Optimal. Leaf size=29 \[ \text{Unintegrable}\left (\frac{\text{sech}(a+b x)}{x^2},x\right )-\text{Unintegrable}\left (\frac{\text{sech}^3(a+b x)}{x^2},x\right ) \]
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Rubi [A] time = 0.0685913, 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 = {} \[ \int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x^2} \, dx &=\int \frac{\text{sech}(a+b x)}{x^2} \, dx-\int \frac{\text{sech}^3(a+b x)}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 12.8311, size = 0, normalized size = 0. \[ \int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.195, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm sech} \left (bx+a\right ) \right ) ^{3} \left ( \sinh \left ( bx+a \right ) \right ) ^{2}}{{x}^{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{{\left (b x e^{\left (3 \, a\right )} - 2 \, e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} -{\left (b x e^{a} + 2 \, e^{a}\right )} e^{\left (b x\right )}}{b^{2} x^{3} e^{\left (4 \, b x + 4 \, a\right )} + 2 \, b^{2} x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{3}} + 2 \, \int \frac{{\left (b^{2} x^{2} e^{a} + 6 \, e^{a}\right )} e^{\left (b x\right )}}{2 \,{\left (b^{2} x^{4} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{4}\right )}}\,{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{\operatorname{sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )^{2}}{x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [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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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )^{2}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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