Optimal. Leaf size=17 \[ -\frac{b \sqrt{b x^2}}{2 x^3} \]
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Rubi [A] time = 0.001592, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {15, 30} \[ -\frac{b \sqrt{b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{3/2}}{x^6} \, dx &=\frac{\left (b \sqrt{b x^2}\right ) \int \frac{1}{x^3} \, dx}{x}\\ &=-\frac{b \sqrt{b x^2}}{2 x^3}\\ \end{align*}
Mathematica [A] time = 0.0012062, size = 16, normalized size = 0.94 \[ -\frac{\left (b x^2\right )^{3/2}}{2 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{2\,{x}^{5}} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19052, size = 32, normalized size = 1.88 \begin{align*} -\frac{\sqrt{b x^{2}} b}{2 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.40309, size = 17, normalized size = 1. \begin{align*} - \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{2 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14402, size = 14, normalized size = 0.82 \begin{align*} -\frac{b^{\frac{3}{2}} \mathrm{sgn}\left (x\right )}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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