Optimal. Leaf size=16 \[ -\frac{\sqrt{b x^2}}{3 x^4} \]
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Rubi [A] time = 0.001575, 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} \[ -\frac{\sqrt{b x^2}}{3 x^4} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\sqrt{b x^2}}{x^5} \, dx &=\frac{\sqrt{b x^2} \int \frac{1}{x^4} \, dx}{x}\\ &=-\frac{\sqrt{b x^2}}{3 x^4}\\ \end{align*}
Mathematica [A] time = 0.0013541, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{3 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{3\,{x}^{4}}\sqrt{b{x}^{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 = 1.19454, size = 30, normalized size = 1.88 \begin{align*} -\frac{\sqrt{b x^{2}}}{3 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.683411, size = 17, normalized size = 1.06 \begin{align*} - \frac{\sqrt{b} \sqrt{x^{2}}}{3 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19977, size = 14, normalized size = 0.88 \begin{align*} -\frac{\sqrt{b} \mathrm{sgn}\left (x\right )}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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