Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{x^4}{a+b \sec \left (c+d x^2\right )},x\right ) \]
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Rubi [A] time = 0.0257448, 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 = {} \[ \int \frac{x^4}{a+b \sec \left (c+d x^2\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{x^4}{a+b \sec \left (c+d x^2\right )} \, dx &=\int \frac{x^4}{a+b \sec \left (c+d x^2\right )} \, dx\\ \end{align*}
Mathematica [A] time = 1.32978, size = 0, normalized size = 0. \[ \int \frac{x^4}{a+b \sec \left (c+d x^2\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.122, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{4}}{a+b\sec \left ( d{x}^{2}+c \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [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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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{x^{4}}{b \sec \left (d x^{2} + c\right ) + a}, 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{x^{4}}{a + b \sec{\left (c + d x^{2} \right )}}\, 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{x^{4}}{b \sec \left (d x^{2} + c\right ) + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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