Question

Нужна помощь 4 и 6 плиз срочно

Answer 1

 $4$ 
$int ( frac{ x^{-frac{1}{4}}-2 }{x^{frac{3}{4}}} ) dx = int frac{1}{x} dx - int 2*x^{-frac{3}{4}} dx = ln|x| - 8*x^{frac{1}{4}}$ 
  
$4.2$
$intlimits^ frac{pi}{2}_0 { frac{cosx}{(3-sinx)^2} dx$ 
$3-sinx = u \ -cosxdx=du \ int frac{-du}{u^2} = frac{1}{u} = frac{1}{3-sinx}$  
$frac{1}{3-sinfrac{pi}{2}} - frac{1}{3-sin0} = frac{1}{2}-frac{1}{3} = frac{1}{6}$ 

$6$ 
$ydx+ctgxdy = 0 \ tgx= frac{y'}{y} \ frac{sinx}{cosx} = frac{y'}{y} \ y=C_{1}*cosx \ C_{1} = frac{-1}{cosfrac{pi}{3}} = -2 \ y=-2*cosx$