Optimal. Leaf size=16 \[ \frac{b \sqrt{b x^2} \log (x)}{x} \]
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Rubi [A] time = 0.0014149, 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, 29} \[ \frac{b \sqrt{b x^2} \log (x)}{x} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{3/2}}{x^4} \, dx &=\frac{\left (b \sqrt{b x^2}\right ) \int \frac{1}{x} \, dx}{x}\\ &=\frac{b \sqrt{b x^2} \log (x)}{x}\\ \end{align*}
Mathematica [A] time = 0.0017927, size = 15, normalized size = 0.94 \[ \frac{\left (b x^2\right )^{3/2} \log (x)}{x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \begin{align*}{\frac{\ln \left ( x \right ) }{{x}^{3}} \left ( b{x}^{2} \right ) ^{{\frac{3}{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 = 1.29819, size = 32, normalized size = 2. \begin{align*} \frac{\sqrt{b x^{2}} b \log \left (x\right )}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (b x^{2}\right )^{\frac{3}{2}}}{x^{4}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16444, size = 12, normalized size = 0.75 \begin{align*} b^{\frac{3}{2}} \log \left ({\left | x \right |}\right ) \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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