Optimal. Leaf size=26 \[ -\frac {2 x^{-n/2} \sqrt {a+b x^n}}{a n} \]
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Rubi [A] time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.00 \[ -\frac {2 x^{-n/2} \sqrt {a+b x^n}}{a n} \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{-\frac {1}{2} \, n - 1}}{\sqrt {b x^{n} + a}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.22, size = 0, normalized size = 0.00 \[ \int \frac {x^{-\frac {n}{2}-1}}{\sqrt {b \,x^{n}+a}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{-\frac {1}{2} \, n - 1}}{\sqrt {b x^{n} + a}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.31, size = 24, normalized size = 0.92 \[ -\frac {2\,\sqrt {a+b\,x^n}}{a\,n\,x^{n/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 34.93, size = 22, normalized size = 0.85 \[ - \frac {2 \sqrt {b} \sqrt {\frac {a x^{- n}}{b} + 1}}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
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