Integrand size = 22, antiderivative size = 22 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\text {Int}\left (\frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 22, 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 = {} \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 10.04 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82
\[\int \frac {1}{x^{\frac {3}{2}} \left (a +b \,\operatorname {sech}\left (c +d \sqrt {x}\right )\right )}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.23 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int { \frac {1}{{\left (b \operatorname {sech}\left (d \sqrt {x} + c\right ) + a\right )} x^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 2.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x^{\frac {3}{2}} \left (a + b \operatorname {sech}{\left (c + d \sqrt {x} \right )}\right )}\, dx \]
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Not integrable
Time = 0.49 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.00 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int { \frac {1}{{\left (b \operatorname {sech}\left (d \sqrt {x} + c\right ) + a\right )} x^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int { \frac {1}{{\left (b \operatorname {sech}\left (d \sqrt {x} + c\right ) + a\right )} x^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 2.13 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x^{3/2}\,\left (a+\frac {b}{\mathrm {cosh}\left (c+d\,\sqrt {x}\right )}\right )} \,d x \]
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