Optimal. Leaf size=16 \[ -\frac{1}{2 x \sqrt{b x^2}} \]
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Rubi [A] time = 0.0014971, 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} \[ -\frac{1}{2 x \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{b x^2}} \, dx &=\frac{x \int \frac{1}{x^3} \, dx}{\sqrt{b x^2}}\\ &=-\frac{1}{2 x \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0016589, size = 15, normalized size = 0.94 \[ -\frac{b x}{2 \left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{2\,x}{\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 = 0.984722, size = 11, normalized size = 0.69 \begin{align*} -\frac{1}{2 \, \sqrt{b} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43818, size = 35, normalized size = 2.19 \begin{align*} -\frac{\sqrt{b x^{2}}}{2 \, b x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.646963, size = 17, normalized size = 1.06 \begin{align*} - \frac{1}{2 \sqrt{b} x \sqrt{x^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \mathit{sage}_{0} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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