### 3.341 $$\int x^m \text{sech}(a+b x) \tanh (a+b x) \, dx$$

Optimal. Leaf size=18 $\text{CannotIntegrate}\left (x^m \tanh (a+b x) \text{sech}(a+b x),x\right )$

[Out]

CannotIntegrate[x^m*Sech[a + b*x]*Tanh[a + b*x], x]

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Rubi [A]  time = 0.394424, 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 = {} $\int x^m \text{sech}(a+b x) \tanh (a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 3.16931, size = 0, normalized size = 0. $\int x^m \text{sech}(a+b x) \tanh (a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.033, size = 0, normalized size = 0. \begin{align*} \int{x}^{m} \left ({\rm sech} \left (bx+a\right ) \right ) ^{2}\sinh \left ( bx+a \right ) \, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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