Optimal. Leaf size=66 \[ a^2 b^3 x^{10}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{8} a^4 b x^8+\frac{a^5 x^7}{7}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12} \]
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Rubi [A] time = 0.031675, antiderivative size = 66, 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} \[ a^2 b^3 x^{10}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{8} a^4 b x^8+\frac{a^5 x^7}{7}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^6 (a+b x)^5 \, dx &=\int \left (a^5 x^6+5 a^4 b x^7+10 a^3 b^2 x^8+10 a^2 b^3 x^9+5 a b^4 x^{10}+b^5 x^{11}\right ) \, dx\\ &=\frac{a^5 x^7}{7}+\frac{5}{8} a^4 b x^8+\frac{10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12}\\ \end{align*}
Mathematica [A] time = 0.0028657, size = 66, normalized size = 1. \[ a^2 b^3 x^{10}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{8} a^4 b x^8+\frac{a^5 x^7}{7}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 57, normalized size = 0.9 \begin{align*}{\frac{{a}^{5}{x}^{7}}{7}}+{\frac{5\,{a}^{4}b{x}^{8}}{8}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{9}}{9}}+{a}^{2}{b}^{3}{x}^{10}+{\frac{5\,a{b}^{4}{x}^{11}}{11}}+{\frac{{b}^{5}{x}^{12}}{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01192, size = 76, normalized size = 1.15 \begin{align*} \frac{1}{12} \, b^{5} x^{12} + \frac{5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{7} \, a^{5} x^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29006, size = 131, normalized size = 1.98 \begin{align*} \frac{1}{12} x^{12} b^{5} + \frac{5}{11} x^{11} b^{4} a + x^{10} b^{3} a^{2} + \frac{10}{9} x^{9} b^{2} a^{3} + \frac{5}{8} x^{8} b a^{4} + \frac{1}{7} x^{7} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.087194, size = 63, normalized size = 0.95 \begin{align*} \frac{a^{5} x^{7}}{7} + \frac{5 a^{4} b x^{8}}{8} + \frac{10 a^{3} b^{2} x^{9}}{9} + a^{2} b^{3} x^{10} + \frac{5 a b^{4} x^{11}}{11} + \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 = 1.18553, size = 76, normalized size = 1.15 \begin{align*} \frac{1}{12} \, b^{5} x^{12} + \frac{5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{7} \, a^{5} x^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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