Integrand size = 16, antiderivative size = 16 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\text {Int}\left (\frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x},x\right ) \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx \\ \end{align*}
Not integrable
Time = 2.82 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {arccoth}\left (1+d +d \tanh \left (b x +a \right )\right )}{x}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int { \frac {\operatorname {arcoth}\left (d \tanh \left (b x + a\right ) + d + 1\right )}{x} \,d x } \]
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Not integrable
Time = 0.53 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int \frac {\operatorname {acoth}{\left (d \tanh {\left (a + b x \right )} + d + 1 \right )}}{x}\, dx \]
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Not integrable
Time = 0.92 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int { \frac {\operatorname {arcoth}\left (d \tanh \left (b x + a\right ) + d + 1\right )}{x} \,d x } \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int { \frac {\operatorname {arcoth}\left (d \tanh \left (b x + a\right ) + d + 1\right )}{x} \,d x } \]
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Not integrable
Time = 4.21 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx=\int \frac {\mathrm {acoth}\left (d+d\,\mathrm {tanh}\left (a+b\,x\right )+1\right )}{x} \,d x \]
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