Integrand size = 27, antiderivative size = 27 \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\text {Int}\left (\frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r},x\right ) \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 27, 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 = {} \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx \\ \end{align*}
Not integrable
Time = 1.13 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx \]
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Not integrable
Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00
\[\int \frac {\left (f x \right )^{m} {\left (a +b \ln \left (c \,x^{n}\right )\right )}^{p}}{d +e \,x^{r}}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\int { \frac {\left (f x\right )^{m} {\left (b \log \left (c x^{n}\right ) + a\right )}^{p}}{e x^{r} + d} \,d x } \]
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Not integrable
Time = 92.38 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\int \frac {\left (f x\right )^{m} \left (a + b \log {\left (c x^{n} \right )}\right )^{p}}{d + e x^{r}}\, dx \]
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Exception generated. \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\text {Exception raised: RuntimeError} \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\int { \frac {\left (f x\right )^{m} {\left (b \log \left (c x^{n}\right ) + a\right )}^{p}}{e x^{r} + d} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )^p}{d+e x^r} \, dx=\int \frac {{\left (f\,x\right )}^m\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^p}{d+e\,x^r} \,d x \]
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