Solution. Since the degree of the numerator is higher than the denominator, we should perform the long-division. We get
We concentrate on the fraction . The partial decomposition technique gives
This gives x + 2 = A(x-1) + B(x+1). If we substitute x=1, we get B = 3/2 and we substitute x=-1, we get A = -1/2. Therefore, we have
Now we are in position to perform the desired integration. Indeed, we have
Since we have ,
Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.
Author: Mohamed Amine Khamsi