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

We have

We'll apply integration by components:

Thus,

Resolving the residual integral:

So,

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The antiderivative of ln(x+1) is ∫ln(x+1) dx = (x+1)(ln(x+1) - 1) + C, where C is the constant of integration.

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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.

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.

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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