Integrand size = 26, antiderivative size = 26 \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\text {Int}\left ((f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2},x\right ) \]
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Not integrable
Time = 0.04 (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 = {} \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx \\ \end{align*}
Not integrable
Time = 9.50 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx \]
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Not integrable
Time = 0.15 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92
\[\int \left (g x +f \right )^{m} {\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )}^{\frac {3}{2}}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.85 \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\int { {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {3}{2}} {\left (g x + f\right )}^{m} \,d x } \]
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Timed out. \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\text {Timed out} \]
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Not integrable
Time = 0.67 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\int { {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {3}{2}} {\left (g x + f\right )}^{m} \,d x } \]
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Not integrable
Time = 1.86 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\int { {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {3}{2}} {\left (g x + f\right )}^{m} \,d x } \]
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Not integrable
Time = 1.41 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx=\int {\left (f+g\,x\right )}^m\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^{3/2} \,d x \]
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