Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x) (a+b \tanh (e+f x))},x\right ) \]
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Rubi [A] time = 0.0627407, 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 = {} \[ \int \frac{1}{(c+d x) (a+b \tanh (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(c+d x) (a+b \tanh (e+f x))} \, dx &=\int \frac{1}{(c+d x) (a+b \tanh (e+f x))} \, dx\\ \end{align*}
Mathematica [A] time = 13.9082, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x) (a+b \tanh (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.146, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) \left ( a+b\tanh \left ( fx+e \right ) \right ) }}\, 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*} 2 \, b \int \frac{1}{a^{2} c - b^{2} c +{\left (a^{2} d - b^{2} d\right )} x +{\left (a^{2} c e^{\left (2 \, e\right )} + 2 \, a b c e^{\left (2 \, e\right )} + b^{2} c e^{\left (2 \, e\right )} +{\left (a^{2} d e^{\left (2 \, e\right )} + 2 \, a b d e^{\left (2 \, e\right )} + b^{2} d e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )}}\,{d x} + \frac{\log \left (d x + c\right )}{a d + b d} \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{1}{a d x + a c +{\left (b d x + b c\right )} \tanh \left (f x + e\right )}, 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{1}{\left (a + b \tanh{\left (e + f x \right )}\right ) \left (c + d x\right )}\, 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{1}{{\left (d x + c\right )}{\left (b \tanh \left (f x + e\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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