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Find the most general antiderivative or indefinite integral. ? ( ( 1/ x ) ? ( 3 / ( x^ 2 + 1 ) )...

Question:

Find the most general antiderivative or indefinite integral.{eq}\int \left ( (\frac{1}{x})-(\frac{3}{(x^{2}+1)}) \right )dx {/eq} Use C as the arbitrary constant

The Most General Antiderivative of {eq}\frac{1}{x} - \frac{3}{x^2+1}: {/eq}

A function {eq}F {/eq} is called an antiderivative of another function, {eq}f {/eq} on a given interval if {eq}F'(x) = f(x) {/eq} for all {eq}x {/eq} in the interval. The most general antiderivative of {eq}f {/eq} is given by {eq}F(x) + C. {/eq} In other words, to compute an indefinite integral, we only need to find one antiderivative of the given function.

Answer and Explanation:

To find the most general antiderivative, we only need to find one antiderivative. Well,

{eq}\displaystyle \int \left( \frac{1}{x} - \frac{3}{x^2+1}...

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Antiderivative: Rules, Formula & Examples

from Calculus: Help and Review

Chapter 8 / Lesson 12
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