Integrand size = 28, antiderivative size = 28 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\text {Int}\left (\frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )},x\right ) \]
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Not integrable
Time = 0.04 (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 = {} \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.48 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \]
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Not integrable
Time = 0.19 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (h x +g \right )^{2} \left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int { \frac {1}{{\left (h x + g\right )}^{2} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}} \,d x } \]
[In]
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Not integrable
Time = 3.77 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right ) \left (g + h x\right )^{2}}\, dx \]
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Not integrable
Time = 0.86 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int { \frac {1}{{\left (h x + g\right )}^{2} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int { \frac {1}{{\left (h x + g\right )}^{2} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 1.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(g+h x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{{\left (g+h\,x\right )}^2\,\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )} \,d x \]
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