Question

Помогите найти интеграл

Answer 1

$\int \frac{( \arctg(x) + 1) {}^{4} }{1 + {x}^{2} } dx = \int \frac{ {t}^{4} }{ {x}^{2} + 1}( {x}^{2} + 1) dt = \\ \arctg(x) + 1 = t, \: dx = {x}^{2} + 1dt \\ = \int {t}^{4} dt = \frac{ {t}^{5} }{5} = \frac{( \arctg(x) + 1)^{5} }{5} + C$