\(\int (c+d x)^m \text {csch}^2(a+b x) \, dx\) [77]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\text {Int}\left ((c+d x)^m \text {csch}^2(a+b x),x\right ) \]

[Out]

Unintegrable((d*x+c)^m*csch(b*x+a)^2,x)

Rubi [N/A]

Not integrable

Time = 0.02 (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 = {} \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int (c+d x)^m \text {csch}^2(a+b x) \, dx \]

[In]

Int[(c + d*x)^m*Csch[a + b*x]^2,x]

[Out]

Defer[Int][(c + d*x)^m*Csch[a + b*x]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \text {csch}^2(a+b x) \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 3.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int (c+d x)^m \text {csch}^2(a+b x) \, dx \]

[In]

Integrate[(c + d*x)^m*Csch[a + b*x]^2,x]

[Out]

Integrate[(c + d*x)^m*Csch[a + b*x]^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.34 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

\[\int \left (d x +c \right )^{m} \operatorname {csch}\left (b x +a \right )^{2}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \operatorname {csch}\left (b x + a\right )^{2} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int \left (c + d x\right )^{m} \operatorname {csch}^{2}{\left (a + b x \right )}\, dx \]

[In]

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

[Out]

Integral((c + d*x)**m*csch(a + b*x)**2, x)

Maxima [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \operatorname {csch}\left (b x + a\right )^{2} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \operatorname {csch}\left (b x + a\right )^{2} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 0.84 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {csch}^2(a+b x) \, dx=\int \frac {{\left (c+d\,x\right )}^m}{{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]

[In]

int((c + d*x)^m/sinh(a + b*x)^2,x)

[Out]

int((c + d*x)^m/sinh(a + b*x)^2, x)