Question

Integration x^2/(root x+5) dx​

Answer 1

$Consider, I=∫ x 2 +2x+5​ dxI=∫ x 2 +2x+1+4​ dxI=∫ (x+1) 2 +2 2 ​ dxNow, ∫ x 2 +a 2 ​ dx= 2x​ x 2 +a 2 ​ + 2a 2 ​ log ∣∣∣∣​ x+ x 2 +a 2 ​ ∣∣∣∣​ +C∴I= 2(x+1)​ (x+1) 2 +2 2 ​ + 22 2 ​ log ∣∣∣∣∣​ x+1+ (x+1) 2 +2 2 ​ ∣∣∣∣∣​ +CI= 21​ (x+1) x 2 +2x+5​ +2log ∣∣∣​ x+1+ x 2 +2x+5​ ∣∣∣​ +C$