PLEASE ANSWER THIS QUESTION: find the integration of: [(x2+2)(x2+1)]/[(x2+3)(x2+4)]

Put x² = y

The function reduces to: (y+1)(y+2) / (y+3)(y+4)

Add and subtract 1,

Function = 1 + [(y+1)(y+2) - (y+3)(y+4)/ (y+3)(y+4)]

By partial fractions, we get,

Function = 1 + 2/y+3 - 6/y+4 = 1 + 2/x²+3 - 6/x²+4

 

Now, this function can easily be integrated.