Integrand size = 21, antiderivative size = 21 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\text {Int}\left (\frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}},x\right ) \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 21, 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 = {} \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx \\ \end{align*}
Not integrable
Time = 4.86 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90
\[\int \frac {a +b \,\operatorname {arccsch}\left (c x \right )}{x \sqrt {e x +d}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int { \frac {b \operatorname {arcsch}\left (c x\right ) + a}{\sqrt {e x + d} x} \,d x } \]
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Not integrable
Time = 8.54 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int \frac {a + b \operatorname {acsch}{\left (c x \right )}}{x \sqrt {d + e x}}\, dx \]
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Not integrable
Time = 1.11 (sec) , antiderivative size = 116, normalized size of antiderivative = 5.52 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int { \frac {b \operatorname {arcsch}\left (c x\right ) + a}{\sqrt {e x + d} x} \,d x } \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int { \frac {b \operatorname {arcsch}\left (c x\right ) + a}{\sqrt {e x + d} x} \,d x } \]
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Not integrable
Time = 4.87 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x \sqrt {d+e x}} \, dx=\int \frac {a+b\,\mathrm {asinh}\left (\frac {1}{c\,x}\right )}{x\,\sqrt {d+e\,x}} \,d x \]
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