Integrand size = 26, antiderivative size = 26 \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\text {Int}\left (\left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p,x\right ) \]
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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 = {} \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx \\ \end{align*}
Not integrable
Time = 1.33 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00
\[\int \left (d +e \,x^{n}\right )^{q} \left (a +b \,x^{n}+c \,x^{2 n}\right )^{p}d x\]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\int { {\left (c x^{2 \, n} + b x^{n} + a\right )}^{p} {\left (e x^{n} + d\right )}^{q} \,d x } \]
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Timed out. \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\text {Timed out} \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\int { {\left (c x^{2 \, n} + b x^{n} + a\right )}^{p} {\left (e x^{n} + d\right )}^{q} \,d x } \]
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Not integrable
Time = 1.20 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\int { {\left (c x^{2 \, n} + b x^{n} + a\right )}^{p} {\left (e x^{n} + d\right )}^{q} \,d x } \]
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Not integrable
Time = 10.63 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx=\int {\left (d+e\,x^n\right )}^q\,{\left (a+b\,x^n+c\,x^{2\,n}\right )}^p \,d x \]
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