Optimal. Leaf size=23 \[ \text{Unintegrable}\left (\frac{1}{x \sqrt{a+i a \sinh (e+f x)}},x\right ) \]
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Rubi [A] time = 0.0776774, 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 = {} \[ \int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx &=\int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx\\ \end{align*}
Mathematica [A] time = 3.84339, size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.052, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x}{\frac{1}{\sqrt{a+ia\sinh \left ( fx+e \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}{\sqrt{i \, a \sinh \left (f x + e\right ) + a} 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{2 i \, \sqrt{\frac{1}{2}} \sqrt{i \, a e^{\left (2 \, f x + 2 \, e\right )} + 2 \, a e^{\left (f x + e\right )} - i \, a} e^{\left (\frac{1}{2} \, f x + \frac{1}{2} \, e\right )}}{a x e^{\left (2 \, f x + 2 \, e\right )} - 2 i \, a x e^{\left (f x + e\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 \sqrt{a \left (i \sinh{\left (e + f x \right )} + 1\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}{\sqrt{i \, a \sinh \left (f x + e\right ) + a} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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