6.6 Problem number 582

\[ \int \text {sech}^{\frac {23}{4}}(x) \sinh ^5(x) \, dx \]

Optimal antiderivative \[ -\frac {4 \mathrm {sech}\left (x \right )^{\frac {3}{4}}}{3}+\frac {8 \mathrm {sech}\left (x \right )^{\frac {11}{4}}}{11}-\frac {4 \mathrm {sech}\left (x \right )^{\frac {19}{4}}}{19} \]

command

integrate(sech(x)**(3/4)*tanh(x)**5,x)

Sympy 1.10.1 under Python 3.10.4 output

\[ - \frac {4 \tanh ^{4}{\left (x \right )} \operatorname {sech}^{\frac {3}{4}}{\left (x \right )}}{19} - \frac {64 \tanh ^{2}{\left (x \right )} \operatorname {sech}^{\frac {3}{4}}{\left (x \right )}}{209} - \frac {512 \operatorname {sech}^{\frac {3}{4}}{\left (x \right )}}{627} \]

Sympy 1.8 under Python 3.8.8 output

\[ \text {Timed out} \]________________________________________________________________________________________