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What is antiderivative of function y=1/(n+1), if n is natural?

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snsett | Student, Undergraduate | eNoter

Posted June 26, 2013 at 1:13 PM via web

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What is antiderivative of function y=1/(n+1), if n is natural?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 26, 2013 at 1:38 PM (Answer #1)

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You need to evaluate the anti-derivative of the given function, hence, you need to find its indefinite integral, such that:

`int 1/(n+1)dx`

Since the problem provides the information that `n in N` , hence, the coefficient `1/(n+1)` is a constant, thus, you need to bring this coefficient out of integral, such that:

`int 1/(n+1)dx = 1/(n+1) int dx`

`1/(n+1) int dx = 1/(n+1)*x + c`

Hence, evaluating the antiderivative of the given function, under the given conditions, yields` int 1/(n+1)dx = x/(n + 1) + c.`

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