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What is #int 1 / csc xdx#?

Answer 1

Luke Alvarez

-cosx+c

#int1/(cscx)dx#

#=intsinxdx#

#=-cosx+c#

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Answer 2

Emily Ammerman

The integral of ( \frac{1}{\csc(x)} ) with respect to ( x ) is equal to ( -\ln|\csc(x) + \cot(x)| + C ), where ( C ) is the constant of integration.

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Answer 3

Christopher Agresta

The integral of ( \int \frac{1}{\csc(x)} , dx ) can be simplified using trigonometric identities. Rewrite ( \csc(x) ) as ( \frac{1}{\sin(x)} ), then multiply the numerator and denominator by ( \sin(x) ) to rationalize the expression. This yields ( \sin(x) ).

So, ( \int \frac{1}{\csc(x)} , dx = \int \sin(x) , dx ).

Integrating ( \sin(x) ) gives ( -\cos(x) + C ), where ( C ) is the constant of integration.

Therefore, ( \int \frac{1}{\csc(x)} , dx = -\cos(x) + C ).

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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.