Integrand size = 26, antiderivative size = 26 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\text {Int}\left (\frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 26, 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 = {} \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.72 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92
\[\int \frac {1}{\left (g x +f \right )^{\frac {3}{2}} \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.42 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{\frac {3}{2}} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 7.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int \frac {1}{\left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right ) \left (f + g x\right )^{\frac {3}{2}}}\, dx \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 166, normalized size of antiderivative = 6.38 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{\frac {3}{2}} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{\frac {3}{2}} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 1.34 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx=\int \frac {1}{{\left (f+g\,x\right )}^{3/2}\,\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )} \,d x \]
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