Integrand size = 24, antiderivative size = 24 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\text {Int}\left (\frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 24, 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 = {} \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx \\ \end{align*}
Not integrable
Time = 2.41 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {{\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}^{2}}{g \,x^{2}+f}d x\]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int { \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{g x^{2} + f} \,d x } \]
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Not integrable
Time = 10.87 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int \frac {\log {\left (c \left (d + e x^{2}\right )^{p} \right )}^{2}}{f + g x^{2}}\, dx \]
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Not integrable
Time = 1.10 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int { \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{g x^{2} + f} \,d x } \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int { \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{g x^{2} + f} \,d x } \]
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Not integrable
Time = 1.38 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx=\int \frac {{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2}{g\,x^2+f} \,d x \]
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