Find the most general antiderivative of the function. Check your answer by differentiation

Question

4) f(x) = 2sin x - sec^2 x        5) f(x) = e ^ (2x) 6) f(x) = 2/(sqrt(1 - x ^ 2))

please answer these 3 questions

Answer 1

The derivative of cos(x) is -sin(x) making the antiderivative of sin(x) as -cos(x) so the antiderivative of 2sin(x) is -2cos(x)

The derivative of tan(x) is sec²(x) making the antiderivative of sec²(x) as tan(x)

So the antiderivative of f(x) = 2sin(x) - sec²(x) is -2cos(x) - tan(x) + C

The derivative and the antiderivative of e^x is e^x, so the antiderivative of e^2x is 1/2e^2x + C

The derivative of arcsin(x) is 1/√(1 - x²) making the antiderivative of 2/√(1 - x²) as 2arcsin(x) + C