Optimal. Leaf size=22 \[ \text{CannotIntegrate}\left (\frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x},x\right ) \]
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Rubi [A] time = 0.276633, 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 = {} \[ \int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x} \, dx &=\int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x} \, dx\\ \end{align*}
Mathematica [A] time = 64.2115, size = 0, normalized size = 0. \[ \int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.39, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (bx+a\right ) \right ) ^{3} \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 \, b x e^{\left (3 \, b x + 3 \, a\right )} -{\left (3 \, b x e^{\left (5 \, a\right )} - e^{\left (5 \, a\right )}\right )} e^{\left (5 \, b x\right )} -{\left (3 \, b x e^{a} + e^{a}\right )} e^{\left (b x\right )}}{b^{2} x^{2} e^{\left (6 \, b x + 6 \, a\right )} - b^{2} x^{2} e^{\left (4 \, b x + 4 \, a\right )} - b^{2} x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{2}} - 32 \, \int \frac{3 \, b^{2} x^{2} - 2}{64 \,{\left (b^{2} x^{3} e^{\left (b x + a\right )} + b^{2} x^{3}\right )}}\,{d x} - 32 \, \int \frac{3 \, b^{2} x^{2} - 2}{64 \,{\left (b^{2} x^{3} e^{\left (b x + a\right )} - b^{2} x^{3}\right )}}\,{d x} - 32 \, \int \frac{e^{\left (b x + a\right )}}{16 \,{\left (b x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b x^{2}\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 )^{3} \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}^{3}{\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 )^{3} \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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