\[ \int \sinh ^4(c+d x) \left (a+b \tanh ^3(c+d x)\right )^3 \, dx \]
Optimal antiderivative \[ \frac {3 a \left (a^{2}+63 b^{2}\right ) x}{8}+\frac {3 b \left (3 a^{2}+5 b^{2}\right ) \ln \left (\cosh \left (d x +c \right )\right )}{d}-\frac {18 a \,b^{2} \tanh \left (d x +c \right )}{d}-\frac {b \left (3 a^{2}+10 b^{2}\right ) \left (\tanh ^{2}\left (d x +c \right )\right )}{2 d}-\frac {3 a \,b^{2} \left (\tanh ^{3}\left (d x +c \right )\right )}{d}-\frac {3 b^{3} \left (\tanh ^{4}\left (d x +c \right )\right )}{2 d}-\frac {3 a \,b^{2} \left (\tanh ^{5}\left (d x +c \right )\right )}{5 d}-\frac {b^{3} \left (\tanh ^{6}\left (d x +c \right )\right )}{2 d}-\frac {b^{3} \left (\tanh ^{8}\left (d x +c \right )\right )}{8 d}+\frac {\left (\cosh ^{3}\left (d x +c \right )\right ) \sinh \left (d x +c \right ) \left (a \left (a^{2}+3 b^{2}\right )+b \left (3 a^{2}+b^{2}\right ) \tanh \left (d x +c \right )\right )}{4 d}-\frac {\cosh \left (d x +c \right ) \sinh \left (d x +c \right ) \left (a \left (5 a^{2}+51 b^{2}\right )+2 b \left (15 a^{2}+11 b^{2}\right ) \tanh \left (d x +c \right )\right )}{8 d} \]
command
integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^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 \[ \text {Timed out} \]