Optimal. Leaf size=23 \[ -\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x \]
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Rubi [A] time = 0.009359, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {270} \[ -\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2}{x^6} \, dx &=\int \left (b^2+\frac{a^2}{x^6}+\frac{2 a b}{x^3}\right ) \, dx\\ &=-\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x\\ \end{align*}
Mathematica [A] time = 0.0006647, size = 23, normalized size = 1. \[ -\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 22, normalized size = 1. \begin{align*} -{\frac{{a}^{2}}{5\,{x}^{5}}}-{\frac{ab}{{x}^{2}}}+{b}^{2}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.973086, size = 30, normalized size = 1.3 \begin{align*} b^{2} x - \frac{5 \, a b x^{3} + a^{2}}{5 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67737, size = 53, normalized size = 2.3 \begin{align*} \frac{5 \, b^{2} x^{6} - 5 \, a b x^{3} - a^{2}}{5 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.392294, size = 20, normalized size = 0.87 \begin{align*} b^{2} x - \frac{a^{2} + 5 a b x^{3}}{5 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09615, size = 30, normalized size = 1.3 \begin{align*} b^{2} x - \frac{5 \, a b x^{3} + a^{2}}{5 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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