Optimal. Leaf size=19 \[ \text{Unintegrable}\left (\frac{1}{x \left (a+\frac{1}{2} b \sinh (2 x)\right )},x\right ) \]
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Rubi [A] time = 0.0939793, 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 = {} \[ \int \frac{1}{x (a+b \cosh (x) \sinh (x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x (a+b \cosh (x) \sinh (x))} \, dx &=\int \frac{1}{x \left (a+\frac{1}{2} b \sinh (2 x)\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.964546, size = 0, normalized size = 0. \[ \int \frac{1}{x (a+b \cosh (x) \sinh (x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.05, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ( a+b\cosh \left ( x \right ) \sinh \left ( x \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*} \int \frac{1}{{\left (b \cosh \left (x\right ) \sinh \left (x\right ) + a\right )} x}\,{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{1}{b x \cosh \left (x\right ) \sinh \left (x\right ) + a 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{1}{x \left (a + b \sinh{\left (x \right )} \cosh{\left (x \right )}\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 (b \cosh \left (x\right ) \sinh \left (x\right ) + a\right )} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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