Optimal. Leaf size=112 \[ \frac{a \sqrt{1-x^2} \sqrt{\frac{a \left (x^2+1\right )}{a+b x^2}} \Pi \left (\frac{b}{a+b};\sin ^{-1}\left (\frac{\sqrt{a+b} x}{\sqrt{b x^2+a}}\right )|-\frac{a-b}{a+b}\right )}{\sqrt{x^2+1} \sqrt{a+b} \sqrt{\frac{a \left (1-x^2\right )}{a+b x^2}}} \]
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Rubi [F] time = 0.0094724, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx &=\int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx\\ \end{align*}
Mathematica [F] time = 0.0598551, size = 0, normalized size = 0. \[ \int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx \]
Verification is Not applicable to the result.
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Maple [F] time = 0.144, size = 0, normalized size = 0. \begin{align*} \int{\sqrt{b{x}^{2}+a}{\frac{1}{\sqrt{-{x}^{4}+1}}}}\, 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{\sqrt{b x^{2} + a}}{\sqrt{-x^{4} + 1}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\sqrt{-x^{4} + 1} \sqrt{b x^{2} + a}}{x^{4} - 1}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{a + b x^{2}}}{\sqrt{- \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right )}}\, dx \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^{2} + a}}{\sqrt{-x^{4} + 1}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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