\[ \int \left (b \coth ^3(c+d x)\right )^{4/3} \, dx \]
Optimal antiderivative \[ -\frac {b \left (b \left (\coth ^{3}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}{d}-\frac {b \left (\coth ^{2}\left (d x +c \right )\right ) \left (b \left (\coth ^{3}\left (d x +c \right )\right )\right )^{\frac {1}{3}}}{3 d}+b x \left (b \left (\coth ^{3}\left (d x +c \right )\right )\right )^{\frac {1}{3}} \tanh \left (d x +c \right ) \]
command
integrate((b*coth(d*x+c)**3)**(4/3),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} x \left (b \coth ^{3}{\left (c \right )}\right )^{\frac {4}{3}} & \text {for}\: d = 0 \\- \frac {\left (b \coth ^{3}{\left (d x + \log {\left (- e^{- d x} \right )} \right )}\right )^{\frac {4}{3}} \log {\left (- e^{- d x} \right )}}{d} & \text {for}\: c = \log {\left (- e^{- d x} \right )} \\- \frac {\left (b \coth ^{3}{\left (d x + \log {\left (e^{- d x} \right )} \right )}\right )^{\frac {4}{3}} \log {\left (e^{- d x} \right )}}{d} & \text {for}\: c = \log {\left (e^{- d x} \right )} \\x \left (\frac {b}{\tanh ^{3}{\left (c + d x \right )}}\right )^{\frac {4}{3}} \tanh ^{4}{\left (c + d x \right )} - \frac {\left (\frac {b}{\tanh ^{3}{\left (c + d x \right )}}\right )^{\frac {4}{3}} \tanh ^{3}{\left (c + d x \right )}}{d} - \frac {\left (\frac {b}{\tanh ^{3}{\left (c + d x \right )}}\right )^{\frac {4}{3}} \tanh {\left (c + d x \right )}}{3 d} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________