# How do you integrate #-1 / (x(ln x)^2)#?

We have:

We then have:

Thus,

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To integrate ( -\frac{1}{x(\ln x)^2} ), you can use the substitution method. Let ( u = \ln x ), then ( du = \frac{1}{x} dx ).

Substitute ( u = \ln x ) and ( du = \frac{1}{x} dx ) into the integral:

[ \int -\frac{1}{x(\ln x)^2} , dx = \int -\frac{1}{u^2} , du ]

Now, integrate ( -\frac{1}{u^2} ) with respect to ( u ) to get:

[ = \frac{1}{u} + C = \frac{1}{\ln 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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