Integrand size = 23, antiderivative size = 23 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\text {Int}\left (\frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )},x\right ) \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 23, 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 = {} \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 1.02 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00
\[\int \frac {1}{x^{2} \left (e x +d \right ) \left (a +b \ln \left (c \,x^{n}\right )\right )}d x\]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.61 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int { \frac {1}{{\left (e x + d\right )} {\left (b \log \left (c x^{n}\right ) + a\right )} x^{2}} \,d x } \]
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Not integrable
Time = 1.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{x^{2} \left (a + b \log {\left (c x^{n} \right )}\right ) \left (d + e x\right )}\, dx \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int { \frac {1}{{\left (e x + d\right )} {\left (b \log \left (c x^{n}\right ) + a\right )} x^{2}} \,d x } \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int { \frac {1}{{\left (e x + d\right )} {\left (b \log \left (c x^{n}\right ) + a\right )} x^{2}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{x^2\,\left (a+b\,\ln \left (c\,x^n\right )\right )\,\left (d+e\,x\right )} \,d x \]
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