Optimal. Leaf size=38 \[ \text{Unintegrable}\left (\frac{\sinh ^2(c+d x) \cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.125769, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [F] time = 180.001, size = 0, normalized size = 0. \[ \text{\$Aborted} \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.135, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \cosh \left ( dx+c \right ) \right ) ^{2} \left ( \sinh \left ( dx+c \right ) \right ) ^{2}}{ \left ( fx+e \right ) \left ( a+b\sinh \left ( dx+c \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} 2 \,{\left (a^{4} e^{c} + a^{2} b^{2} e^{c}\right )} \int -\frac{e^{\left (d x\right )}}{b^{5} f x + b^{5} e -{\left (b^{5} f x e^{\left (2 \, c\right )} + b^{5} e e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )} - 2 \,{\left (a b^{4} f x e^{c} + a b^{4} e e^{c}\right )} e^{\left (d x\right )}}\,{d x} + \frac{e^{\left (-3 \, c + \frac{3 \, d e}{f}\right )} E_{1}\left (\frac{3 \,{\left (f x + e\right )} d}{f}\right )}{8 \, b f} + \frac{a e^{\left (-2 \, c + \frac{2 \, d e}{f}\right )} E_{1}\left (\frac{2 \,{\left (f x + e\right )} d}{f}\right )}{4 \, b^{2} f} + \frac{a e^{\left (2 \, c - \frac{2 \, d e}{f}\right )} E_{1}\left (-\frac{2 \,{\left (f x + e\right )} d}{f}\right )}{4 \, b^{2} f} - \frac{e^{\left (3 \, c - \frac{3 \, d e}{f}\right )} E_{1}\left (-\frac{3 \,{\left (f x + e\right )} d}{f}\right )}{8 \, b f} + \frac{{\left (4 \, a^{2} + b^{2}\right )} e^{\left (-c + \frac{d e}{f}\right )} E_{1}\left (\frac{{\left (f x + e\right )} d}{f}\right )}{8 \, b^{3} f} - \frac{{\left (4 \, a^{2} e^{c} + b^{2} e^{c}\right )} e^{\left (-\frac{d e}{f}\right )} E_{1}\left (-\frac{{\left (f x + e\right )} d}{f}\right )}{8 \, b^{3} f} - \frac{{\left (2 \, a^{3} + a b^{2}\right )} \log \left (f x + e\right )}{2 \, b^{4} f} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cosh \left (d x + c\right )^{2} \sinh \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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \mathit{sage}_{0} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]