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

We have:

We'll employ integration by components, which looks like this:

Including this in the formula for integration by parts:

You could use long division to integrate the second bit, but this is easier:

These two integrals are quite basic:

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The indefinite integral of ln(1+x) is ∫ln(1+x) dx = (x + 1) ln(1 + x) - x + 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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