Optimal. Leaf size=29 \[ \text{Unintegrable}\left (\frac{\text{sech}(a+b x)}{x},x\right )-\text{Unintegrable}\left (\frac{\text{sech}^3(a+b x)}{x},x\right ) \]
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Rubi [A] time = 0.0642935, 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 = {} \[ \int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx \]
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} \, dx &=\int \frac{\text{sech}(a+b x)}{x} \, dx-\int \frac{\text{sech}^3(a+b x)}{x} \, dx\\ \end{align*}
Mathematica [A] time = 16.0396, size = 0, normalized size = 0. \[ \int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.145, 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}}\, 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 )} - e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} -{\left (b x e^{a} + e^{a}\right )} e^{\left (b x\right )}}{b^{2} x^{2} e^{\left (4 \, b x + 4 \, a\right )} + 2 \, b^{2} x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{2}} + 2 \, \int \frac{{\left (b^{2} x^{2} e^{a} + 2 \, e^{a}\right )} e^{\left (b x\right )}}{2 \,{\left (b^{2} x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} 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{sech}\left (b x + a\right )^{3} \sinh \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{\sinh ^{2}{\left (a + b x \right )} \operatorname{sech}^{3}{\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{sech}\left (b x + a\right )^{3} \sinh \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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