Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{\left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2}{x^{3/2}},x\right ) \]
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Rubi [A] time = 0.0249023, 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 = {} \[ \int \frac{\left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2}{x^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2}{x^{3/2}} \, dx &=\int \frac{\left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2}{x^{3/2}} \, dx\\ \end{align*}
Mathematica [A] time = 26.4028, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \text{sech}\left (c+d \sqrt{x}\right )\right )^2}{x^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.07, size = 0, normalized size = 0. \begin{align*} \int{ \left ( a+b{\rm sech} \left (c+d\sqrt{x}\right ) \right ) ^{2}{x}^{-{\frac{3}{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{2 \,{\left (a^{2} d \sqrt{x} e^{\left (2 \, d \sqrt{x} + 2 \, c\right )} + a^{2} d \sqrt{x} + 2 \, b^{2}\right )}}{d x e^{\left (2 \, d \sqrt{x} + 2 \, c\right )} + d x} + \int \frac{4 \,{\left (a b d x e^{\left (d \sqrt{x} + c\right )} - b^{2} \sqrt{x}\right )}}{d x^{\frac{5}{2}} e^{\left (2 \, d \sqrt{x} + 2 \, c\right )} + d x^{\frac{5}{2}}}\,{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{b^{2} \sqrt{x} \operatorname{sech}\left (d \sqrt{x} + c\right )^{2} + 2 \, a b \sqrt{x} \operatorname{sech}\left (d \sqrt{x} + c\right ) + a^{2} \sqrt{x}}{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{\left (a + b \operatorname{sech}{\left (c + d \sqrt{x} \right )}\right )^{2}}{x^{\frac{3}{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 \operatorname{sech}\left (d \sqrt{x} + c\right ) + a\right )}^{2}}{x^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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