3.1.27 \(\int (e x)^m \text {csch}(a+b x^2) \, dx\) [27]

Optimal. Leaf size=26 \[ x^{-m} (e x)^m \text {Int}\left (x^m \text {csch}\left (a+b x^2\right ),x\right ) \]

[Out]

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

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

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Mathematica [A]
time = 1.87, size = 0, normalized size = 0.00 \begin {gather*} \int (e x)^m \text {csch}\left (a+b x^2\right ) \, dx \end {gather*}

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 = 0.28, size = 0, normalized size = 0.00 \[\int \frac {\left (e x \right )^{m}}{\sinh \left (x^{2} b +a \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((x*e)^m/sinh(b*x^2 + a), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((x*e)^m/sinh(b*x^2 + a), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (e x\right )^{m}}{\sinh {\left (a + b x^{2} \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((e*x)^m/sinh(b*x^2 + a), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (e\,x\right )}^m}{\mathrm {sinh}\left (b\,x^2+a\right )} \,d x \end {gather*}

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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