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What is the antiderivative of # x/(x+1)#?

Answer 1

William Abdalla

#x + ln abs(x+1) +C#
Note: This is the same answer as the one Selim has given. It just has a different constant.

#int x/(x+1) dx = int ((x+1)-1)/(x+1) dx#

# = int (1 - 1/(x+1))dx#

# = x +ln abs(x+1) +C#

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Answer 2

Luke Alvarez

The antiderivative of ( \frac{x}{x+1} ) with respect to ( x ) is ( x - \ln|x+1| + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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