Optimal. Leaf size=36 \[ \text{Unintegrable}\left (\frac{\sqrt{c+d x^2}}{\left (a+b x^2\right )^{3/2} \left (e+f x^2\right )^{3/2}},x\right ) \]
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Rubi [A] time = 0.0600382, 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 = {} \[ \int \frac{\sqrt{c+d x^2}}{\left (a+b x^2\right )^{3/2} \left (e+f x^2\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt{c+d x^2}}{\left (a+b x^2\right )^{3/2} \left (e+f x^2\right )^{3/2}} \, dx &=\int \frac{\sqrt{c+d x^2}}{\left (a+b x^2\right )^{3/2} \left (e+f x^2\right )^{3/2}} \, dx\\ \end{align*}
Mathematica [A] time = 0.967956, size = 0, normalized size = 0. \[ \int \frac{\sqrt{c+d x^2}}{\left (a+b x^2\right )^{3/2} \left (e+f x^2\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.069, size = 0, normalized size = 0. \begin{align*} \int{\sqrt{d{x}^{2}+c} \left ( b{x}^{2}+a \right ) ^{-{\frac{3}{2}}} \left ( f{x}^{2}+e \right ) ^{-{\frac{3}{2}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{d x^{2} + c}}{{\left (b x^{2} + a\right )}^{\frac{3}{2}}{\left (f x^{2} + e\right )}^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{b^{2} f^{2} x^{8} + 2 \,{\left (b^{2} e f + a b f^{2}\right )} x^{6} +{\left (b^{2} e^{2} + 4 \, a b e f + a^{2} f^{2}\right )} x^{4} + a^{2} e^{2} + 2 \,{\left (a b e^{2} + a^{2} e f\right )} x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{c + d x^{2}}}{\left (a + b x^{2}\right )^{\frac{3}{2}} \left (e + f x^{2}\right )^{\frac{3}{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{d x^{2} + c}}{{\left (b x^{2} + a\right )}^{\frac{3}{2}}{\left (f x^{2} + e\right )}^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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