Optimal. Leaf size=26 \[ -\frac{2 x^{-n/2} \sqrt{a+b x^n}}{a n} \]
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Rubi [A] time = 0.00625, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {264} \[ -\frac{2 x^{-n/2} \sqrt{a+b x^n}}{a n} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x^{-1-\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx &=-\frac{2 x^{-n/2} \sqrt{a+b x^n}}{a n}\\ \end{align*}
Mathematica [A] time = 0.0074433, size = 26, normalized size = 1. \[ -\frac{2 x^{-n/2} \sqrt{a+b x^n}}{a n} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.077, size = 0, normalized size = 0. \begin{align*} \int{{x}^{-1-{\frac{n}{2}}}{\frac{1}{\sqrt{a+b{x}^{n}}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{-\frac{1}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x} \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(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{x^{-\frac{1}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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