`f(x) = 2sqrt(x) + 6cos(x)` Find the most general antiderivative of the function. (Check your answer by differentiation.)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the most general antiderivative, using the following rule, such that:

`int f(x) dx = F(x) + c`

`int (2sqrtx + 6cos x) dx = int 2sqrt x dx + int 6cos x dx`

`int (2sqrtx + 6cos x) dx =2*(2/3)*x^(3/2) + 6sin x + c`

`int (2sqrtx + 6cos x) dx =(4/3)*x*sqrt x+ 6sin x + c`

Hence, evaluating the most general antiderivative yields `F(x) = (4/3)*x*sqrt x+ 6sin x + c.`