\(\int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx\) [466]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\text {Int}\left (x^m \text {csch}(a+b x) \text {sech}(a+b x),x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.17 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx \]

[In]

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

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 8.76 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.10 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

\[\int x^{m} \operatorname {csch}\left (b x +a \right ) \operatorname {sech}\left (b x +a \right )d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int { x^{m} \operatorname {csch}\left (b x + a\right ) \operatorname {sech}\left (b x + a\right ) \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int x^{m} \operatorname {csch}{\left (a + b x \right )} \operatorname {sech}{\left (a + b x \right )}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int { x^{m} \operatorname {csch}\left (b x + a\right ) \operatorname {sech}\left (b x + a\right ) \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int { x^{m} \operatorname {csch}\left (b x + a\right ) \operatorname {sech}\left (b x + a\right ) \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 2.39 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38 \[ \int x^m \text {csch}(a+b x) \text {sech}(a+b x) \, dx=\int \frac {x^m}{\mathrm {cosh}\left (a+b\,x\right )\,\mathrm {sinh}\left (a+b\,x\right )} \,d x \]

[In]

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

[Out]

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