\[ \int \frac {1}{a+b \sinh ^8(x)} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \left (\frac {\sqrt {\left (-a \right )^{\frac {1}{4}}-b^{\frac {1}{4}}}\, \tanh \left (x \right )}{\left (-a \right )^{\frac {1}{8}}}\right )}{4 \left (-a \right )^{\frac {7}{8}} \sqrt {\left (-a \right )^{\frac {1}{4}}-b^{\frac {1}{4}}}}-\frac {\arctanh \left (\frac {\sqrt {\left (-a \right )^{\frac {1}{4}}-i b^{\frac {1}{4}}}\, \tanh \left (x \right )}{\left (-a \right )^{\frac {1}{8}}}\right )}{4 \left (-a \right )^{\frac {7}{8}} \sqrt {\left (-a \right )^{\frac {1}{4}}-i b^{\frac {1}{4}}}}-\frac {\arctanh \left (\frac {\sqrt {\left (-a \right )^{\frac {1}{4}}+i b^{\frac {1}{4}}}\, \tanh \left (x \right )}{\left (-a \right )^{\frac {1}{8}}}\right )}{4 \left (-a \right )^{\frac {7}{8}} \sqrt {\left (-a \right )^{\frac {1}{4}}+i b^{\frac {1}{4}}}}-\frac {\arctanh \left (\frac {\sqrt {\left (-a \right )^{\frac {1}{4}}+b^{\frac {1}{4}}}\, \tanh \left (x \right )}{\left (-a \right )^{\frac {1}{8}}}\right )}{4 \left (-a \right )^{\frac {7}{8}} \sqrt {\left (-a \right )^{\frac {1}{4}}+b^{\frac {1}{4}}}} \]
command
integrate(1/(a+b*sinh(x)^8),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 \[ \text {Timed out} \]