Solution. First let us complete the square for . We get
which suggests the secant-substitution . Hence we have and . Note that for x=0, we have which gives t=0 and for x=3, we have which gives . Therefore, we have
Using the trigonometric identities (you will find them at the end of this page), we get
The technique of integration related to the powers of the secant-function gives and
One would check easily that
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Author: Mohamed Amine Khamsi