Answer to question 5.1.14

Answer to 5.1.14

We have the question,

 

Since the fraction is improper, we need to single out the integral part(Refer 5.1.3 solved example in the textbook). Dividing numerator by denominator, we obtain :

Hence using this, our integral becomes :

Expand the remaining proper fraction into simple ones using partial fraction :

Hence :

 

Putting x = -1, we get 2A = -1 + 1 +2, or, A = 1

Now, expanding and comparing coefficients of similar terms on both sides and solving the equation, we get B = -2 and C = 1.

So,we have :

So, the integral becomes :

Integrating, we get the answer as :