Optimal. Leaf size=39 \[ \text {Int}\left (\frac {\text {csch}^2(c+d x) \text {sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.13, 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 = {} \[ \int \frac {\text {csch}^2(c+d x) \text {sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\text {csch}^2(c+d x) \text {sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac {\text {csch}^2(c+d x) \text {sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 153.97, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^2(c+d x) \text {sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.64, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (d x + c\right )^{2} \operatorname {sech}\left (d x + c\right )^{2}}{a f x + a e + {\left (b f x + b e\right )} \sinh \left (d x + c\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 2.20, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (d x +c \right )^{2} \mathrm {sech}\left (d x +c \right )^{2}}{\left (f x +e \right ) \left (a +b \sinh \left (d x +c \right )\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ 16 \, b^{4} \int -\frac {e^{\left (d x + c\right )}}{8 \, {\left (a^{4} b e + a^{2} b^{3} e + {\left (a^{4} b f + a^{2} b^{3} f\right )} x - {\left (a^{4} b e e^{\left (2 \, c\right )} + a^{2} b^{3} e e^{\left (2 \, c\right )} + {\left (a^{4} b f e^{\left (2 \, c\right )} + a^{2} b^{3} f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\right )} - 2 \, {\left (a^{5} e e^{c} + a^{3} b^{2} e e^{c} + {\left (a^{5} f e^{c} + a^{3} b^{2} f e^{c}\right )} x\right )} e^{\left (d x\right )}\right )}}\,{d x} + \frac {2 \, {\left (a b e^{\left (3 \, d x + 3 \, c\right )} + b^{2} e^{\left (2 \, d x + 2 \, c\right )} - a b e^{\left (d x + c\right )} + 2 \, a^{2} + b^{2}\right )}}{a^{3} d e + a b^{2} d e + {\left (a^{3} d f + a b^{2} d f\right )} x - {\left (a^{3} d e e^{\left (4 \, c\right )} + a b^{2} d e e^{\left (4 \, c\right )} + {\left (a^{3} d f e^{\left (4 \, c\right )} + a b^{2} d f e^{\left (4 \, c\right )}\right )} x\right )} e^{\left (4 \, d x\right )}} - 16 \, \int -\frac {b d f x + b d e + a f}{16 \, {\left (a^{2} d f^{2} x^{2} + 2 \, a^{2} d e f x + a^{2} d e^{2} - {\left (a^{2} d f^{2} x^{2} e^{c} + 2 \, a^{2} d e f x e^{c} + a^{2} d e^{2} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} - 16 \, \int \frac {b d f x + b d e - a f}{16 \, {\left (a^{2} d f^{2} x^{2} + 2 \, a^{2} d e f x + a^{2} d e^{2} + {\left (a^{2} d f^{2} x^{2} e^{c} + 2 \, a^{2} d e f x e^{c} + a^{2} d e^{2} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} - 16 \, \int \frac {b f e^{\left (d x + c\right )} - a f}{8 \, {\left (a^{2} d e^{2} + b^{2} d e^{2} + {\left (a^{2} d f^{2} + b^{2} d f^{2}\right )} x^{2} + 2 \, {\left (a^{2} d e f + b^{2} d e f\right )} x + {\left (a^{2} d e^{2} e^{\left (2 \, c\right )} + b^{2} d e^{2} e^{\left (2 \, c\right )} + {\left (a^{2} d f^{2} e^{\left (2 \, c\right )} + b^{2} d f^{2} e^{\left (2 \, c\right )}\right )} x^{2} + 2 \, {\left (a^{2} d e f e^{\left (2 \, c\right )} + b^{2} d e f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\right )}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {1}{{\mathrm {cosh}\left (c+d\,x\right )}^2\,{\mathrm {sinh}\left (c+d\,x\right )}^2\,\left (e+f\,x\right )\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________