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How do you find the antiderivative of # ln(cosx) #?

Answer 1

Christopher Allers

The antiderivative is pretty much the indefinite integral, so:

#int ln(cosx)dx = ?#

But the indefinite integral cannot be done with elementary functions.

You would have to do it numerically if you have defined bounds and you are in your early years of Calculus.

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Answer 2

Christopher Allers

To find the antiderivative of ln(cosx), you can use integration by parts. Let u = ln(cosx) and dv = dx. Then, differentiate u to find du, and integrate dv to find v. After that, apply the integration by parts formula: ∫u dv = uv - ∫v du. Once you've performed the integration by parts, simplify the expression to obtain the antiderivative of ln(cosx).

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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.