Integrand size = 28, antiderivative size = 28 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\text {Int}\left (\frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 28, 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 = {} \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx \\ \end{align*}
Not integrable
Time = 3.14 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx \]
[In]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
\[\int \frac {F^{f {\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )}^{2}}}{\left (h x +g \right )^{2}}d x\]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.18 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{2}} \,d x } \]
[In]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 1, normalized size of antiderivative = 0.04 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int \frac {F^{f \left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right )^{2}}}{\left (g + h x\right )^{2}} \, dx \]
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Not integrable
Time = 0.79 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{2}} \,d x } \]
[In]
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Not integrable
Time = 2.11 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^2} \, dx=\int \frac {{\mathrm {e}}^{f\,\ln \left (F\right )\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^2}}{{\left (g+h\,x\right )}^2} \,d x \]
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