Integrand size = 33, antiderivative size = 33 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\text {Int}\left (\frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2},x\right ) \]
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Not integrable
Time = 0.19 (sec) , antiderivative size = 33, 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 = {} \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 1.36 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.00
\[\int \frac {j x +i}{\left (h x +g \right ) {\left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}^{2}}d x\]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.33 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int { \frac {j x + i}{{\left (h x + g\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}} \,d x } \]
[In]
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Not integrable
Time = 16.90 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.88 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int \frac {i + j x}{\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right )^{2} \left (g + h x\right )}\, dx \]
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Not integrable
Time = 2.06 (sec) , antiderivative size = 302, normalized size of antiderivative = 9.15 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int { \frac {j x + i}{{\left (h x + g\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int { \frac {j x + i}{{\left (h x + g\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 1.48 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\int \frac {i+j\,x}{\left (g+h\,x\right )\,{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^2} \,d x \]
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