Integrand size = 32, antiderivative size = 32 \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\text {Int}\left (\frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}},x\right ) \]
[Out]
Not integrable
Time = 0.07 (sec) , antiderivative size = 32, 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 = {} \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx \\ \end{align*}
Not integrable
Time = 4.00 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx \]
[In]
[Out]
Not integrable
Time = 0.18 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88
\[\int \frac {\sqrt {h x +g}}{\sqrt {a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}}d x\]
[In]
[Out]
Exception generated. \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 1.06 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.91 \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\int \frac {\sqrt {g + h x}}{\sqrt {a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}}}\, dx \]
[In]
[Out]
Not integrable
Time = 11.08 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94 \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\int { \frac {\sqrt {h x + g}}{\sqrt {b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.37 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94 \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\int { \frac {\sqrt {h x + g}}{\sqrt {b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.31 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94 \[ \int \frac {\sqrt {g+h x}}{\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}} \, dx=\int \frac {\sqrt {g+h\,x}}{\sqrt {a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )}} \,d x \]
[In]
[Out]