Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^3}{6 a x^6} \]
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Rubi [A] time = 0.0034544, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ -\frac{\left (a+b x^2\right )^3}{6 a x^6} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^2}{x^7} \, dx &=-\frac{\left (a+b x^2\right )^3}{6 a x^6}\\ \end{align*}
Mathematica [A] time = 0.0007695, size = 30, normalized size = 1.58 \[ -\frac{a^2}{6 x^6}-\frac{a b}{2 x^4}-\frac{b^2}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 1.3 \begin{align*} -{\frac{ab}{2\,{x}^{4}}}-{\frac{{b}^{2}}{2\,{x}^{2}}}-{\frac{{a}^{2}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.73741, size = 32, normalized size = 1.68 \begin{align*} -\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42218, size = 54, normalized size = 2.84 \begin{align*} -\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.353072, size = 26, normalized size = 1.37 \begin{align*} - \frac{a^{2} + 3 a b x^{2} + 3 b^{2} x^{4}}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.44744, size = 32, normalized size = 1.68 \begin{align*} -\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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