# Find # int ln^2x dx #?

# int \ ln^2x \ dx = x^2lnx-2xlnx+2x + C #

We seek:

We can apply integration by Parts:

Then plugging into the IBP formula:

We have:

Now consider the last integral:

We can again apply integration by parts a second time for the second integral:

Then plugging into the IBP formula:

Using this result along with the earlier result we find:

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[ \int \ln^2(x) , dx ]

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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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