Integrand size = 22, antiderivative size = 22 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\text {Int}\left (\frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}},x\right ) \]
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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 = {} \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx \\ \end{align*}
Not integrable
Time = 72.66 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx \]
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Not integrable
Time = 0.80 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82
\[\int \frac {\left (a +b \sec \left (c +d \sqrt {x}\right )\right )^{2}}{x^{\frac {3}{2}}}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.09 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int { \frac {{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )}^{2}}{x^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 1.96 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int \frac {\left (a + b \sec {\left (c + d \sqrt {x} \right )}\right )^{2}}{x^{\frac {3}{2}}}\, dx \]
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Not integrable
Time = 1.58 (sec) , antiderivative size = 718, normalized size of antiderivative = 32.64 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int { \frac {{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )}^{2}}{x^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int { \frac {{\left (b \sec \left (d \sqrt {x} + c\right ) + a\right )}^{2}}{x^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 13.54 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \sec \left (c+d \sqrt {x}\right )\right )^2}{x^{3/2}} \, dx=\int \frac {{\left (a+\frac {b}{\cos \left (c+d\,\sqrt {x}\right )}\right )}^2}{x^{3/2}} \,d x \]
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