Integrand size = 20, antiderivative size = 20 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\text {Int}\left (\frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x},x\right ) \]
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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 = {} \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx \\ \end{align*}
Not integrable
Time = 130.41 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx \]
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Not integrable
Time = 0.97 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
\[\int \frac {\left (a +b \tan \left (c +d \sqrt {x}\right )\right )^{2}}{x}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.80 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int { \frac {{\left (b \tan \left (d \sqrt {x} + c\right ) + a\right )}^{2}}{x} \,d x } \]
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Not integrable
Time = 8.72 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int \frac {\left (a + b \tan {\left (c + d \sqrt {x} \right )}\right )^{2}}{x}\, dx \]
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Not integrable
Time = 0.73 (sec) , antiderivative size = 298, normalized size of antiderivative = 14.90 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int { \frac {{\left (b \tan \left (d \sqrt {x} + c\right ) + a\right )}^{2}}{x} \,d x } \]
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Not integrable
Time = 0.85 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int { \frac {{\left (b \tan \left (d \sqrt {x} + c\right ) + a\right )}^{2}}{x} \,d x } \]
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Not integrable
Time = 4.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \tan \left (c+d \sqrt {x}\right )\right )^2}{x} \, dx=\int \frac {{\left (a+b\,\mathrm {tan}\left (c+d\,\sqrt {x}\right )\right )}^2}{x} \,d x \]
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