Integrand size = 30, antiderivative size = 30 \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\text {Int}\left ((g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2},x\right ) \]
[Out]
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 = {} \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int (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 = 15.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx \]
[In]
[Out]
Not integrable
Time = 0.20 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
\[\int \left (h x +g \right )^{m} {\left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}^{\frac {3}{2}}d x\]
[In]
[Out]
Not integrable
Time = 0.30 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.87 \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\int { {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}} {\left (h x + g\right )}^{m} \,d x } \]
[In]
[Out]
Timed out. \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 11.31 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\int { {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}} {\left (h x + g\right )}^{m} \,d x } \]
[In]
[Out]
Not integrable
Time = 3.23 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\int { {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{\frac {3}{2}} {\left (h x + g\right )}^{m} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.33 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2} \, dx=\int {\left (g+h\,x\right )}^m\,{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^{3/2} \,d x \]
[In]
[Out]