Optimal. Leaf size=37 \[ \text {Int}\left (\frac {\text {csch}^3(c+d x) \text {sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.09, 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 = {} \[ \int \frac {\text {csch}^3(c+d x) \text {sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\text {csch}^3(c+d x) \text {sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac {\text {csch}^3(c+d x) \text {sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 158.10, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^3(c+d x) \text {sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 83.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (d x + c\right )^{3} \operatorname {sech}\left (d x + c\right )}{a f x + a e + {\left (b f x + b e\right )} \sinh \left (d x + c\right )}, x\right ) \]
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 = 4.13, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (d x +c \right )^{3} \mathrm {sech}\left (d x +c \right )}{\left (f x +e \right ) \left (a +b \sinh \left (d x +c \right )\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {a f - 2 \, {\left (b d f x e^{\left (3 \, c\right )} + b d e e^{\left (3 \, c\right )}\right )} e^{\left (3 \, d x\right )} + {\left (2 \, a d f x e^{\left (2 \, c\right )} + {\left (2 \, d e - f\right )} a e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )} + 2 \, {\left (b d f x e^{c} + b d e e^{c}\right )} e^{\left (d x\right )}}{a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + a^{2} d^{2} e^{2} + {\left (a^{2} d^{2} f^{2} x^{2} e^{\left (4 \, c\right )} + 2 \, a^{2} d^{2} e f x e^{\left (4 \, c\right )} + a^{2} d^{2} e^{2} e^{\left (4 \, c\right )}\right )} e^{\left (4 \, d x\right )} - 2 \, {\left (a^{2} d^{2} f^{2} x^{2} e^{\left (2 \, c\right )} + 2 \, a^{2} d^{2} e f x e^{\left (2 \, c\right )} + a^{2} d^{2} e^{2} e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )}} - 16 \, \int \frac {b^{2} d^{2} e^{2} + a b d e f - {\left (d^{2} e^{2} - f^{2}\right )} a^{2} - {\left (a^{2} d^{2} f^{2} - b^{2} d^{2} f^{2}\right )} x^{2} - {\left (2 \, a^{2} d^{2} e f - 2 \, b^{2} d^{2} e f - a b d f^{2}\right )} x}{16 \, {\left (a^{3} d^{2} f^{3} x^{3} + 3 \, a^{3} d^{2} e f^{2} x^{2} + 3 \, a^{3} d^{2} e^{2} f x + a^{3} d^{2} e^{3} - {\left (a^{3} d^{2} f^{3} x^{3} e^{c} + 3 \, a^{3} d^{2} e f^{2} x^{2} e^{c} + 3 \, a^{3} d^{2} e^{2} f x e^{c} + a^{3} d^{2} e^{3} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} + 16 \, \int -\frac {b^{2} d^{2} e^{2} - a b d e f - {\left (d^{2} e^{2} - f^{2}\right )} a^{2} - {\left (a^{2} d^{2} f^{2} - b^{2} d^{2} f^{2}\right )} x^{2} - {\left (2 \, a^{2} d^{2} e f - 2 \, b^{2} d^{2} e f + a b d f^{2}\right )} x}{16 \, {\left (a^{3} d^{2} f^{3} x^{3} + 3 \, a^{3} d^{2} e f^{2} x^{2} + 3 \, a^{3} d^{2} e^{2} f x + a^{3} d^{2} e^{3} + {\left (a^{3} d^{2} f^{3} x^{3} e^{c} + 3 \, a^{3} d^{2} e f^{2} x^{2} e^{c} + 3 \, a^{3} d^{2} e^{2} f x e^{c} + a^{3} d^{2} e^{3} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} + 16 \, \int -\frac {a b^{4} e^{\left (d x + c\right )} - b^{5}}{8 \, {\left (a^{5} b e + a^{3} b^{3} e + {\left (a^{5} b f + a^{3} b^{3} f\right )} x - {\left (a^{5} b e e^{\left (2 \, c\right )} + a^{3} b^{3} e e^{\left (2 \, c\right )} + {\left (a^{5} b f e^{\left (2 \, c\right )} + a^{3} b^{3} f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\right )} - 2 \, {\left (a^{6} e e^{c} + a^{4} b^{2} e e^{c} + {\left (a^{6} f e^{c} + a^{4} b^{2} f e^{c}\right )} x\right )} e^{\left (d x\right )}\right )}}\,{d x} + 16 \, \int \frac {b e^{\left (d x + c\right )} - a}{8 \, {\left (a^{2} e + b^{2} e + {\left (a^{2} f + b^{2} f\right )} x + {\left (a^{2} e e^{\left (2 \, c\right )} + b^{2} e e^{\left (2 \, c\right )} + {\left (a^{2} f e^{\left (2 \, c\right )} + b^{2} 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 \[ \int \frac {1}{\mathrm {cosh}\left (c+d\,x\right )\,{\mathrm {sinh}\left (c+d\,x\right )}^3\,\left (e+f\,x\right )\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \]
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]
________________________________________________________________________________________