We recognize here a rational function. The technique of integrationg such functions is the partial decomposition technique. In this case, the degree of the denominator is 2 with an irreducible polynomial function. So no need to perform the long-division. One may also use the table for this integration.
First we will get ridd of the term in the numerator by using the derivative of the denominator. Indeed, we have
It is a common mistake to forget the constant .
Remark. Recall the formula
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Mohamed A. Khamsi