Problems on Techniques of Integration
We recognize here a rational function. The technique of integrationg such functions is the partial decomposition technique. In this case, the degree of the numerator is bigger than the degree of the denominator. So we need to perform the long-division. We get
So
In order to integrate
, we will first get ridd of the term in the numerator by using the derivative of the denominator. Indeed, we have
which implies
Hence
On one hand, we have
In order to integrate
, we will complete the square in the denominator and then use the formula to get
Hence
It is a common mistake to forget the constant .
Remark. Recall the formula
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