Integrand size = 16, antiderivative size = 16 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=-\frac {a}{x}+b \text {Int}\left (\frac {\text {sech}\left (c+d x^2\right )}{x^2},x\right ) \]
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Not integrable
Time = 0.01 (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 = {} \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x^2}+\frac {b \text {sech}\left (c+d x^2\right )}{x^2}\right ) \, dx \\ & = -\frac {a}{x}+b \int \frac {\text {sech}\left (c+d x^2\right )}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 0.09 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {a +b \,\operatorname {sech}\left (d \,x^{2}+c \right )}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int { \frac {b \operatorname {sech}\left (d x^{2} + c\right ) + a}{x^{2}} \,d x } \]
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Not integrable
Time = 0.70 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int \frac {a + b \operatorname {sech}{\left (c + d x^{2} \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 38, normalized size of antiderivative = 2.38 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int { \frac {b \operatorname {sech}\left (d x^{2} + c\right ) + a}{x^{2}} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int { \frac {b \operatorname {sech}\left (d x^{2} + c\right ) + a}{x^{2}} \,d x } \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {a+b \text {sech}\left (c+d x^2\right )}{x^2} \, dx=\int \frac {a+\frac {b}{\mathrm {cosh}\left (d\,x^2+c\right )}}{x^2} \,d x \]
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