\[ \int \frac {1}{(a+b \cosh (x)+c \sinh (x))^4} \, dx \]
Optimal antiderivative \[ -\frac {a \left (2 a^{2}+3 b^{2}-3 c^{2}\right ) \arctanh \left (\frac {c -\left (a -b \right ) \tanh \left (\frac {x}{2}\right )}{\sqrt {a^{2}-b^{2}+c^{2}}}\right )}{\left (a^{2}-b^{2}+c^{2}\right )^{\frac {7}{2}}}+\frac {-c \cosh \left (x \right )-b \sinh \left (x \right )}{3 \left (a^{2}-b^{2}+c^{2}\right ) \left (a +b \cosh \left (x \right )+c \sinh \left (x \right )\right )^{3}}-\frac {5 \left (a c \cosh \left (x \right )+a b \sinh \left (x \right )\right )}{6 \left (a^{2}-b^{2}+c^{2}\right )^{2} \left (a +b \cosh \left (x \right )+c \sinh \left (x \right )\right )^{2}}+\frac {-c \left (11 a^{2}+4 b^{2}-4 c^{2}\right ) \cosh \left (x \right )-b \left (11 a^{2}+4 b^{2}-4 c^{2}\right ) \sinh \left (x \right )}{6 \left (a^{2}-b^{2}+c^{2}\right )^{3} \left (a +b \cosh \left (x \right )+c \sinh \left (x \right )\right )} \]
command
integrate(1/(a+b*cosh(x)+c*sinh(x))^4,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]