Optimal. Leaf size=20 \[ \text{Unintegrable}\left (x^4 \left (a+b \sec \left (c+d x^2\right )\right )^2,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0232077, 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 = {} \[ \int x^4 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int x^4 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx &=\int x^4 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx\\ \end{align*}
Mathematica [A] time = 9.05866, size = 0, normalized size = 0. \[ \int x^4 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.163, size = 0, normalized size = 0. \begin{align*} \int{x}^{4} \left ( a+b\sec \left ( d{x}^{2}+c \right ) \right ) ^{2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (b^{2} x^{4} \sec \left (d x^{2} + c\right )^{2} + 2 \, a b x^{4} \sec \left (d x^{2} + c\right ) + a^{2} x^{4}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{4} \left (a + b \sec{\left (c + d x^{2} \right )}\right )^{2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b \sec \left (d x^{2} + c\right ) + a\right )}^{2} x^{4}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]