Optimal. Leaf size=19 \[ \frac{2 x}{(2-n) \sqrt{b x^n}} \]
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Rubi [A] time = 0.0039118, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{2 x}{(2-n) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{b x^n}} \, dx &=\frac{x^{n/2} \int x^{-n/2} \, dx}{\sqrt{b x^n}}\\ &=\frac{2 x}{(2-n) \sqrt{b x^n}}\\ \end{align*}
Mathematica [A] time = 0.0025948, size = 17, normalized size = 0.89 \[ -\frac{2 x}{(n-2) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 16, normalized size = 0.8 \begin{align*} -2\,{\frac{x}{ \left ( -2+n \right ) \sqrt{b{x}^{n}}}} \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{1}{\sqrt{b x^{n}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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