Optimal. Leaf size=14 \[ -\frac{1}{b^2 \sqrt{b x^2}} \]
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Rubi [A] time = 0.0016415, antiderivative size = 14, 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} \[ -\frac{1}{b^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x^3}{\left (b x^2\right )^{5/2}} \, dx &=\frac{x \int \frac{1}{x^2} \, dx}{b^2 \sqrt{b x^2}}\\ &=-\frac{1}{b^2 \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0012045, size = 14, normalized size = 1. \[ -\frac{x^4}{\left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \begin{align*} -{{x}^{4} \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 = 1.02632, size = 20, normalized size = 1.43 \begin{align*} -\frac{x^{2}}{\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 = 1.44643, size = 32, normalized size = 2.29 \begin{align*} -\frac{\sqrt{b x^{2}}}{b^{3} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.08275, size = 15, normalized size = 1.07 \begin{align*} - \frac{x^{4}}{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 = 1.17641, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{\sqrt{b x^{2}} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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