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 = 0.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}
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Mathematica [F] time = 0.06, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {a+b x^2}}{\sqrt {1-x^4}} \, dx \]
Verification is Not applicable to the result.
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fricas [F] time = 0.95, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-x^{4} + 1} \sqrt {b x^{2} + a}}{x^{4} - 1}, x\right ) \]
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 \[ \int \frac {\sqrt {b x^{2} + a}}{\sqrt {-x^{4} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {b \,x^{2}+a}}{\sqrt {-x^{4}+1}}\, dx \]
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 \[ \int \frac {\sqrt {b x^{2} + a}}{\sqrt {-x^{4} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {\sqrt {b\,x^2+a}}{\sqrt {1-x^4}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {a + b x^{2}}}{\sqrt {- \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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