X^=2^x+1
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Natwar Deep Tandon
Asked: 3 years ago2022-11-04T06:31:28+05:30
2022-11-04T06:31:28+05:30In: General Awareness
X^2/(x+1)
X^2/(x+1)
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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