Struggling with Indefinite Integrals: Can You Solve These Tricky Functions?

asap9993
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Homework Statement



I need help finding the anti-derivatives (indefinite integrals) of the 2 functions below:

1) e^(sqrt(x))


2) Sqrt(2x - x^2)

Homework Equations





The Attempt at a Solution



I tried forever at these 2 but I can't figure out a way for either of them. Any help would be very much appreciated.
 
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Hi asap9993! :smile:

For (1), try the substitution u=\sqrt{x}.

For (2), complete the square.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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