3.397 \(\int x^m \coth (a+b x) \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (x^m \coth (a+b x),x\right ) \]

[Out]

Unintegrable(x^m*coth(b*x+a),x)

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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 = {} \[ \int x^m \coth (a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^m*Coth[a + b*x],x]

[Out]

Defer[Int][x^m*Coth[a + b*x], x]

Rubi steps

\begin {align*} \int x^m \coth (a+b x) \, dx &=\int x^m \coth (a+b x) \, dx\\ \end {align*}

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Mathematica [A]  time = 7.58, size = 0, normalized size = 0.00 \[ \int x^m \coth (a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^m*Coth[a + b*x],x]

[Out]

Integrate[x^m*Coth[a + b*x], x]

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fricas [A]  time = 0.82, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} \cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*cosh(b*x+a)*csch(b*x+a),x, algorithm="fricas")

[Out]

integral(x^m*cosh(b*x + a)*csch(b*x + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*cosh(b*x+a)*csch(b*x+a),x, algorithm="giac")

[Out]

integrate(x^m*cosh(b*x + a)*csch(b*x + a), x)

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maple [A]  time = 0.21, size = 0, normalized size = 0.00 \[ \int x^{m} \cosh \left (b x +a \right ) \mathrm {csch}\left (b x +a \right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*cosh(b*x+a)*csch(b*x+a),x)

[Out]

int(x^m*cosh(b*x+a)*csch(b*x+a),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {x e^{\left (2 \, b x + m \log \relax (x) + 2 \, a\right )}}{{\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} - m - 1} + \int \frac {{\left ({\left (2 \, b x e^{\left (2 \, a\right )} + {\left (m + 1\right )} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )} - m - 1\right )} x^{m}}{{\left (m + 1\right )} e^{\left (4 \, b x + 4 \, a\right )} - 2 \, {\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} + m + 1}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*cosh(b*x+a)*csch(b*x+a),x, algorithm="maxima")

[Out]

x*e^(2*b*x + m*log(x) + 2*a)/((m + 1)*e^(2*b*x + 2*a) - m - 1) + integrate(((2*b*x*e^(2*a) + (m + 1)*e^(2*a))*
e^(2*b*x) - m - 1)*x^m/((m + 1)*e^(4*b*x + 4*a) - 2*(m + 1)*e^(2*b*x + 2*a) + m + 1), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {x^m\,\mathrm {cosh}\left (a+b\,x\right )}{\mathrm {sinh}\left (a+b\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*cosh(b*x+a)*csch(b*x+a),x)

[Out]

Integral(x**m*cosh(a + b*x)*csch(a + b*x), x)

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