### 3.501 $$\int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx$$

Optimal. Leaf size=22 $\text{CannotIntegrate}\left (x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x),x\right )$

[Out]

CannotIntegrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^3, x]

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Rubi [A]  time = 0.57759, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[x^m*Csch[a + b*x]^2*Sech[a + b*x]^3,x]

[Out]

Defer[Int][x^m*Csch[a + b*x]^2*Sech[a + b*x]^3, x]

Rubi steps

\begin{align*} \int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx &=\int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx\\ \end{align*}

Mathematica [A]  time = 23.0535, size = 0, normalized size = 0. $\int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^3,x]

[Out]

Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^3, x]

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Maple [A]  time = 0.043, size = 0, normalized size = 0. \begin{align*} \int{x}^{m} \left ({\rm csch} \left (bx+a\right ) \right ) ^{2} \left ({\rm sech} \left (bx+a\right ) \right ) ^{3}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*csch(b*x+a)^2*sech(b*x+a)^3,x)

[Out]

int(x^m*csch(b*x+a)^2*sech(b*x+a)^3,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \operatorname{csch}\left (b x + a\right )^{2} \operatorname{sech}\left (b x + a\right )^{3}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*csch(b*x+a)^2*sech(b*x+a)^3,x, algorithm="maxima")

[Out]

integrate(x^m*csch(b*x + a)^2*sech(b*x + a)^3, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (x^{m} \operatorname{csch}\left (b x + a\right )^{2} \operatorname{sech}\left (b x + a\right )^{3}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*csch(b*x+a)^2*sech(b*x+a)^3,x, algorithm="fricas")

[Out]

integral(x^m*csch(b*x + a)^2*sech(b*x + a)^3, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \operatorname{csch}^{2}{\left (a + b x \right )} \operatorname{sech}^{3}{\left (a + b x \right )}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*csch(b*x+a)**2*sech(b*x+a)**3,x)

[Out]

Integral(x**m*csch(a + b*x)**2*sech(a + b*x)**3, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \operatorname{csch}\left (b x + a\right )^{2} \operatorname{sech}\left (b x + a\right )^{3}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*csch(b*x+a)^2*sech(b*x+a)^3,x, algorithm="giac")

[Out]

integrate(x^m*csch(b*x + a)^2*sech(b*x + a)^3, x)