Optimal. Leaf size=43 \[ -\frac{3 a^2 b}{5 x^5}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3} \]
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Rubi [A] time = 0.0126824, 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} \[ -\frac{3 a^2 b}{5 x^5}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x^7} \, dx &=\int \left (\frac{a^3}{x^7}+\frac{3 a^2 b}{x^6}+\frac{3 a b^2}{x^5}+\frac{b^3}{x^4}\right ) \, dx\\ &=-\frac{a^3}{6 x^6}-\frac{3 a^2 b}{5 x^5}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.003698, size = 43, normalized size = 1. \[ -\frac{3 a^2 b}{5 x^5}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{6\,{x}^{6}}}-{\frac{3\,{a}^{2}b}{5\,{x}^{5}}}-{\frac{3\,{b}^{2}a}{4\,{x}^{4}}}-{\frac{{b}^{3}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04416, size = 47, normalized size = 1.09 \begin{align*} -\frac{20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51823, size = 82, normalized size = 1.91 \begin{align*} -\frac{20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.552533, size = 37, normalized size = 0.86 \begin{align*} - \frac{10 a^{3} + 36 a^{2} b x + 45 a b^{2} x^{2} + 20 b^{3} x^{3}}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10676, size = 47, normalized size = 1.09 \begin{align*} -\frac{20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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