Integrand size = 26, antiderivative size = 26 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\text {Int}\left (\frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n},x\right ) \]
[Out]
Not integrable
Time = 0.01 (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 = {} \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx \\ \end{align*}
Not integrable
Time = 0.80 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx \]
[In]
[Out]
Not integrable
Time = 0.13 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00
\[\int \frac {\left (a +b \,x^{n}+c \,x^{2 n}\right )^{p}}{d +e \,x^{n}}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\int { \frac {{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{e x^{n} + d} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\int { \frac {{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{e x^{n} + d} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.37 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\int { \frac {{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{e x^{n} + d} \,d x } \]
[In]
[Out]
Not integrable
Time = 10.36 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx=\int \frac {{\left (a+b\,x^n+c\,x^{2\,n}\right )}^p}{d+e\,x^n} \,d x \]
[In]
[Out]