# How do you find the integral of #int dx/[5x(ln(5x))^2]# from 2 to infinity?

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To find the integral of ( \int_{2}^{\infty} \frac{dx}{5x(\ln(5x))^2} ), you can use the method of substitution. Let ( u = \ln(5x) ), then ( du = \frac{1}{x} dx ). Substituting these into the integral, you get:

[ \int_{2}^{\infty} \frac{dx}{5x(\ln(5x))^2} = \int_{?}^{?} \frac{du}{5u^2} ]

The limits of integration change when you change variables, but the infinity remains infinity. Now integrate ( \frac{1}{5u^2} ) with respect to ( u ) from ( ? ) to ( \infty ). Then evaluate this definite integral to find the value of the original integral.

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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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