3.5.73 \(\int x^m \text {csch}(a+b x) \text {sech}^2(a+b x) \, dx\) [473]

Optimal. Leaf size=21 \[ \text {Int}\left (x^m \text {csch}(a+b x) \text {sech}^2(a+b x),x\right ) \]

[Out]

CannotIntegrate(x^m*csch(b*x+a)*sech(b*x+a)^2,x)

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Rubi [A]
time = 0.36, 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 \text {csch}(a+b x) \text {sech}^2(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^m*Csch[a + b*x]*Sech[a + b*x]^2,x]

[Out]

Defer[Int][x^m*Csch[a + b*x]*Sech[a + b*x]^2, x]

Rubi steps

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

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Mathematica [A]
time = 83.63, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \text {csch}(a+b x) \text {sech}^2(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^m*Csch[a + b*x]*Sech[a + b*x]^2,x]

[Out]

Integrate[x^m*Csch[a + b*x]*Sech[a + b*x]^2, x]

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Maple [A]
time = 0.77, size = 0, normalized size = 0.00 \[\int x^{m} \mathrm {csch}\left (b x +a \right ) \mathrm {sech}\left (b x +a \right )^{2}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

integrate(x^m*csch(b*x + a)*sech(b*x + a)^2, 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*csch(b*x+a)*sech(b*x+a)^2,x, algorithm="fricas")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {x^m}{{\mathrm {cosh}\left (a+b\,x\right )}^2\,\mathrm {sinh}\left (a+b\,x\right )} \,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)),x)

[Out]

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

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