Integrating arcsinx: Solving a Challenging Calculus Problem

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The discussion focuses on integrating the function arcsin(x), with participants expressing difficulty in approaching the problem. A suggestion is made to use integration by parts, similar to methods applied for arctan(x) and ln(x). The initial attempt indicates confusion despite having seen the answer. The conversation emphasizes the need for clarity in applying integration techniques to arcsin(x). Overall, integration by parts is highlighted as a potential solution strategy.
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Homework Statement



Intergrate arcsinx

Homework Equations





The Attempt at a Solution



I couldn't even touch this question. I saw the answer but still can not understand how to do this.
 
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Use the "same" method as for arctan x and for ln x.

arcsin x = (arcsin x) * 1

Now integrate by parts!
 
Thanks a lot!
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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