# How do you integrate #ln(x)^35#?

Now

so

This recurrence equation has the solution https://tutor.hix.ai

then

so

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To integrate ( \ln(x)^{35} ), you can use integration by parts or a clever substitution. Let's use a substitution method. Let ( u = \ln(x) ). Then ( du = \frac{1}{x} dx ).

Now, rewrite the integral in terms of ( u ) and ( du ):

[ \int u^{35} , du ]

Integrate ( u^{35} ) with respect to ( u ):

[ \frac{1}{36} u^{36} + C ]

Substitute back for ( u ) using the original substitution ( u = \ln(x) ):

[ \frac{1}{36} \ln(x)^{36} + C ]

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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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