Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\text {Int}\left (\frac {\text {csch}^2(a+b x)}{c+d x},x\right ) \]
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Not integrable
Time = 0.03 (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 = {} \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 22.43 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {csch}\left (b x +a \right )^{2}}{d x +c}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int \frac {\operatorname {csch}^{2}{\left (a + b x \right )}}{c + d x}\, dx \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 157, normalized size of antiderivative = 9.81 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.84 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx=\int \frac {1}{{\mathrm {sinh}\left (a+b\,x\right )}^2\,\left (c+d\,x\right )} \,d x \]
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