1) ∫(2x^2 - 1/(x^2 + 5)dx = 2) ∫ (x-2)cos3x dx = 3) ∫ (4x^3 + x^2 + 2) / (x(x-1)(x-2)) 4) ∫ dx/(cosx(1+cosx)) = 5) ∫

1) f(x)\' = (x * (x – 4))’ = (x)’ * (x – 4) + x * (x – 4)’ = (x)’ * (x – 4) + x * ((x)’ – (4)’) = 1 * (x – 4) + x * (1 – 0) = x – 4 + x = 2x – 4.

2) f(x)\'  = (3 – 2х)’ = (3)’ – (2х)’ = 0 – 2 * 1 * x^{(1 – 1)} = -2 * x⁰ = -2 * 1 = -2.

3) f(x)\' = ((-x^2 + 2x^2)^3 + (x - 3)^4)’ = ((-x^2 + 2x^2)^3)’ + ((x - 3)^4)’ = (-x^2 + 2x^2)’ * ((-x^2 + 2x^2)^3)’ + (x - 3)’ * ((x - 3)^4)’ = ((-x^2)’ + (2x^2)’) * ((-x^2 + 2x^2)^3)’ + ((x)’ – (3)’) * ((x - 3)^4)’ = (-2x + 4x) * (3 * (-x^2 + 2x^2)^2) + (1 - 0) * (4 * (x - 3)^3) = 2x * 3 * (x^2)^2 + 1 * (4 * (x - 3)^3) = 6x * x^4 + 4(x - 3)^3 = 6x^5 + 4(x - 3)^3.

4) f(x)\' = (x^2 * tg (x))’ = (x^2)’ * tg (x) + x^2 * (tg (x))’ = 2x * tg (x) + x^2 * (1 / (cos^2 (x))) = 2xtg (x) + x^2 / (cos^2 (x)).

5) f(x)\' = (sin^2 (x))’ = (sin (x))’ * (sin^2 (x))’ = cos (x) * 2 * sin^(2 – 1) (x) = cos (x) * 2 * sin^(1) (x) = cos (x) * 2 * sin (x) = 2cos (x) sin (x).