Integrand size = 24, antiderivative size = 24 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\text {Int}\left (\frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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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 = {} \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.18 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {\left (g \,x^{3}+f \right )^{2}}{\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {{\left (g x^{3} + f\right )}^{2}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]
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Not integrable
Time = 14.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {\left (f + g x^{3}\right )^{2}}{\log {\left (c \left (d + e x^{2}\right )^{p} \right )}}\, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {{\left (g x^{3} + f\right )}^{2}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {{\left (g x^{3} + f\right )}^{2}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]
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Not integrable
Time = 1.61 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\left (f+g x^3\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {{\left (g\,x^3+f\right )}^2}{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )} \,d x \]
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