Question

вычислить интеграл
dx/(cos^(4)x

Answer 1

$\int {sec^m(x)} \, dx =$  (sin(x) sec^(m-1)(x))/(m-1) + (m-2)/(m-1) $\int {sec^(-2+m) (x)} \, dx$
где m=4


 == 1/3 tan(x) sec^2(x)+2/3 $\int {sec^2(x)} dx$

 == (2 tan(x))/3+1/3 tan(x) sec^2(x)+constant