`f(x) = 1/5 - 2/x` Find the most general antiderivative of the function. (Check your answer by differentiation.)

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Chapter 4, 4.9 - Problem 13 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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lemjay | High School Teacher | (Level 3) Senior Educator

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`f(x) =1/5-2/x`

To determine the most general antiderivative of this function, take the integral of it.

`F(x)=int f(x)dx = int(1/5-2/x)dx`

Then, apply the integral formula `int cdu=cu +C`  and `int 1/u du=ln|u|+C` .

`=1/5x-2ln|x| + C`

Thus, antiderivative of `f(x) = 1/5-2/x`  is  `F(x) = 1/5x - 2ln|x| + C` .

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