Integrand size = 30, antiderivative size = 30 \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\text {Int}\left (\frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x},x\right ) \]
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Not integrable
Time = 0.08 (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 = {} \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx \\ \end{align*}
Not integrable
Time = 2.66 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx \]
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Not integrable
Time = 0.16 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
\[\int \frac {{\left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}^{\frac {3}{2}}}{h x +g}d x\]
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Exception generated. \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 52.80 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\int \frac {\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right )^{\frac {3}{2}}}{g + h x}\, dx \]
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Not integrable
Time = 10.80 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\int { \frac {{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}}}{h x + g} \,d x } \]
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Not integrable
Time = 0.54 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\int { \frac {{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}}}{h x + g} \,d x } \]
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Not integrable
Time = 1.45 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}}{g+h x} \, dx=\int \frac {{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^{3/2}}{g+h\,x} \,d x \]
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