Integrand size = 24, antiderivative size = 24 \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\text {Int}\left (\frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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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 = {} \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \\ \end{align*}
Not integrable
Time = 10.86 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (g \,x^{3}+f \right )^{2} {\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}^{2}}d x\]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.54 \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {1}{{\left (g x^{3} + f\right )}^{2} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}} \,d x } \]
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Timed out. \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\text {Timed out} \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 215, normalized size of antiderivative = 8.96 \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {1}{{\left (g x^{3} + f\right )}^{2} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}} \,d x } \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {1}{{\left (g x^{3} + f\right )}^{2} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}} \,d x } \]
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Not integrable
Time = 1.53 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2\,{\left (g\,x^3+f\right )}^2} \,d x \]
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