# What is the integral of #arctanx/x^2#?

We have:

Let:

The original integral therefore equals:

Consequently:

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The integral of ( \frac{\arctan(x)}{x^2} ) is not expressible in terms of elementary functions. It cannot be represented using standard functions such as polynomials, exponentials, logarithms, trigonometric functions, and their inverses. However, it can be expressed in terms of special functions, such as the dilogarithm function.

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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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