Optimal. Leaf size=19 \[ 4 \text{Unintegrable}\left (\frac{\text{csch}^2(2 a+2 b x)}{x^2},x\right ) \]
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Rubi [A] time = 0.0706101, 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 = {} \[ \int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx &=4 \int \frac{\text{csch}^2(2 a+2 b x)}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 20.4321, size = 0, normalized size = 0. \[ \int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.057, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (bx+a\right ) \right ) ^{2} \left ({\rm sech} \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{4}{b x^{2} e^{\left (4 \, b x + 4 \, a\right )} - b x^{2}} + 16 \, \int \frac{1}{4 \,{\left (b x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b x^{3}\right )}}\,{d x} + 16 \, \int \frac{1}{8 \,{\left (b x^{3} e^{\left (b x + a\right )} + b x^{3}\right )}}\,{d x} - 16 \, \int \frac{1}{8 \,{\left (b x^{3} e^{\left (b x + a\right )} - b x^{3}\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{csch}\left (b x + a\right )^{2} \operatorname{sech}\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 [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{csch}^{2}{\left (a + b x \right )} \operatorname{sech}^{2}{\left (a + b x \right )}}{x^{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{\operatorname{csch}\left (b x + a\right )^{2} \operatorname{sech}\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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