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What is the Integral of #1/tan(x) dx#?

Answer 1

Isabella Ackerman

#lnabs(sinx) +C#

#1/tanx = cotx = cosx/sinx#

#int1/tanx dx= intcotx dx#

# = int cosx/sinx dx#

Let #u = sinx#, so #du = cosx dx# to get

# = int 1/u du#

# = ln absu +C#

# = ln abs sinx +C#

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Answer 2

Evelyn Agard

The integral of ( \frac{1}{\tan(x)} ) with respect to ( x ) can be found by using a trigonometric identity to rewrite the expression in terms of sine and cosine. The integral is ( -\ln|\cos(x)| + C ), where ( C ) is the constant of integration.

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Answer 3

Ezra Adams

The integral of 1/tan(x) dx is equal to ln|sec(x)| + C, where C is the constant of integration.

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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.