Optimal. Leaf size=69 \[ \frac{5}{4} a^2 b^3 x^8+\frac{10}{7} a^3 b^2 x^7+\frac{5}{6} a^4 b x^6+\frac{a^5 x^5}{5}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10} \]
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Rubi [A] time = 0.0250605, 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} \[ \frac{5}{4} a^2 b^3 x^8+\frac{10}{7} a^3 b^2 x^7+\frac{5}{6} a^4 b x^6+\frac{a^5 x^5}{5}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^4 (a+b x)^5 \, dx &=\int \left (a^5 x^4+5 a^4 b x^5+10 a^3 b^2 x^6+10 a^2 b^3 x^7+5 a b^4 x^8+b^5 x^9\right ) \, dx\\ &=\frac{a^5 x^5}{5}+\frac{5}{6} a^4 b x^6+\frac{10}{7} a^3 b^2 x^7+\frac{5}{4} a^2 b^3 x^8+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10}\\ \end{align*}
Mathematica [A] time = 0.0059638, size = 69, normalized size = 1. \[ \frac{5}{4} a^2 b^3 x^8+\frac{10}{7} a^3 b^2 x^7+\frac{5}{6} a^4 b x^6+\frac{a^5 x^5}{5}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 58, normalized size = 0.8 \begin{align*}{\frac{{a}^{5}{x}^{5}}{5}}+{\frac{5\,{a}^{4}b{x}^{6}}{6}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{7}}{7}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{8}}{4}}+{\frac{5\,a{b}^{4}{x}^{9}}{9}}+{\frac{{b}^{5}{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02455, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{10} \, b^{5} x^{10} + \frac{5}{9} \, a b^{4} x^{9} + \frac{5}{4} \, a^{2} b^{3} x^{8} + \frac{10}{7} \, a^{3} b^{2} x^{7} + \frac{5}{6} \, a^{4} b x^{6} + \frac{1}{5} \, a^{5} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.23133, size = 132, normalized size = 1.91 \begin{align*} \frac{1}{10} x^{10} b^{5} + \frac{5}{9} x^{9} b^{4} a + \frac{5}{4} x^{8} b^{3} a^{2} + \frac{10}{7} x^{7} b^{2} a^{3} + \frac{5}{6} x^{6} b a^{4} + \frac{1}{5} x^{5} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.082492, size = 66, normalized size = 0.96 \begin{align*} \frac{a^{5} x^{5}}{5} + \frac{5 a^{4} b x^{6}}{6} + \frac{10 a^{3} b^{2} x^{7}}{7} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{10}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19006, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{10} \, b^{5} x^{10} + \frac{5}{9} \, a b^{4} x^{9} + \frac{5}{4} \, a^{2} b^{3} x^{8} + \frac{10}{7} \, a^{3} b^{2} x^{7} + \frac{5}{6} \, a^{4} b x^{6} + \frac{1}{5} \, a^{5} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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