Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\text{sech}^2(a+b x)}{c+d x},x\right ) \]
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Rubi [A] time = 0.0371998, 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 = {} \[ \int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx &=\int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx\\ \end{align*}
Mathematica [A] time = 17.409, size = 0, normalized size = 0. \[ \int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.073, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm sech} \left (bx+a\right ) \right ) ^{2}}{dx+c}}\, 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*} -4 \, d \int \frac{1}{2 \,{\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} +{\left (b d^{2} x^{2} e^{\left (2 \, a\right )} + 2 \, b c d x e^{\left (2 \, a\right )} + b c^{2} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}\right )}}\,{d x} - \frac{2}{b d x + b c +{\left (b d x e^{\left (2 \, a\right )} + b c e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} \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 )^{2}}{d x + c}, 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{sech}^{2}{\left (a + b x \right )}}{c + d 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 )^{2}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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