Integrand size = 28, antiderivative size = 28 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\text {Int}\left (\frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3},x\right ) \]
[Out]
Not integrable
Time = 0.02 (sec) , antiderivative size = 28, 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 = {} \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx \\ \end{align*}
Not integrable
Time = 2.48 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx \]
[In]
[Out]
Not integrable
Time = 0.03 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
\[\int \frac {F^{f \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )^{2}\right )}}{\left (h x +g \right )^{3}}d x\]
[In]
[Out]
Not integrable
Time = 0.30 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.89 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{{\left (h x + g\right )}^{3}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.00 (sec) , antiderivative size = 1, normalized size of antiderivative = 0.04 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int \frac {F^{f \left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}^{2}\right )}}{\left (g + h x\right )^{3}} \, dx \]
[In]
[Out]
Not integrable
Time = 0.53 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{{\left (h x + g\right )}^{3}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.52 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{{\left (h x + g\right )}^{3}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.30 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^3} \, dx=\int \frac {{\mathrm {e}}^{f\,\ln \left (F\right )\,\left (b\,{\ln \left (c\,{\left (d+e\,x\right )}^n\right )}^2+a\right )}}{{\left (g+h\,x\right )}^3} \,d x \]
[In]
[Out]