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

Textbook Question

Chapter 4, 4.9 - Problem 22 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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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 (2 +x^2)/(1+x^2) dx = int(1+x^2)/(1+x^2) dx + int 1/(1+x^2)dx `

`int (2 +x^2)/(1+x^2) dx = x + arctan x + c`

Hence, evaluating the most general antiderivative yields `F(x) = x + arctan x + c.`

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