Optimal. Leaf size=20 \[ \text{CannotIntegrate}\left (\frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x},x\right ) \]
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Rubi [A] time = 0.213599, 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 = {} \[ \int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x} \, dx &=\int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x} \, dx\\ \end{align*}
Mathematica [A] time = 33.6089, size = 0, normalized size = 0. \[ \int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.256, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm csch} \left (bx+a\right ) \left ({\rm sech} \left (bx+a\right ) \right ) ^{2}}{x}}\, 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 \, e^{\left (b x + a\right )}}{b x e^{\left (2 \, b x + 2 \, a\right )} + b x} + 8 \, \int \frac{e^{\left (b x + a\right )}}{4 \,{\left (b x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b x^{2}\right )}}\,{d x} + 8 \, \int \frac{1}{8 \,{\left (x e^{\left (b x + a\right )} + x\right )}}\,{d x} + 8 \, \int \frac{1}{8 \,{\left (x e^{\left (b x + a\right )} - x\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 ) \operatorname{sech}\left (b x + a\right )^{2}}{x}, 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}{\left (a + b x \right )} \operatorname{sech}^{2}{\left (a + b x \right )}}{x}\, 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 ) \operatorname{sech}\left (b x + a\right )^{2}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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