Integrand size = 10, antiderivative size = 10 \[ \int \frac {\coth (a+b x)}{x} \, dx=\text {Int}\left (\frac {\coth (a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\coth (a+b x)}{x} \, dx=\int \frac {\coth (a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth (a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\coth (a+b x)}{x} \, dx=\int \frac {\coth (a+b x)}{x} \, dx \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.60
\[\int \frac {\cosh \left (b x +a \right ) \operatorname {csch}\left (b x +a \right )}{x}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int \frac {\coth (a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 3.29 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.50 \[ \int \frac {\coth (a+b x)}{x} \, dx=\int \frac {\cosh {\left (a + b x \right )} \operatorname {csch}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 35, normalized size of antiderivative = 3.50 \[ \int \frac {\coth (a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int \frac {\coth (a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 2.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 2.00 \[ \int \frac {\coth (a+b x)}{x} \, dx=\int \frac {\mathrm {cosh}\left (a+b\,x\right )}{x\,\mathrm {sinh}\left (a+b\,x\right )} \,d x \]
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