I have an integration problem that I am a bit perplexed about. The question stat

Question

I have an integration problem that I am a bit perplexed about. The question states:

(1) Find the integral of arcsin(x) by making the substitution u=arcsin(x).

(2) Generalize the above result to write the integral of f^-1(x)dx in terms of the integral of f(x)dx.

I know the 1st part is an integration by parts problem and the answer is sqrt(1-x^2)+xsin^-1(x) + C. However, I'm not even sure what the second question is asking. If someone could solve for the second part and explain the process I would be overjoyed.

Explanation / Answer

What you should do is take the substitution

take f(x) = sin(x)

=> f^-1(x) = arcsin(x) = u

now apply the process that you did in 1 and get a generalized result for integrals of an inverse function

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