3.71 \(\int (e x)^m (a+b \text{csch}(c+d x^n))^p \, dx\)

Optimal. Leaf size=31 \[ x^{-m} (e x)^m \text{Unintegrable}\left (x^m \left (a+b \text{csch}\left (c+d x^n\right )\right )^p,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0553266, 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 = {} \[ \int (e x)^m \left (a+b \text{csch}\left (c+d x^n\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 17.2655, size = 0, normalized size = 0. \[ \int (e x)^m \left (a+b \text{csch}\left (c+d x^n\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.282, size = 0, normalized size = 0. \begin{align*} \int \left ( ex \right ) ^{m} \left ( a+b{\rm csch} \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*(a+b*csch(c+d*x^n))^p,x)

[Out]

int((e*x)^m*(a+b*csch(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 \operatorname{csch}\left (d x^{n} + c\right ) + a\right )}^{p}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((e*x)^m*(b*csch(d*x^n + c) + a)^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 \operatorname{csch}\left (d x^{n} + c\right ) + a\right )}^{p}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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