Optimal. Leaf size=26 \[ -\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)} \]
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Rubi [A] time = 0.0054398, antiderivative size = 26, 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} \[ -\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^n\right )^{3/2}}{x^4} \, dx &=\left (b x^{-n/2} \sqrt{b x^n}\right ) \int x^{-4+\frac{3 n}{2}} \, dx\\ &=-\frac{2 b x^{-3+n} \sqrt{b x^n}}{3 (2-n)}\\ \end{align*}
Mathematica [A] time = 0.0055524, size = 22, normalized size = 0.85 \[ \frac{\left (b x^n\right )^{3/2}}{\left (\frac{3 n}{2}-3\right ) x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.7 \begin{align*}{\frac{2}{3\,{x}^{3} \left ( -2+n \right ) } \left ( b{x}^{n} \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: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \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*} \int \frac{\left (b x^{n}\right )^{\frac{3}{2}}}{x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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