Optimal. Leaf size=16 \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]
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Rubi [A] time = 0.0014343, antiderivative size = 16, 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} \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt{b x^2}} \, dx &=\frac{x \int \frac{1}{x^4} \, dx}{\sqrt{b x^2}}\\ &=-\frac{1}{3 x^2 \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0021913, size = 16, normalized size = 1. \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{3\,{x}^{2}}{\frac{1}{\sqrt{b{x}^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02403, size = 11, normalized size = 0.69 \begin{align*} -\frac{1}{3 \, \sqrt{b} x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43501, size = 35, normalized size = 2.19 \begin{align*} -\frac{\sqrt{b x^{2}}}{3 \, b x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.770225, size = 19, normalized size = 1.19 \begin{align*} - \frac{1}{3 \sqrt{b} x^{2} \sqrt{x^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23565, size = 16, normalized size = 1. \begin{align*} -\frac{1}{3 \, \sqrt{b x^{2}} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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