Evaluate the following: (x^2+2) x+1 dx - Vidyadip

Question

Evaluate the following:
$\int\frac{(\text{x}^2+2)}{\text{x}+1}\text{dx}$

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Answer

Let $\text{I}=\int\frac{\text{x}^2+2}{\text{x}+1}\text{dx}$$=\int\Big(\text{x}-1+\frac{3}{\text{x}+1}\Big)\text{dx}$
$=\int(\text{x}-1)\text{dx}+3\int\frac{1}{\text{x}+1}\text{dx}$
$=\frac{\text{x}^2}{2}-\text{x}+3\log\big|(\text{x}+1)\big|+\text{C}$

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