# How do you integrate #(tan(x))/x#?

I don't believe there is an intrinsic function that is the anti-derivative

The power series solution is:

# :. int tanx/xdx = x+1/3x^3/3+2/15x^5/5-17/315x^7/7+62/2835x^9/9+...

# :. int tanx/xdx = x+1/9x^3+2/75x^5-17/2205x^7+62/25515x^9+...

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The integral of (tan(x))/x with respect to x is not expressible in terms of elementary functions. It is a special function called the dilogarithm function, denoted as Li2(x), and can be expressed in terms of it as -Li2(-e^(2i*x)).

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The integral of (\frac{\tan(x)}{x}) does not have an elementary antiderivative. However, it can be expressed in terms of special functions. The integral is denoted by (\text{Ci}(x)), the cosine integral function. Therefore, the integral can be written as:

[\int \frac{\tan(x)}{x} dx = \text{Ci}(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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