1.94 \begin{align*} \frac{1}{11} x^{11} b^{5} + \frac{1}{2} x^{10} b^{4} a + \frac{10}{9} x^{9} b^{3} a^{2} + \frac{5}{4} x^{8} b^{2} a^{3} + \frac{5}{7} x^{7} 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 [A] time = 0.084904, size = 65, normalized size = 0.94 \begin{align*} \frac{a^{5} x^{6}}{6} + \frac{5 a^{4} b x^{7}}{7} + \frac{5 a^{3} b^{2} x^{8}}{4} + \frac{10 a^{2} b^{3} x^{9}}{9} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14324, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{11} \, b^{5} x^{11} + \frac{1}{2} \, a b^{4} x^{10} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{4} \, a^{3} b^{2} x^{8} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{6} \, a^{5} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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