Question

Нужна помощь 4 и 6 плиз срочно

Answer 1

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

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