Optimal. Leaf size=43 \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^7}{7}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^4}{4} \]
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Rubi [A] time = 0.0199591, antiderivative size = 43, 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 = {263, 43} \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^7}{7}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Rule 263
Rule 43
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x}\right )^3 x^6 \, dx &=\int x^3 (b+a x)^3 \, dx\\ &=\int \left (b^3 x^3+3 a b^2 x^4+3 a^2 b x^5+a^3 x^6\right ) \, dx\\ &=\frac{b^3 x^4}{4}+\frac{3}{5} a b^2 x^5+\frac{1}{2} a^2 b x^6+\frac{a^3 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0018376, size = 43, normalized size = 1. \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^7}{7}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 36, normalized size = 0.8 \begin{align*}{\frac{{b}^{3}{x}^{4}}{4}}+{\frac{3\,{x}^{5}a{b}^{2}}{5}}+{\frac{{a}^{2}b{x}^{6}}{2}}+{\frac{{a}^{3}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992243, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{7} \, a^{3} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42561, size = 80, normalized size = 1.86 \begin{align*} \frac{1}{7} \, a^{3} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063521, size = 37, normalized size = 0.86 \begin{align*} \frac{a^{3} x^{7}}{7} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19027, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{7} \, a^{3} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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