Спервообразными! f(у)=5sin7xcos7x f(у)=sin^2 5x - вопрос №680573557725252 от gv8ux 15.02.2022 03:40

Question

Алгебра: Спервообразными! f(у)=5sin7xcos7x f(у)=sin^2 5x - cos^2 5x f(у)=x + tg^2 3x f(у)=2 - 2sin^2 x

gv8ux · Answer

∫ 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 .