Question

1.(x^2+1)dx=(3y^2-2)dy
2.cos^2xdy=dx
3.cos^2xdy=(2+y)dx

Answer 1

$1)quad (x^2+1)dx=(3y^2-2)dy\\int (x^2+1)dx=int (3y^2-2)dy\\frac{x^3}{3}+x=y^3-2y+C\\2)quad cos^2x, dy=dx\\int dy=int frac{dx}{cos^2x}\\y=tgx+C\\3)quad cos^2x, dy=(2+y)dx\\int frac{dy}{2+y} =int frac{dx}{cos^2x}\\ln|2+y|=tgx+C$