Optimal. Leaf size=43 \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^5}{5}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8} \]
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Rubi [A] time = 0.0181752, antiderivative size = 43, 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} \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^5}{5}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^4 (a+b x)^3 \, dx &=\int \left (a^3 x^4+3 a^2 b x^5+3 a b^2 x^6+b^3 x^7\right ) \, dx\\ &=\frac{a^3 x^5}{5}+\frac{1}{2} a^2 b x^6+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8}\\ \end{align*}
Mathematica [A] time = 0.0021594, size = 43, normalized size = 1. \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^5}{5}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 36, normalized size = 0.8 \begin{align*}{\frac{{a}^{3}{x}^{5}}{5}}+{\frac{{a}^{2}b{x}^{6}}{2}}+{\frac{3\,a{b}^{2}{x}^{7}}{7}}+{\frac{{b}^{3}{x}^{8}}{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01717, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{8} \, b^{3} x^{8} + \frac{3}{7} \, a b^{2} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{5} \, a^{3} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29981, size = 80, normalized size = 1.86 \begin{align*} \frac{1}{8} x^{8} b^{3} + \frac{3}{7} x^{7} b^{2} a + \frac{1}{2} x^{6} b a^{2} + \frac{1}{5} x^{5} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.072973, size = 37, normalized size = 0.86 \begin{align*} \frac{a^{3} x^{5}}{5} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{8}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17695, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{8} \, b^{3} x^{8} + \frac{3}{7} \, a b^{2} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{5} \, a^{3} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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