3.41 \(\int (e x)^m (b \cosh (c+d x^n))^p \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left ((e x)^m \left (b \cosh \left (c+d x^n\right )\right )^p,x\right ) \]

[Out]

Unintegrable[(e*x)^m*(b*Cosh[c + d*x^n])^p, x]

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Rubi [A]  time = 0.0222553, 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 = {} \[ \int (e x)^m \left (b \cosh \left (c+d x^n\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Int[(e*x)^m*(b*Cosh[c + d*x^n])^p,x]

[Out]

Defer[Int][(e*x)^m*(b*Cosh[c + d*x^n])^p, x]

Rubi steps

\begin{align*} \int (e x)^m \left (b \cosh \left (c+d x^n\right )\right )^p \, dx &=\int (e x)^m \left (b \cosh \left (c+d x^n\right )\right )^p \, dx\\ \end{align*}

Mathematica [A]  time = 5.23851, size = 0, normalized size = 0. \[ \int (e x)^m \left (b \cosh \left (c+d x^n\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(e*x)^m*(b*Cosh[c + d*x^n])^p,x]

[Out]

Integrate[(e*x)^m*(b*Cosh[c + d*x^n])^p, x]

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Maple [A]  time = 0.698, size = 0, normalized size = 0. \begin{align*} \int \left ( ex \right ) ^{m} \left ( b\cosh \left ( c+d{x}^{n} \right ) \right ) ^{p}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m*(b*cosh(c+d*x^n))^p,x)

[Out]

int((e*x)^m*(b*cosh(c+d*x^n))^p,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \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.

[In]

integrate((e*x)^m*(b*cosh(c+d*x^n))^p,x, algorithm="maxima")

[Out]

integrate((e*x)^m*(b*cosh(d*x^n + c))^p, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\left (e x\right )^{m} \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.

[In]

integrate((e*x)^m*(b*cosh(c+d*x^n))^p,x, algorithm="fricas")

[Out]

integral((e*x)^m*(b*cosh(d*x^n + c))^p, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (b \cosh{\left (c + d x^{n} \right )}\right )^{p} \left (e x\right )^{m}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)**m*(b*cosh(c+d*x**n))**p,x)

[Out]

Integral((b*cosh(c + d*x**n))**p*(e*x)**m, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \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.

[In]

integrate((e*x)^m*(b*cosh(c+d*x^n))^p,x, algorithm="giac")

[Out]

integrate((e*x)^m*(b*cosh(d*x^n + c))^p, x)