\[ \int \frac {1}{\text {sech}^2(a+b x)^{7/2}} \, dx \]
Optimal antiderivative \[ \frac {\tanh \left (b x +a \right )}{7 b \left (\mathrm {sech}\left (b x +a \right )^{2}\right )^{\frac {7}{2}}}+\frac {6 \tanh \left (b x +a \right )}{35 b \left (\mathrm {sech}\left (b x +a \right )^{2}\right )^{\frac {5}{2}}}+\frac {8 \tanh \left (b x +a \right )}{35 b \left (\mathrm {sech}\left (b x +a \right )^{2}\right )^{\frac {3}{2}}}+\frac {16 \tanh \left (b x +a \right )}{35 b \sqrt {\mathrm {sech}\left (b x +a \right )^{2}}} \]
command
integrate(1/(sech(b*x+a)**2)**(7/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {16 \tanh ^{7}{\left (a + b x \right )}}{35 b \left (\operatorname {sech}^{2}{\left (a + b x \right )}\right )^{\frac {7}{2}}} + \frac {8 \tanh ^{5}{\left (a + b x \right )}}{5 b \left (\operatorname {sech}^{2}{\left (a + b x \right )}\right )^{\frac {7}{2}}} - \frac {2 \tanh ^{3}{\left (a + b x \right )}}{b \left (\operatorname {sech}^{2}{\left (a + b x \right )}\right )^{\frac {7}{2}}} + \frac {\tanh {\left (a + b x \right )}}{b \left (\operatorname {sech}^{2}{\left (a + b x \right )}\right )^{\frac {7}{2}}} & \text {for}\: b \neq 0 \\\frac {x}{\left (\operatorname {sech}^{2}{\left (a \right )}\right )^{\frac {7}{2}}} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________