Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x)^2 (a+b \coth (e+f x))},x\right ) \]
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Rubi [A] time = 0.0599392, 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 = {} \[ \int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx &=\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx\\ \end{align*}
Mathematica [A] time = 22.4706, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.156, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) ^{2} \left ( a+b{\rm coth} \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^{2} - b^{2} c^{2} +{\left (a^{2} d^{2} - b^{2} d^{2}\right )} x^{2} + 2 \,{\left (a^{2} c d - b^{2} c d\right )} x -{\left (a^{2} c^{2} e^{\left (2 \, e\right )} + 2 \, a b c^{2} e^{\left (2 \, e\right )} + b^{2} c^{2} e^{\left (2 \, e\right )} +{\left (a^{2} d^{2} e^{\left (2 \, e\right )} + 2 \, a b d^{2} e^{\left (2 \, e\right )} + b^{2} d^{2} e^{\left (2 \, e\right )}\right )} x^{2} + 2 \,{\left (a^{2} c d e^{\left (2 \, e\right )} + 2 \, a b c d e^{\left (2 \, e\right )} + b^{2} c d e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )}}\,{d x} - \frac{1}{a c d + b c d +{\left (a d^{2} + b d^{2}\right )} 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{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} +{\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \coth \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 \coth{\left (e + f x \right )}\right ) \left (c + d x\right )^{2}}\, 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 )}^{2}{\left (b \coth \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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