Optimal. Leaf size=30 \[ -\frac{a^2}{10 x^{10}}-\frac{2 a b}{7 x^7}-\frac{b^2}{4 x^4} \]
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Rubi [A] time = 0.0103513, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {270} \[ -\frac{a^2}{10 x^{10}}-\frac{2 a b}{7 x^7}-\frac{b^2}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2}{x^{11}} \, dx &=\int \left (\frac{a^2}{x^{11}}+\frac{2 a b}{x^8}+\frac{b^2}{x^5}\right ) \, dx\\ &=-\frac{a^2}{10 x^{10}}-\frac{2 a b}{7 x^7}-\frac{b^2}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.000869, size = 30, normalized size = 1. \[ -\frac{a^2}{10 x^{10}}-\frac{2 a b}{7 x^7}-\frac{b^2}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{10\,{x}^{10}}}-{\frac{2\,ab}{7\,{x}^{7}}}-{\frac{{b}^{2}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983578, size = 35, normalized size = 1.17 \begin{align*} -\frac{35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92519, size = 65, normalized size = 2.17 \begin{align*} -\frac{35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.453512, size = 27, normalized size = 0.9 \begin{align*} - \frac{14 a^{2} + 40 a b x^{3} + 35 b^{2} x^{6}}{140 x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10009, size = 35, normalized size = 1.17 \begin{align*} -\frac{35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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