Question

Evaluate: ∫ (x² + 4x + 2/ (x + 1) √(x² + 2x + 3)) dx

Answer 1

Put x² + 4x + 2 

= l(x + 1)(2x + 2) + m(x + 1) + n 

= l(2x² + 4x + 2) + m(x + 1) + n 

= 2lx² + (4l + m) x + (2l + m + n) 

Comparing the coefficients of the like terms of both the sides, we get 

L = 1/2, M = 2, N = –1. 

Thus, the given integral reduces to