Optimal. Leaf size=18 \[ \text {Int}\left (\frac {\tanh ^{-1}(d \coth (a+b x)+c)}{x},x\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx &=\int \frac {\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 14.62, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.73, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {artanh}\left (d \coth \left (b x + a\right ) + c\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {artanh}\left (d \coth \left (b x + a\right ) + c\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.57, size = 0, normalized size = 0.00 \[ \int \frac {\arctanh \left (c +d \coth \left (b x +a \right )\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {artanh}\left (d \coth \left (b x + a\right ) + c\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {\mathrm {atanh}\left (c+d\,\mathrm {coth}\left (a+b\,x\right )\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {atanh}{\left (c + d \coth {\left (a + b x \right )} \right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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