Integrand size = 22, antiderivative size = 22 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\text {Int}\left (\frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2},x\right ) \]
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Not integrable
Time = 0.04 (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 = {} \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 2 \text {Subst}\left (\int \frac {(a+b \log (c (d+e x)))^p}{x^3} \, dx,x,\sqrt {x}\right ) \\ \end{align*}
Not integrable
Time = 0.10 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
\[\int \frac {\left (a +b \ln \left (c \left (d +e \sqrt {x}\right )\right )\right )^{p}}{x^{2}}d x\]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\int { \frac {{\left (b \log \left ({\left (e \sqrt {x} + d\right )} c\right ) + a\right )}^{p}}{x^{2}} \,d x } \]
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Timed out. \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\text {Timed out} \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\int { \frac {{\left (b \log \left ({\left (e \sqrt {x} + d\right )} c\right ) + a\right )}^{p}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\int { \frac {{\left (b \log \left ({\left (e \sqrt {x} + d\right )} c\right ) + a\right )}^{p}}{x^{2}} \,d x } \]
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Not integrable
Time = 1.61 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )\right )\right )^p}{x^2} \, dx=\int \frac {{\left (a+b\,\ln \left (c\,\left (d+e\,\sqrt {x}\right )\right )\right )}^p}{x^2} \,d x \]
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