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

Optimal. Leaf size=26 \[ x^{-m} (e x)^m \text {Int}\left (x^m \text {csch}\left (a+\frac {b}{x}\right ),x\right ) \]

[Out]

(e*x)^m*Unintegrable(x^m*csch(a+b/x),x)/(x^m)

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Rubi [A]  time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (e x)^m \text {csch}\left (a+\frac {b}{x}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[(e*x)^m*Csch[a + b/x],x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 3.42, size = 0, normalized size = 0.00 \[ \int (e x)^m \text {csch}\left (a+\frac {b}{x}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(e*x)^m*Csch[a + b/x],x]

[Out]

Integrate[(e*x)^m*Csch[a + b/x], x]

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\left (e x\right )^{m}}{\sinh \left (\frac {a x + b}{x}\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (e x\right )^{m}}{\sinh \left (a + \frac {b}{x}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((e*x)^m/sinh(a + b/x), x)

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maple [A]  time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\left (e x \right )^{m}}{\sinh \left (a +\frac {b}{x}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (e x\right )^{m}}{\sinh \left (a + \frac {b}{x}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((e*x)^m/sinh(a + b/x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (e\,x\right )}^m}{\mathrm {sinh}\left (a+\frac {b}{x}\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m/sinh(a + b/x),x)

[Out]

int((e*x)^m/sinh(a + b/x), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (e x\right )^{m}}{\sinh {\left (a + \frac {b}{x} \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral((e*x)**m/sinh(a + b/x), x)

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