Optimal. Leaf size=30 \[ -\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6} \]
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Rubi [A] time = 0.0135996, antiderivative size = 30, 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 = {266, 43} \[ -\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2}{x^{13}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x^5} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^2}{x^5}+\frac{2 a b}{x^4}+\frac{b^2}{x^3}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6}\\ \end{align*}
Mathematica [A] time = 0.000766, size = 30, normalized size = 1. \[ -\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{12\,{x}^{12}}}-{\frac{2\,ab}{9\,{x}^{9}}}-{\frac{{b}^{2}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.951495, size = 35, normalized size = 1.17 \begin{align*} -\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99672, size = 59, normalized size = 1.97 \begin{align*} -\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.439586, size = 27, normalized size = 0.9 \begin{align*} - \frac{3 a^{2} + 8 a b x^{3} + 6 b^{2} x^{6}}{36 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10653, size = 35, normalized size = 1.17 \begin{align*} -\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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