1. Выделяем полные квадраты из x2<span> - 4x:
</span>(x²-2•2x + 22) -1•2² = (x-2)²<span>-4
</span><span>2. С учетом c = 3 получаем:
</span>(x-2)²<span> -1
</span>
x²-4x+3=(x-2)²-1
∫ 5sin7xcos7x dx =∫ (5/2) *2*sin7xcos7x dx=
(5/2) ∫ sin (2*<span>7x) dx=(5/2) *(1/14)*( - cos14x) + C = -(5/28)*cos14x +C.
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</span>∫( sin² 5x - cos²5x )dx = ∫ -(cos²5x - sin² 5x ) dx = ∫- cos(2*5x) ) dx =
- (1/10)*<span>sin10x +C .
</span><span>----------</span>
∫ (2 - 2sin² x )dx = ∫ 2(1 - sin² x) dx = ∫ 2cos² x dx = ∫ (1+cos2x)<span> dx =
x +(1/2 )*</span>sin2x +C .