Integrand size = 26, antiderivative size = 26 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\text {Int}\left (\frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}},x\right ) \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 26, 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 = {} \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx \\ \end{align*}
Not integrable
Time = 0.85 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92
\[\int \frac {a +b \,\operatorname {arcsech}\left (c x \right )}{x \sqrt {-c^{4} x^{4}+1}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int { \frac {b \operatorname {arsech}\left (c x\right ) + a}{\sqrt {-c^{4} x^{4} + 1} x} \,d x } \]
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Not integrable
Time = 2.72 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.31 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int \frac {a + b \operatorname {asech}{\left (c x \right )}}{x \sqrt {- \left (c x - 1\right ) \left (c x + 1\right ) \left (c^{2} x^{2} + 1\right )}}\, dx \]
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Not integrable
Time = 0.79 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.85 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int { \frac {b \operatorname {arsech}\left (c x\right ) + a}{\sqrt {-c^{4} x^{4} + 1} x} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int { \frac {b \operatorname {arsech}\left (c x\right ) + a}{\sqrt {-c^{4} x^{4} + 1} x} \,d x } \]
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Not integrable
Time = 5.32 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx=\int \frac {a+b\,\mathrm {acosh}\left (\frac {1}{c\,x}\right )}{x\,\sqrt {1-c^4\,x^4}} \,d x \]
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