Integrand size = 22, antiderivative size = 22 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\text {Int}\left (\frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 22, 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 = {} \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 2.38 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (e \,x^{2}+d \right )^{2} \left (a +b \ln \left (c \,x^{n}\right )\right )}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.50 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int { \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \log \left (c x^{n}\right ) + a\right )}} \,d x } \]
[In]
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Not integrable
Time = 77.41 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{\left (a + b \log {\left (c x^{n} \right )}\right ) \left (d + e x^{2}\right )^{2}}\, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int { \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \log \left (c x^{n}\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.32 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int { \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \log \left (c x^{n}\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx=\int \frac {1}{{\left (e\,x^2+d\right )}^2\,\left (a+b\,\ln \left (c\,x^n\right )\right )} \,d x \]
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