# How do you evaluate #int_1^oo 1/x^x dx# ?

By numerical Integration:

This definite integral requires numerical methods to solve. See article: https://tutor.hix.ai for an introductory explanation if you are not familiar with this.

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To evaluate the integral ( \int_1^\infty \frac{1}{x^x} , dx ), you can use a technique called the comparison test.

First, note that for ( x \geq 1 ), ( x^x \geq x ). So, ( \frac{1}{x^x} \leq \frac{1}{x} ).

Since ( \frac{1}{x} ) is integrable over the interval ( [1, \infty) ), and ( \frac{1}{x^x} ) is less than or equal to ( \frac{1}{x} ) over that interval, we can conclude that ( \frac{1}{x^x} ) is also integrable over the interval ( [1, \infty) ).

Therefore, ( \int_1^\infty \frac{1}{x^x} , dx ) converges.

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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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