Question

Помогите с Первообразными!
F(у)=5sin7xcos7x
F(у)=sin^2 5x - cos^2 5x
F(у)=x + tg^2 3x
F(у)=2 - 2sin^2 x

Answer 1

∫ 5sin7xcos7x dx =∫ (5/2) *2*sin7xcos7x dx=
(5/2) ∫  sin (2*7x) dx=(5/2) *(1/14)*( - cos14x) + C  = -(5/28)*cos14x +C. 
----------
∫( sin² 5x - cos²5x )dx  = ∫ -(cos²5x - sin² 5x ) dx  =  ∫- cos(2*5x) ) dx =  
- (1/10)*sin10x +C .
----------
∫ (2 - 2sin² x )dx  = ∫ 2(1 - sin² x) dx = ∫ 2cos² x dx =  ∫ (1+cos2x) dx  =
x +(1/2 )*sin2x +C .