Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{x^2 \left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0261299, 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 = {} \[ \int \frac{1}{x^2 \left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x^2 \left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2} \, dx &=\int \frac{1}{x^2 \left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 68.3164, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.093, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2}} \left ( a+b{\rm sech} \left (c+d\sqrt{x}\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{4 \, a b^{2} \sqrt{x} +{\left (a^{3} d e^{\left (2 \, c\right )} - a b^{2} d e^{\left (2 \, c\right )}\right )} x e^{\left (2 \, d \sqrt{x}\right )} +{\left (a^{3} d - a b^{2} d\right )} x + 2 \,{\left (2 \, b^{3} \sqrt{x} e^{c} +{\left (a^{2} b d e^{c} - b^{3} d e^{c}\right )} x\right )} e^{\left (d \sqrt{x}\right )}}{{\left (a^{5} d e^{\left (2 \, c\right )} - a^{3} b^{2} d e^{\left (2 \, c\right )}\right )} x^{2} e^{\left (2 \, d \sqrt{x}\right )} + 2 \,{\left (a^{4} b d e^{c} - a^{2} b^{3} d e^{c}\right )} x^{2} e^{\left (d \sqrt{x}\right )} +{\left (a^{5} d - a^{3} b^{2} d\right )} x^{2}} - \int \frac{2 \,{\left (3 \, a b^{2} \sqrt{x} +{\left (3 \, b^{3} \sqrt{x} e^{c} +{\left (2 \, a^{2} b d e^{c} - b^{3} d e^{c}\right )} x\right )} e^{\left (d \sqrt{x}\right )}\right )}}{{\left (a^{5} d e^{\left (2 \, c\right )} - a^{3} b^{2} d e^{\left (2 \, c\right )}\right )} x^{3} e^{\left (2 \, d \sqrt{x}\right )} + 2 \,{\left (a^{4} b d e^{c} - a^{2} b^{3} d e^{c}\right )} x^{3} e^{\left (d \sqrt{x}\right )} +{\left (a^{5} d - a^{3} b^{2} d\right )} x^{3}}\,{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{1}{b^{2} x^{2} \operatorname{sech}\left (d \sqrt{x} + c\right )^{2} + 2 \, a b x^{2} \operatorname{sech}\left (d \sqrt{x} + 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 \frac{1}{x^{2} \left (a + b \operatorname{sech}{\left (c + d \sqrt{x} \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 \frac{1}{{\left (b \operatorname{sech}\left (d \sqrt{x} + 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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