Optimal. Leaf size=40 \[ \frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}-b^3 \log (x) \]
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Rubi [A] time = 0.0231058, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {266, 43} \[ \frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}-b^3 \log (x) \]
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^7} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(a-b x)^3}{x^4} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (\frac{a^3}{x^4}-\frac{3 a^2 b}{x^3}+\frac{3 a b^2}{x^2}-\frac{b^3}{x}\right ) \, dx,x,x^2\right )\\ &=-\frac{a^3}{6 x^6}+\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}-b^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0054169, size = 40, normalized size = 1. \[ \frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}-b^3 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 35, normalized size = 0.9 \begin{align*} -{\frac{{a}^{3}}{6\,{x}^{6}}}+{\frac{3\,{a}^{2}b}{4\,{x}^{4}}}-{\frac{3\,{b}^{2}a}{2\,{x}^{2}}}-{b}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.930659, size = 53, normalized size = 1.32 \begin{align*} -\frac{1}{2} \, b^{3} \log \left (x^{2}\right ) - \frac{18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73601, size = 92, normalized size = 2.3 \begin{align*} -\frac{12 \, b^{3} x^{6} \log \left (x\right ) + 18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.377801, size = 37, normalized size = 0.92 \begin{align*} - b^{3} \log{\left (x \right )} - \frac{2 a^{3} - 9 a^{2} b x^{2} + 18 a b^{2} x^{4}}{12 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05544, size = 63, normalized size = 1.58 \begin{align*} -\frac{1}{2} \, b^{3} \log \left (x^{2}\right ) + \frac{11 \, b^{3} x^{6} - 18 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} - 2 \, a^{3}}{12 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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