Optimal. Leaf size=19 \[ -\frac{1}{3 b^2 x^2 \sqrt{b x^2}} \]
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Rubi [A] time = 0.0018456, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {15, 30} \[ -\frac{1}{3 b^2 x^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x}{\left (b x^2\right )^{5/2}} \, dx &=\frac{x \int \frac{1}{x^4} \, dx}{b^2 \sqrt{b x^2}}\\ &=-\frac{1}{3 b^2 x^2 \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0006245, size = 16, normalized size = 0.84 \[ -\frac{x^2}{3 \left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.7 \begin{align*} -{\frac{{x}^{2}}{3} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.996883, size = 16, normalized size = 0.84 \begin{align*} -\frac{1}{3 \, \left (b x^{2}\right )^{\frac{3}{2}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40845, size = 38, normalized size = 2. \begin{align*} -\frac{\sqrt{b x^{2}}}{3 \, b^{3} x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.905236, size = 17, normalized size = 0.89 \begin{align*} - \frac{x^{2}}{3 b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18078, size = 20, normalized size = 1.05 \begin{align*} -\frac{1}{3 \, \sqrt{b x^{2}} b^{2} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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