Integrand size = 21, antiderivative size = 21 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\text {Int}\left (\frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}},x\right ) \]
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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 = {} \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx \\ \end{align*}
Not integrable
Time = 8.45 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90
\[\int \frac {a +b \,\operatorname {arccsch}\left (c x \right )}{x^{2} \sqrt {e x +d}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.48 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int { \frac {b \operatorname {arcsch}\left (c x\right ) + a}{\sqrt {e x + d} x^{2}} \,d x } \]
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Not integrable
Time = 17.81 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int \frac {a + b \operatorname {acsch}{\left (c x \right )}}{x^{2} \sqrt {d + e x}}\, dx \]
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Not integrable
Time = 2.38 (sec) , antiderivative size = 175, normalized size of antiderivative = 8.33 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int { \frac {b \operatorname {arcsch}\left (c x\right ) + a}{\sqrt {e x + d} x^{2}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int { \frac {b \operatorname {arcsch}\left (c x\right ) + a}{\sqrt {e x + d} x^{2}} \,d x } \]
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Not integrable
Time = 5.47 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19 \[ \int \frac {a+b \text {csch}^{-1}(c x)}{x^2 \sqrt {d+e x}} \, dx=\int \frac {a+b\,\mathrm {asinh}\left (\frac {1}{c\,x}\right )}{x^2\,\sqrt {d+e\,x}} \,d x \]
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