3.5.31 \(\int x^m \coth ^2(a+b x) \, dx\) [431]

Optimal. Leaf size=15 \[ \text {Int}\left (x^m \coth ^2(a+b x),x\right ) \]

[Out]

Unintegrable(x^m*coth(b*x+a)^2,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 = {} \begin {gather*} \int x^m \coth ^2(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^m*Coth[a + b*x]^2,x]

[Out]

Defer[Int][x^m*Coth[a + b*x]^2, x]

Rubi steps

\begin {align*} \int x^m \coth ^2(a+b x) \, dx &=\int x^m \coth ^2(a+b x) \, dx\\ \end {align*}

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Mathematica [A]
time = 6.83, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \coth ^2(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^m*Coth[a + b*x]^2,x]

[Out]

Integrate[x^m*Coth[a + b*x]^2, x]

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Maple [A]
time = 1.22, size = 0, normalized size = 0.00 \[\int x^{m} \left (\cosh ^{2}\left (b x +a \right )\right ) \mathrm {csch}\left (b x +a \right )^{2}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*cosh(b*x+a)^2*csch(b*x+a)^2,x)

[Out]

int(x^m*cosh(b*x+a)^2*csch(b*x+a)^2,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(x^m*cosh(b*x+a)^2*csch(b*x+a)^2,x, algorithm="maxima")

[Out]

x*e^(4*b*x + m*log(x) + 4*a)/((m + 1)*e^(4*b*x + 4*a) - 2*(m + 1)*e^(2*b*x + 2*a) + m + 1) + integrate((2*(2*b
*x*e^(4*a) + (m + 1)*e^(4*a))*e^(4*b*x) - (m + 1)*e^(2*b*x + 2*a) - m - 1)*x^m/((m + 1)*e^(6*b*x + 6*a) - 3*(m
+ 1)*e^(4*b*x + 4*a) + 3*(m + 1)*e^(2*b*x + 2*a) - m - 1), 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(x^m*cosh(b*x+a)^2*csch(b*x+a)^2,x, algorithm="fricas")

[Out]

integral(x^m*cosh(b*x + a)^2*csch(b*x + a)^2, x)

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*cosh(b*x+a)**2*csch(b*x+a)**2,x)

[Out]

Exception raised: SystemError >> excessive stack use: stack is 5007 deep

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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(x^m*cosh(b*x+a)^2*csch(b*x+a)^2,x, algorithm="giac")

[Out]

integrate(x^m*cosh(b*x + a)^2*csch(b*x + a)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {x^m\,{\mathrm {cosh}\left (a+b\,x\right )}^2}{{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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