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What's the integral of #int (tan(x))/x dx #?

Answer 1

Neither WolframAlpha nor I can find an answer.

WolframAlpha says no answer is found using standard mathematical functions (And Wolfram uses some sophisticated 'standard' functions, like #L_i#, #S_i# #"erf"# and #"erfc"# and so on.)

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Answer 2

Emma Aldridge

The integral of ( \frac{\tan(x)}{x} ) with respect to ( x ) does not have an elementary antiderivative. It is a special function called the sine integral, denoted as ( \text{Si}(x) ). Therefore, the integral cannot be expressed in terms of elementary functions such as polynomials, exponentials, trigonometric functions, and their inverses.

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Answer from HIX Tutor

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.