3.56 \(\int (e x)^m \text{csch}(a+\frac{b}{x^2}) \, dx\)

Optimal. Leaf size=25 \[ x^{-m} (e x)^m \text{Unintegrable}\left (x^m \text{csch}\left (a+\frac{b}{x^2}\right ),x\right ) \]

[Out]

((e*x)^m*Unintegrable[x^m*Csch[a + b/x^2], x])/x^m

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Rubi [A]  time = 0.0240249, 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 = {} \[ \int (e x)^m \text{csch}\left (a+\frac{b}{x^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[(e*x)^m*Csch[a + b/x^2],x]

[Out]

((e*x)^m*Defer[Int][x^m*Csch[a + b/x^2], x])/x^m

Rubi steps

\begin{align*} \int (e x)^m \text{csch}\left (a+\frac{b}{x^2}\right ) \, dx &=\left (x^{-m} (e x)^m\right ) \int x^m \text{csch}\left (a+\frac{b}{x^2}\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 3.13314, size = 0, normalized size = 0. \[ \int (e x)^m \text{csch}\left (a+\frac{b}{x^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(e*x)^m*Csch[a + b/x^2],x]

[Out]

Integrate[(e*x)^m*Csch[a + b/x^2], x]

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Maple [A]  time = 0.034, size = 0, normalized size = 0. \begin{align*} \int{ \left ( ex \right ) ^{m} \left ( \sinh \left ( a+{\frac{b}{{x}^{2}}} \right ) \right ) ^{-1}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m/sinh(a+b/x^2),x)

[Out]

int((e*x)^m/sinh(a+b/x^2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (e x\right )^{m}}{\sinh \left (a + \frac{b}{x^{2}}\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m/sinh(a+b/x^2),x, algorithm="maxima")

[Out]

integrate((e*x)^m/sinh(a + b/x^2), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\left (e x\right )^{m}}{\sinh \left (\frac{a x^{2} + b}{x^{2}}\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m/sinh(a+b/x^2),x, algorithm="fricas")

[Out]

integral((e*x)^m/sinh((a*x^2 + b)/x^2), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (e x\right )^{m}}{\sinh{\left (a + \frac{b}{x^{2}} \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)**m/sinh(a+b/x**2),x)

[Out]

Integral((e*x)**m/sinh(a + b/x**2), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (e x\right )^{m}}{\sinh \left (a + \frac{b}{x^{2}}\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m/sinh(a+b/x^2),x, algorithm="giac")

[Out]

integrate((e*x)^m/sinh(a + b/x^2), x)