Integrand size = 28, antiderivative size = 28 \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\text {Int}\left (\frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}},x\right ) \]
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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 = {} \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx \\ \end{align*}
Not integrable
Time = 0.07 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86
\[\int \frac {1}{\left (g x +f \right )^{\frac {3}{2}} \sqrt {a +b \ln \left (c \left (e x +d \right )^{n}\right )}}d x\]
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Exception generated. \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 26.94 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\int \frac {1}{\sqrt {a + b \log {\left (c \left (d + e x\right )^{n} \right )}} \left (f + g x\right )^{\frac {3}{2}}}\, dx \]
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Not integrable
Time = 0.67 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{\frac {3}{2}} \sqrt {b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}} \,d x } \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{\frac {3}{2}} \sqrt {b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}} \,d x } \]
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Not integrable
Time = 1.49 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {1}{(f+g x)^{3/2} \sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx=\int \frac {1}{{\left (f+g\,x\right )}^{3/2}\,\sqrt {a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )}} \,d x \]
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