Integrand size = 35, antiderivative size = 35 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\text {Int}\left (\frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )},x\right ) \]
[Out]
Not integrable
Time = 0.19 (sec) , antiderivative size = 35, 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 = {} \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.61 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \]
[In]
[Out]
Not integrable
Time = 0.33 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (h x +g \right ) \left (j x +i \right ) \left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}d x\]
[In]
[Out]
Not integrable
Time = 0.34 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.86 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int { \frac {1}{{\left (h x + g\right )} {\left (j x + i\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 3.73 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right ) \left (g + h x\right ) \left (i + j x\right )}\, dx \]
[In]
[Out]
Not integrable
Time = 0.88 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int { \frac {1}{{\left (h x + g\right )} {\left (j x + i\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.29 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int { \frac {1}{{\left (h x + g\right )} {\left (j x + i\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx=\int \frac {1}{\left (g+h\,x\right )\,\left (i+j\,x\right )\,\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )} \,d x \]
[In]
[Out]