Integrand size = 30, antiderivative size = 30 \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\text {Int}\left (\frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}},x\right ) \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 30, 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 = {} \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx \\ \end{align*}
Not integrable
Time = 13.56 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx \]
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Not integrable
Time = 0.20 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
\[\int \frac {\left (h x +g \right )^{m}}{{\left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}^{\frac {3}{2}}}d x\]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.47 \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\int { \frac {{\left (h x + g\right )}^{m}}{{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}}} \,d x } \]
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Exception generated. \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \]
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Not integrable
Time = 11.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\int { \frac {{\left (h x + g\right )}^{m}}{{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\int { \frac {{\left (h x + g\right )}^{m}}{{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 1.56 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\int \frac {{\left (g+h\,x\right )}^m}{{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^{3/2}} \,d x \]
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