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How do you find the integral of #1/tan(x) dx#?

Answer 1

Aurora Alvarado

#ln|sinx| + C#

#int 1/tanx dx =int 1/(sinx/cosx) dx = int cosx/sinxdx = int (d(sinx))/sinx = ln|sinx| + C#

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Answer 2

Charles Anctil

To find the integral of ( \frac{1}{\tan(x)} , dx ), we can use the following steps:

Rewrite ( \frac{1}{\tan(x)} ) using trigonometric identities.
Apply substitution or integration by parts to simplify and solve the integral.

Using the identity ( \tan(x) = \frac{\sin(x)}{\cos(x)} ), we can rewrite ( \frac{1}{\tan(x)} ) as ( \frac{\cos(x)}{\sin(x)} ).

Then, we can use substitution, letting ( u = \sin(x) ) or ( u = \cos(x) ), or apply integration by parts to solve the integral. The specific method chosen depends on preference and the complexity of the integral.

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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.