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

Optimal. Leaf size=19 \[ \text {Int}\left (x^m \tanh (a+b x) \text {sech}(a+b x),x\right ) \]

[Out]

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

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Rubi [A]  time = 0.39, 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 = {} \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx \]

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*}

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Mathematica [A]  time = 22.29, size = 0, normalized size = 0.00 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx \]

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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fricas [A]  time = 0.67, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right ), x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )\,{d x} \]

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)

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maple [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int x^{m} \mathrm {sech}\left (b x +a \right )^{2} \sinh \left (b x +a \right )\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )\,{d x} \]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \sinh {\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \]

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]

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

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