Integrand size = 22, antiderivative size = 22 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\frac {x^{-2 n} (e x)^{2 n} \text {Int}\left (x^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p,x\right )}{e} \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 22, 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 = {} \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\left (x^{-2 n} (e x)^{2 n}\right ) \int x^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx}{e} \\ \end{align*}
Not integrable
Time = 4.38 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx \]
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Not integrable
Time = 0.69 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
\[\int \left (e x \right )^{-1+2 n} {\left (b \sinh \left (c +d \,x^{n}\right )\right )}^{p}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{2 \, n - 1} \left (b \sinh \left (d x^{n} + c\right )\right )^{p} \,d x } \]
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Not integrable
Time = 9.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int \left (b \sinh {\left (c + d x^{n} \right )}\right )^{p} \left (e x\right )^{2 n - 1}\, dx \]
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Not integrable
Time = 0.47 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{2 \, n - 1} \left (b \sinh \left (d x^{n} + c\right )\right )^{p} \,d x } \]
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Not integrable
Time = 1.40 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int { \left (e x\right )^{2 \, n - 1} \left (b \sinh \left (d x^{n} + c\right )\right )^{p} \,d x } \]
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Not integrable
Time = 1.09 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (e x)^{-1+2 n} \left (b \sinh \left (c+d x^n\right )\right )^p \, dx=\int {\left (b\,\mathrm {sinh}\left (c+d\,x^n\right )\right )}^p\,{\left (e\,x\right )}^{2\,n-1} \,d x \]
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