Optimal. Leaf size=20 \[ \text{Unintegrable}\left (x^2 \left (a+b \text{sech}\left (c+d x^2\right )\right )^2,x\right ) \]
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Rubi [A] time = 0.0250254, 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 = {} \[ \int x^2 \left (a+b \text{sech}\left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x^2 \left (a+b \text{sech}\left (c+d x^2\right )\right )^2 \, dx &=\int x^2 \left (a+b \text{sech}\left (c+d x^2\right )\right )^2 \, dx\\ \end{align*}
Mathematica [A] time = 7.19717, size = 0, normalized size = 0. \[ \int x^2 \left (a+b \text{sech}\left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.059, size = 0, normalized size = 0. \begin{align*} \int{x}^{2} \left ( a+b{\rm sech} \left (d{x}^{2}+c\right ) \right ) ^{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*} \frac{1}{3} \, a^{2} x^{3} - \frac{b^{2} x}{d e^{\left (2 \, d x^{2} + 2 \, c\right )} + d} + \int \frac{4 \, a b d x^{2} e^{\left (d x^{2} + c\right )} + b^{2}}{d e^{\left (2 \, d x^{2} + 2 \, c\right )} + d}\,{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 (b^{2} x^{2} \operatorname{sech}\left (d x^{2} + c\right )^{2} + 2 \, a b x^{2} \operatorname{sech}\left (d x^{2} + c\right ) + a^{2} 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 x^{2} \left (a + b \operatorname{sech}{\left (c + d x^{2} \right )}\right )^{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{\left (b \operatorname{sech}\left (d x^{2} + c\right ) + a\right )}^{2} x^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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