What is the Antiderivative of Inverse Sine of x?

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Homework Help Overview

The discussion revolves around finding the antiderivative of the function involving the inverse sine, specifically \(\frac{1}{\sin\alpha}\). Participants are exploring methods for integration within the context of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Some participants suggest rewriting the sine function in terms of exponential functions and consider using partial fractions for integration. Others propose expressing the function as \(\csc\alpha\) to facilitate understanding. There is also a mention of a relationship involving \(\frac{1}{\sin x}\) and \(\cos^2 x\

Discussion Status

The discussion is ongoing, with various approaches being suggested. Participants are sharing insights and attempting to clarify the problem without reaching a consensus on a specific method or solution.

Contextual Notes

Some participants express uncertainty about their current understanding, indicating a potential lack of familiarity with the integration techniques required for this problem.

kristo
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Homework Statement



Find the antiderivative of [tex]\frac{1}{\sin\alpha}[/tex]

Homework Equations





The Attempt at a Solution


Ugh, maybe it's just a temporary brainfreeze, but I have no idea how to go about it.
 
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Try rewriting the sine in terms of exponential functions. After a change of variables and partial fractions you should be able to integrate it.
 
kristo said:

Homework Statement



Find the antiderivative of [tex]\frac{1}{\sin\alpha}[/tex]

Homework Equations





The Attempt at a Solution


Ugh, maybe it's just a temporary brainfreeze, but I have no idea how to go about it.

Maybe if you write that as [tex]{\csc\alpha}[/tex] it will look more familiar.
 
[tex]\frac{1}{\sin x} = \frac{\sin x}{1-\cos^2 x}[/tex]

is a useful thing to know.
 

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