Integrand size = 20, antiderivative size = 20 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\text {Int}\left ((e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p,x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 20, 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 = {} \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx \\ \end{align*}
Not integrable
Time = 1.67 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \left (e x \right )^{m} {\left (a +b \cos \left (c +d \,x^{n}\right )\right )}^{p}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{m} {\left (b \cos \left (d x^{n} + c\right ) + a\right )}^{p} \,d x } \]
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Not integrable
Time = 27.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int \left (e x\right )^{m} \left (a + b \cos {\left (c + d x^{n} \right )}\right )^{p}\, dx \]
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Not integrable
Time = 1.61 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{m} {\left (b \cos \left (d x^{n} + c\right ) + a\right )}^{p} \,d x } \]
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Not integrable
Time = 5.77 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{m} {\left (b \cos \left (d x^{n} + c\right ) + a\right )}^{p} \,d x } \]
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Not integrable
Time = 13.10 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \cos \left (c+d x^n\right )\right )^p \, dx=\int {\left (e\,x\right )}^m\,{\left (a+b\,\cos \left (c+d\,x^n\right )\right )}^p \,d x \]
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