Optimal. Leaf size=30 \[ -\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5} \]
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Rubi [A] time = 0.0081628, antiderivative size = 30, 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} \[ -\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{x^8} \, dx &=\int \left (\frac{a^2}{x^8}+\frac{2 a b}{x^7}+\frac{b^2}{x^6}\right ) \, dx\\ &=-\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0109021, size = 30, normalized size = 1. \[ -\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{7\,{x}^{7}}}-{\frac{ab}{3\,{x}^{6}}}-{\frac{{b}^{2}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07029, size = 32, normalized size = 1.07 \begin{align*} -\frac{21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48804, size = 61, normalized size = 2.03 \begin{align*} -\frac{21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.462055, size = 26, normalized size = 0.87 \begin{align*} - \frac{15 a^{2} + 35 a b x + 21 b^{2} x^{2}}{105 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18508, size = 32, normalized size = 1.07 \begin{align*} -\frac{21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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