Solution. It is easy to see that sine-substitution is the one to use. Set or equivalently . Then which gives us
Easy calculations give
Technique of integration of powers of trigonometric functions give
which suggests the substitution . Hence which implies
Therefore, we have
This will not answer fully the problem because the answer should be given as a function of x. Since , we get after easy simplifications
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Author: Mohamed Amine Khamsi