Integrand size = 20, antiderivative size = 20 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=x^{-m} (e x)^m \text {Int}\left (x^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p,x\right ) \]
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Not integrable
Time = 0.04 (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 = {} \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \left (x^{-m} (e x)^m\right ) \int x^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx \\ \end{align*}
Not integrable
Time = 20.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \left (e x \right )^{m} {\left (a +b \,\operatorname {sech}\left (c +d \,x^{n}\right )\right )}^{p}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{m} {\left (b \operatorname {sech}\left (d x^{n} + c\right ) + a\right )}^{p} \,d x } \]
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Not integrable
Time = 44.28 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int \left (e x\right )^{m} \left (a + b \operatorname {sech}{\left (c + d x^{n} \right )}\right )^{p}\, dx \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{m} {\left (b \operatorname {sech}\left (d x^{n} + c\right ) + a\right )}^{p} \,d x } \]
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Not integrable
Time = 0.78 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{m} {\left (b \operatorname {sech}\left (d x^{n} + c\right ) + a\right )}^{p} \,d x } \]
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Not integrable
Time = 2.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx=\int {\left (a+\frac {b}{\mathrm {cosh}\left (c+d\,x^n\right )}\right )}^p\,{\left (e\,x\right )}^m \,d x \]
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