Optimal. Leaf size=36 \[ \text{Unintegrable}\left (\frac{\left (a+b x^2\right )^{3/2} \sqrt{c+d x^2}}{\sqrt{e+f x^2}},x\right ) \]
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Rubi [A] time = 0.0571239, 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 = {} \[ \int \frac{\left (a+b x^2\right )^{3/2} \sqrt{c+d x^2}}{\sqrt{e+f x^2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^{3/2} \sqrt{c+d x^2}}{\sqrt{e+f x^2}} \, dx &=\int \frac{\left (a+b x^2\right )^{3/2} \sqrt{c+d x^2}}{\sqrt{e+f x^2}} \, dx\\ \end{align*}
Mathematica [A] time = 0.741494, size = 0, normalized size = 0. \[ \int \frac{\left (a+b x^2\right )^{3/2} \sqrt{c+d x^2}}{\sqrt{e+f x^2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.071, size = 0, normalized size = 0. \begin{align*} \int{ \left ( b{x}^{2}+a \right ) ^{{\frac{3}{2}}}\sqrt{d{x}^{2}+c}{\frac{1}{\sqrt{f{x}^{2}+e}}}}\, 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{{\left (b x^{2} + a\right )}^{\frac{3}{2}} \sqrt{d x^{2} + c}}{\sqrt{f x^{2} + e}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [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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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (a + b x^{2}\right )^{\frac{3}{2}} \sqrt{c + d x^{2}}}{\sqrt{e + f x^{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{{\left (b x^{2} + a\right )}^{\frac{3}{2}} \sqrt{d x^{2} + c}}{\sqrt{f x^{2} + e}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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