Optimal. Leaf size=43 \[ -\frac{a^2 b}{4 x^{12}}-\frac{a^3}{14 x^{14}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8} \]
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Rubi [A] time = 0.0185127, 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} \[ -\frac{a^2 b}{4 x^{12}}-\frac{a^3}{14 x^{14}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8} \]
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^{15}} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^8} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\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,x,x^2\right )\\ &=-\frac{a^3}{14 x^{14}}-\frac{a^2 b}{4 x^{12}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8}\\ \end{align*}
Mathematica [A] time = 0.0060612, size = 43, normalized size = 1. \[ -\frac{a^2 b}{4 x^{12}}-\frac{a^3}{14 x^{14}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{14\,{x}^{14}}}-{\frac{{a}^{2}b}{4\,{x}^{12}}}-{\frac{3\,a{b}^{2}}{10\,{x}^{10}}}-{\frac{{b}^{3}}{8\,{x}^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.63808, size = 50, normalized size = 1.16 \begin{align*} -\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27243, size = 88, normalized size = 2.05 \begin{align*} -\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.501027, size = 39, normalized size = 0.91 \begin{align*} - \frac{20 a^{3} + 70 a^{2} b x^{2} + 84 a b^{2} x^{4} + 35 b^{3} x^{6}}{280 x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.01264, size = 50, normalized size = 1.16 \begin{align*} -\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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