Integrand size = 20, antiderivative size = 20 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\text {Int}\left (\frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 3.50 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
\[\int \frac {1}{x \left (a +b \sec \left (c +d \sqrt {x}\right )\right )}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int { \frac {1}{{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )} x} \,d x } \]
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Not integrable
Time = 2.13 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x \left (a + b \sec {\left (c + d \sqrt {x} \right )}\right )}\, dx \]
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Not integrable
Time = 0.83 (sec) , antiderivative size = 241, normalized size of antiderivative = 12.05 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int { \frac {1}{{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )} x} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int { \frac {1}{{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )} x} \,d x } \]
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Not integrable
Time = 13.86 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{x \left (a+b \sec \left (c+d \sqrt {x}\right )\right )} \, dx=\int \frac {1}{x\,\left (a+\frac {b}{\cos \left (c+d\,\sqrt {x}\right )}\right )} \,d x \]
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