How to Integrate Arcsin Functions: Solving the Integral of Arcsin (2x/(1+x^2))

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To evaluate the integral of arcsin(2x/(1+x^2)), integration by parts is suggested, using u = arcsin(x) and dV = dX. Substituting directly into the arcsin formula complicates the problem further, so a careful approach is necessary. The discussion highlights the complexity of the integral and the need for a systematic method. Participants emphasize the importance of following the integration by parts procedure despite the messiness. Ultimately, a structured approach is essential for solving this integral effectively.
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Homework Statement


Evaluate \int arcsin (\frac{2x}{1+x^{2}})

Homework Equations


\int arcsin x = xarcsinx +\sqrt{1-x^{2}} + C

The Attempt at a Solution


I'm not sure where to begin, when I try to substitute the term inside the brackets the equation gets even more complicated. Help?
 
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Are you familiar with integration by parts? The relevant equation you stated uses parts by using u = arcsin x and dV = dX.

Do the same procedure with your above integral... though you are correct that it does get messy!
 
You can't just substitute into the equation for arcsin x, it doesn't work that way
 
Thank you =)
 

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