Integrand size = 22, antiderivative size = 22 \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\text {Int}\left (\frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2},x\right ) \]
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Not integrable
Time = 0.03 (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 = {} \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 47.71 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx \]
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Not integrable
Time = 0.49 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82
\[\int \frac {1}{x^{\frac {5}{2}} \left (a +b \sec \left (c +d \sqrt {x}\right )\right )^{2}}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.18 \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\int { \frac {1}{{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )}^{2} x^{\frac {5}{2}}} \,d x } \]
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Not integrable
Time = 45.72 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^{\frac {5}{2}} \left (a + b \sec {\left (c + d \sqrt {x} \right )}\right )^{2}}\, dx \]
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Timed out. \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\text {Timed out} \]
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Not integrable
Time = 1.80 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\int { \frac {1}{{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )}^{2} x^{\frac {5}{2}}} \,d x } \]
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Not integrable
Time = 13.18 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^{5/2} \left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^{5/2}\,{\left (a+\frac {b}{\cos \left (c+d\,\sqrt {x}\right )}\right )}^2} \,d x \]
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