Optimal. Leaf size=43 \[ -\frac{3 a^2 b}{10 x^{10}}-\frac{a^3}{12 x^{12}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6} \]
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Rubi [A] time = 0.0185851, antiderivative size = 43, 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} \[ -\frac{3 a^2 b}{10 x^{10}}-\frac{a^3}{12 x^{12}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^3}{x^{13}} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^7} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\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,x,x^2\right )\\ &=-\frac{a^3}{12 x^{12}}-\frac{3 a^2 b}{10 x^{10}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6}\\ \end{align*}
Mathematica [A] time = 0.0037502, size = 43, normalized size = 1. \[ -\frac{3 a^2 b}{10 x^{10}}-\frac{a^3}{12 x^{12}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{12\,{x}^{12}}}-{\frac{3\,{a}^{2}b}{10\,{x}^{10}}}-{\frac{3\,a{b}^{2}}{8\,{x}^{8}}}-{\frac{{b}^{3}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.317, size = 50, normalized size = 1.16 \begin{align*} -\frac{20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31164, size = 88, normalized size = 2.05 \begin{align*} -\frac{20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.459102, size = 39, normalized size = 0.91 \begin{align*} - \frac{10 a^{3} + 36 a^{2} b x^{2} + 45 a b^{2} x^{4} + 20 b^{3} x^{6}}{120 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.79705, size = 50, normalized size = 1.16 \begin{align*} -\frac{20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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