## 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

Hence

On one hand, we have

and also

Hence

It is a common mistake to forget the constant .

** Remark.** Recall the formula

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