Optimal. Leaf size=26 \[ -\frac{a^2}{6 x^6}-\frac{2 a b}{3 x^3}+b^2 \log (x) \]
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Rubi [A] time = 0.0130423, antiderivative size = 26, 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} \[ -\frac{a^2}{6 x^6}-\frac{2 a b}{3 x^3}+b^2 \log (x) \]
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^7} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x^3} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^2}{x^3}+\frac{2 a b}{x^2}+\frac{b^2}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^2}{6 x^6}-\frac{2 a b}{3 x^3}+b^2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0008155, size = 26, normalized size = 1. \[ -\frac{a^2}{6 x^6}-\frac{2 a b}{3 x^3}+b^2 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 23, normalized size = 0.9 \begin{align*} -{\frac{{a}^{2}}{6\,{x}^{6}}}-{\frac{2\,ab}{3\,{x}^{3}}}+{b}^{2}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96502, size = 35, normalized size = 1.35 \begin{align*} \frac{1}{3} \, b^{2} \log \left (x^{3}\right ) - \frac{4 \, a b x^{3} + a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61848, size = 62, normalized size = 2.38 \begin{align*} \frac{6 \, b^{2} x^{6} \log \left (x\right ) - 4 \, a b x^{3} - a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.440362, size = 22, normalized size = 0.85 \begin{align*} b^{2} \log{\left (x \right )} - \frac{a^{2} + 4 a b x^{3}}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16146, size = 43, normalized size = 1.65 \begin{align*} b^{2} \log \left ({\left | x \right |}\right ) - \frac{3 \, b^{2} x^{6} + 4 \, a b x^{3} + a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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