Optimal. Leaf size=38 \[ \frac{x^{-2 n} (e x)^{2 n} \text{Unintegrable}\left (x^{2 n-1} \left (b \cosh \left (c+d x^n\right )\right )^p,x\right )}{e} \]
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Rubi [A] time = 0.0521985, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int (e x)^{-1+2 n} \left (b \cosh \left (c+d x^n\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (e x)^{-1+2 n} \left (b \cosh \left (c+d x^n\right )\right )^p \, dx &=\frac{\left (x^{-2 n} (e x)^{2 n}\right ) \int x^{-1+2 n} \left (b \cosh \left (c+d x^n\right )\right )^p \, dx}{e}\\ \end{align*}
Mathematica [A] time = 5.80854, size = 0, normalized size = 0. \[ \int (e x)^{-1+2 n} \left (b \cosh \left (c+d x^n\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.707, size = 0, normalized size = 0. \begin{align*} \int \left ( ex \right ) ^{-1+2\,n} \left ( b\cosh \left ( c+d{x}^{n} \right ) \right ) ^{p}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{2 \, n - 1} \left (b \cosh \left (d x^{n} + c\right )\right )^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\left (e x\right )^{2 \, n - 1} \left (b \cosh \left (d x^{n} + c\right )\right )^{p}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{2 \, n - 1} \left (b \cosh \left (d x^{n} + c\right )\right )^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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