\[ \int \frac {1}{\left (b \coth ^2(c+d x)\right )^{4/3}} \, dx \]
Optimal antiderivative \[ \frac {\arctanh \left (\coth ^{\frac {1}{3}}\left (d x +c \right )\right ) \left (\coth ^{\frac {2}{3}}\left (d x +c \right )\right )}{b d \left (b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}-\frac {\left (\coth ^{\frac {2}{3}}\left (d x +c \right )\right ) \ln \left (1-\left (\coth ^{\frac {1}{3}}\left (d x +c \right )\right )+\coth ^{\frac {2}{3}}\left (d x +c \right )\right )}{4 b d \left (b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}+\frac {\left (\coth ^{\frac {2}{3}}\left (d x +c \right )\right ) \ln \left (1+\coth ^{\frac {1}{3}}\left (d x +c \right )+\coth ^{\frac {2}{3}}\left (d x +c \right )\right )}{4 b d \left (b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}-\frac {\arctan \left (\frac {\left (1-2 \left (\coth ^{\frac {1}{3}}\left (d x +c \right )\right )\right ) \sqrt {3}}{3}\right ) \left (\coth ^{\frac {2}{3}}\left (d x +c \right )\right ) \sqrt {3}}{2 b d \left (b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}+\frac {\arctan \left (\frac {\left (1+2 \left (\coth ^{\frac {1}{3}}\left (d x +c \right )\right )\right ) \sqrt {3}}{3}\right ) \left (\coth ^{\frac {2}{3}}\left (d x +c \right )\right ) \sqrt {3}}{2 b d \left (b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}-\frac {3 \tanh \left (d x +c \right )}{5 b d \left (b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {1}{3}}} \]
command
integrate(1/(b*coth(d*x+c)^2)^(4/3),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 \[ \text {Timed out} \]