Question

Срочнооо xdx/cos^2 x

Answer 1

$int frac{x, dx}{cos^2x}=[, u=x; ,; du=dx; ,dv=frac{dx}{cos^2x}; ,v=int frac{dx}{cos^2x}=tgx, ]=\\=ucdot v-int vcdot du=xcdot tgx-int tgxcdot dx=xcdot tgx-int frac{sinx, dx}{cosx}=\\=xcdot tgx-int frac{-d(cosx)}{cosx}=xcdot tgx+ln|cosx|+C$

Answer 2

u=x;du=dx
dv=dx/cos²x;v=tgx
Sxdx/cos²x=xtgx-Stgxdx=xtgx-S*sinxdx)/cosx
t=cosx;dt=-sinx
=xtgx+Sdt/t=xtgx+lnt=xtgx+ln(cosx)+C