(x-3)(x-5)/(x+3)-2>0
(x²-5x-3x+15-2x-6)/(x+3)>0
(x²-10x+9)/(x+3)>0
x²-10x+9=0
x1+x2=10 U x1*x2=9
x1=1 U x=9
x+3=0⇒x=-3
+ _ + _
------------------(-3)---------------(1)________(9)__________________
x∈(-∞;-3) U (1;9)
1) F(x) = x^-1/-1 + C = -1/x + C
-1 = -1/1 + C
C = 0
Ответ: F(x) = -1/x
2) F(x) = x^-2/-2 +C = -1/2x + C
0 = -1/2*(-1) + C
C = -1/2
Ответ: F(x) = -1/2x -1/2
3) F(x) = 2x - tgx + C
π/2 = 2*π/4 - tgπ/4 + C
π/2 = π/2 - 1 + C
C = 1
Ответ: F(x) = 2x - tgx + 1
4) F(x) = -2Ctgx + x + C
π/4 = -2*Ctgπ/4 + x + C
π/4 = -2*1 + π/4 + C
C = 2
Ответ: F(x) = -2Ctgx + x + 2
2sin2xsinx-sin2x=0
sin2x(2sinx-1)=0
sin2x=0⇒2x=πn,n∈z⇒x=πn/2,n∈z
sinx=1/2⇒x=(-1)^n*π/6+πk,k∈z