Optimal. Leaf size=21 \[ -\frac{2 \sqrt{b x^n}}{(2-n) x} \]
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Rubi [A] time = 0.0052112, antiderivative size = 21, 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} \[ -\frac{2 \sqrt{b x^n}}{(2-n) x} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\sqrt{b x^n}}{x^2} \, dx &=\left (x^{-n/2} \sqrt{b x^n}\right ) \int x^{-2+\frac{n}{2}} \, dx\\ &=-\frac{2 \sqrt{b x^n}}{(2-n) x}\\ \end{align*}
Mathematica [A] time = 0.0020995, size = 19, normalized size = 0.9 \[ \frac{2 \sqrt{b x^n}}{(n-2) x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 18, normalized size = 0.9 \begin{align*} 2\,{\frac{\sqrt{b{x}^{n}}}{x \left ( -2+n \right ) }} \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{\sqrt{b x^{n}}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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