Optimal. Leaf size=43 \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4} \]
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Rubi [A] time = 0.0129022, 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} \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x^8} \, dx &=\int \left (\frac{a^3}{x^8}+\frac{3 a^2 b}{x^7}+\frac{3 a b^2}{x^6}+\frac{b^3}{x^5}\right ) \, dx\\ &=-\frac{a^3}{7 x^7}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.0037817, size = 43, normalized size = 1. \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{7\,{x}^{7}}}-{\frac{{a}^{2}b}{2\,{x}^{6}}}-{\frac{3\,{b}^{2}a}{5\,{x}^{5}}}-{\frac{{b}^{3}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11632, size = 47, normalized size = 1.09 \begin{align*} -\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.62208, size = 84, normalized size = 1.95 \begin{align*} -\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.559754, size = 37, normalized size = 0.86 \begin{align*} - \frac{20 a^{3} + 70 a^{2} b x + 84 a b^{2} x^{2} + 35 b^{3} x^{3}}{140 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16648, size = 47, normalized size = 1.09 \begin{align*} -\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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