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1.	X^2/(x+1)
Answer» let I= ∫ x²/(x+1) dx let x+1=t ⇒dx = dt also since x+1=t ⇒ x=t-1 substituting values ∫ (t-1)²/t dt ⇒ ∫ (t² + 1 -2t)/t dt ⇒ ∫ t²/t dt + ∫ 1/t dt - ∫ 2t/t dt ⇒ ∫ t dt + ∫ 1/t dt - ∫ 2 dt ⇒ t²/2 + log\|t\| - 2t substituting value x+1 =t ⇒ (x+1)²/2 + log\|x+1\| - 2(x+1) + c

X^2/(x+1)

Answer»

let I= ∫ x²/(x+1) dx

let x+1=t

⇒dx = dt

also since x+1=t ⇒ x=t-1

substituting values

∫ (t-1)²/t dt

⇒ ∫ (t² + 1 -2t)/t dt

⇒ ∫ t²/t dt + ∫ 1/t dt - ∫ 2t/t dt

⇒ ∫ t dt + ∫ 1/t dt - ∫ 2 dt

⇒ t²/2 + log|t| - 2t

substituting value x+1 =t

⇒ (x+1)²/2 + log|x+1| - 2(x+1) + c

Discussion